Given's Rotation SVD example, simplified
Time bar (total: 7.9s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 100% | 100% | 0% | 0% | 0% | 0% | 0% | 1 |
Compiled 19 to 11 computations (42.1% saved)
| 897.0ms | 2 913× | 2 | valid |
| 381.0ms | 4 160× | 0 | valid |
| 201.0ms | 1 183× | 1 | valid |
ival-hypot: 455.0ms (37.9% of total)ival-sqrt: 164.0ms (13.6% of total)ival-div: 154.0ms (12.8% of total)adjust: 136.0ms (11.3% of total)ival-mult: 108.0ms (9% of total)ival-add: 89.0ms (7.4% of total)ival-sub: 77.0ms (6.4% of total)exact: 8.0ms (0.7% of total)ival-true: 7.0ms (0.6% of total)ival-assert: 3.0ms (0.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 66 | 1 | (1.409001518054266e-161) | 0 | - | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (hypot.f64 #s(literal 1 binary64) x) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 0 | 0 | - | 0 | - | #s(literal 1/2 binary64) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) | cancellation | 67 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 66 | 0 |
| - | 1 | 189 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 66 | 0 | 0 |
| - | 1 | 0 | 189 |
| number | freq |
|---|---|
| 0 | 189 |
| 1 | 67 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 57.0ms | 192× | 2 | valid |
| 23.0ms | 244× | 0 | valid |
| 14.0ms | 76× | 1 | valid |
Compiled 174 to 31 computations (82.2% saved)
ival-hypot: 28.0ms (38.8% of total)ival-div: 8.0ms (11.1% of total)ival-sub: 8.0ms (11.1% of total)ival-sqrt: 8.0ms (11.1% of total)adjust: 7.0ms (9.7% of total)ival-mult: 7.0ms (9.7% of total)ival-add: 6.0ms (8.3% of total)exact: 1.0ms (1.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
| 36× | lower-+.f32 |
| 34× | lower-+.f64 |
| 26× | associate--r+ |
| 26× | sub-neg |
| 24× | distribute-lft-neg-in |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 31 |
| 1 | 37 | 26 |
| 2 | 75 | 26 |
| 3 | 120 | 26 |
| 4 | 172 | 26 |
| 5 | 202 | 26 |
| 6 | 214 | 26 |
| 0 | 9 | 12 |
| 0 | 18 | 12 |
| 1 | 31 | 10 |
| 2 | 38 | 10 |
| 3 | 43 | 10 |
| 4 | 49 | 10 |
| 5 | 57 | 10 |
| 6 | 67 | 10 |
| 7 | 78 | 10 |
| 8 | 81 | 10 |
| 0 | 81 | 10 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) |
(abs x)
Compiled 12 to 9 computations (25% saved)
Compiled 0 to 1 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 75.9% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
Compiled 12 to 9 computations (25% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) | |
| cost-diff | 320 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 36× | lower-+.f32 |
| 34× | lower-+.f64 |
| 18× | lower-fma.f64 |
| 18× | lower-fma.f32 |
| 18× | lower-*.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 49 |
| 0 | 18 | 49 |
| 1 | 31 | 43 |
| 2 | 38 | 43 |
| 3 | 43 | 43 |
| 4 | 49 | 43 |
| 5 | 57 | 43 |
| 6 | 67 | 43 |
| 7 | 78 | 43 |
| 8 | 81 | 43 |
| 0 | 81 | 43 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
#s(literal 1 binary64) |
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
#s(literal 1/2 binary64) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(hypot.f64 #s(literal 1 binary64) x) |
x |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(+.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(hypot.f64 #s(literal 1 binary64) x) |
x |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.01171875 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.01171875 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 40.0ms | 96× | 2 | valid |
| 10.0ms | 122× | 0 | valid |
| 7.0ms | 38× | 1 | valid |
Compiled 81 to 11 computations (86.4% saved)
adjust: 12.0ms (28% of total)ival-hypot: 12.0ms (28% of total)ival-mult: 5.0ms (11.7% of total)ival-div: 4.0ms (9.3% of total)ival-sqrt: 4.0ms (9.3% of total)ival-sub: 2.0ms (4.7% of total)ival-add: 2.0ms (4.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt 1 (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (- 1 (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 x) (#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt 1/2 (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | 0 | ((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x))))) |
| 1.0ms | x | @ | inf | ((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x))))) |
| 1.0ms | x | @ | -inf | ((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x))))) |
| 1× | egg-herbie |
| 18 030× | lower-fma.f64 |
| 18 030× | lower-fma.f32 |
| 5 336× | lower-*.f64 |
| 5 336× | lower-*.f32 |
| 4 558× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 206 | 855 |
| 1 | 592 | 781 |
| 2 | 1621 | 742 |
| 3 | 4409 | 701 |
| 0 | 8156 | 662 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(* (sqrt 1/2) (sqrt 2)) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
2 |
(+ 2 (* -1/2 (pow x 2))) |
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2))) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))) |
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))) |
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
1 |
(+ 1 (/ 1 x)) |
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3))) |
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3))) |
(/ 1 x) |
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x) |
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x) |
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
1 |
(- 1 (/ 1 x)) |
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))) |
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))) |
(/ -1 x) |
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)) |
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)) |
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)) |
| Outputs |
|---|
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/4 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 11/32 binary64) #s(literal 1/4 binary64))) (*.f64 x x) #s(literal 1 binary64))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 69/256 binary64) #s(literal -11/64 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))) |
(* (sqrt 1/2) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(fma.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 11/32 binary64) #s(literal -1/4 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 69/256 binary64) #s(literal 11/64 binary64))))) |
2 |
#s(literal 2 binary64) |
(+ 2 (* -1/2 (pow x 2))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) |
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (*.f64 x x) #s(literal 3/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (*.f64 x x) #s(literal 3/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))) |
(- 1 (sqrt 1/2)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) |
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal -3/16 binary64) x) x)) (/.f64 #s(literal -1/8 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) |
1 |
#s(literal 1 binary64) |
(+ 1 (/ 1 x)) |
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3))) |
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64)))) |
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3))) |
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64)))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x) |
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x) |
(/.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))) x) |
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x) |
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) x) |
1/2 |
#s(literal 1/2 binary64) |
(- 1/2 (* 1/2 (/ 1 x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x) #s(literal 1/2 binary64)) |
(- 1 (sqrt 1/2)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) |
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(-.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) x)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x)) |
1 |
#s(literal 1 binary64) |
(- 1 (/ 1 x)) |
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) |
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) |
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))) |
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x) #s(literal 1 binary64)) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x)) x) |
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)) |
(/.f64 (-.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x) |
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)) |
(/.f64 (-.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x) |
| 4 098× | lower-fma.f64 |
| 4 098× | lower-fma.f32 |
| 3 010× | lower-*.f32 |
| 3 008× | lower-*.f64 |
| 1 830× | lower-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 43 |
| 0 | 18 | 43 |
| 1 | 78 | 37 |
| 2 | 562 | 37 |
| 3 | 5209 | 37 |
| 0 | 8824 | 37 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)))) (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -4 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))) (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (/.f64 (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)))) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -4 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) (/.f64 (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)))) (hypot.f64 #s(literal 1 binary64) x)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) |
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(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -4 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -6 binary64)))) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -4 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 (pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(fma.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) #s(literal 2 binary64))) |
(-.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))) (pow.f64 (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) |
(-.f64 (pow.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)) (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (expm1.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))))) |
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) |
(-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log1p.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log1p.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) #s(literal 2 binary64))) |
(+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) (neg.f64 (/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) |
(+.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) |
(*.f64 (neg.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))) |
(*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal -1/4 binary64)) |
(pow.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) |
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(/.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(neg.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(sqrt.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) |
(-.f64 #s(literal 0 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal -2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) #s(literal -2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x)))) |
Compiled 10 877 to 1 898 computations (82.6% saved)
13 alts after pruning (13 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 464 | 13 | 477 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 465 | 13 | 478 |
| Status | Accuracy | Program |
|---|---|---|
| 75.8% | (fma.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) #s(literal 1 binary64)) | |
| ▶ | 76.6% | (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
| ▶ | 75.9% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 30.2% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))) | |
| 45.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)))))) | |
| ▶ | 29.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
| 30.2% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) | |
| 29.7% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) | |
| ▶ | 46.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
| 30.5% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) | |
| ▶ | 47.1% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
| 47.1% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) | |
| 75.8% | (exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))) #s(literal -1 binary64))) |
Compiled 366 to 262 computations (28.4% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) | |
| cost-diff | 0 | (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) | |
| cost-diff | 0 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) | |
| cost-diff | 128 | (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) | |
| cost-diff | 192 | (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
| 11 468× | lower-fma.f32 |
| 11 462× | lower-fma.f64 |
| 2 338× | lower-*.f32 |
| 2 336× | lower-*.f64 |
| 1 988× | lower-+.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 336 |
| 0 | 63 | 336 |
| 1 | 107 | 318 |
| 2 | 179 | 312 |
| 3 | 355 | 312 |
| 4 | 720 | 312 |
| 5 | 1287 | 312 |
| 6 | 2048 | 312 |
| 7 | 2931 | 312 |
| 8 | 3145 | 312 |
| 9 | 3382 | 312 |
| 10 | 4513 | 312 |
| 11 | 6062 | 312 |
| 12 | 6473 | 312 |
| 13 | 6948 | 312 |
| 14 | 7231 | 312 |
| 15 | 7450 | 312 |
| 0 | 8264 | 312 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
(hypot.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) |
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) |
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) |
#s(literal -5/32 binary64) |
(*.f64 x x) |
x |
#s(literal 3/16 binary64) |
#s(literal -1/4 binary64) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
#s(literal 1 binary64) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
(hypot.f64 #s(literal 1 binary64) x) |
x |
| Outputs |
|---|
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) |
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
(hypot.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) |
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) |
#s(literal -5/32 binary64) |
(*.f64 x x) |
x |
#s(literal 3/16 binary64) |
#s(literal -1/4 binary64) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
#s(literal 1 binary64) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
(hypot.f64 #s(literal 1 binary64) x) |
x |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.01171875 | (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.01171875 | (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) | |
| accuracy | 0.03515625 | (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) | |
| accuracy | 0.0625 | (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) | |
| accuracy | 29.723784836037048 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| accuracy | 0 | (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) | |
| accuracy | 0.01171875 | (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) | |
| accuracy | 32.464107603526834 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) | |
| accuracy | 0.01171875 | (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) | |
| accuracy | 28.473630073298583 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) | |
| accuracy | 0.01171875 | (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) | |
| accuracy | 0.01171875 | (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 0.015625 | (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) | |
| accuracy | 15.020385963245173 | (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
| 85.0ms | 96× | 2 | valid |
| 40.0ms | 122× | 0 | valid |
| 18.0ms | 38× | 1 | valid |
Compiled 384 to 32 computations (91.7% saved)
adjust: 28.0ms (27.7% of total)ival-div: 17.0ms (16.8% of total)ival-hypot: 13.0ms (12.9% of total)ival-sub: 11.0ms (10.9% of total)ival-mult: 10.0ms (9.9% of total)ival-add: 9.0ms (8.9% of total)ival-sqrt: 7.0ms (6.9% of total)ival-neg: 3.0ms (3% of total)exact: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* -1/4 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt -2 (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/8 (pow x 2)) 2) (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2) (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2) (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- 1 (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
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#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -5/32 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -5/32 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | inf | ((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4)) |
| 3.0ms | x | @ | -inf | ((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4)) |
| 2.0ms | x | @ | 0 | ((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4)) |
| 1× | egg-herbie |
| 12 740× | lower-fma.f64 |
| 12 740× | lower-fma.f32 |
| 5 382× | lower-*.f64 |
| 5 382× | lower-*.f32 |
| 4 604× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 415 | 3886 |
| 1 | 1292 | 3534 |
| 2 | 3999 | 3396 |
| 0 | 8520 | 3235 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/4 (pow x 2)) |
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)) |
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)) |
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4)) |
-2 |
(- (* 1/8 (pow x 2)) 2) |
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2) |
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(* (sqrt 1/2) (sqrt 2)) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(* (sqrt 1/2) (sqrt 2)) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/2 x)) x) |
(/ (+ 1/2 (* 1/2 x)) x) |
(/ (+ 1/2 (* 1/2 x)) x) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(* (sqrt 1/2) (sqrt 2)) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
-1/2 |
(- (* 1/4 (pow x 2)) 1/2) |
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2) |
3/16 |
(+ 3/16 (* -5/32 (pow x 2))) |
(+ 3/16 (* -5/32 (pow x 2))) |
(+ 3/16 (* -5/32 (pow x 2))) |
-1/4 |
(- (* 3/16 (pow x 2)) 1/4) |
(- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4) |
(- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4) |
-1/2 |
(- (* 1/2 (/ 1 x)) 1/2) |
(- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3)))) |
(- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3)))) |
(* -1 (+ 1 (sqrt 1/2))) |
(* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))) |
(- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))) |
(- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))) |
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))) |
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))) |
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))) |
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))) |
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))) |
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))) |
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(* -5/32 (pow x 6)) |
(* (pow x 6) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 6) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(* (pow x 6) (- (+ (* 3/16 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(- 1 (sqrt 1/2)) |
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))) |
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(/ -1/2 x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x) |
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x) |
(* -5/32 (pow x 2)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* -5/32 (pow x 4)) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
-1/2 |
(* -1 (+ 1/2 (* 1/2 (/ 1 x)))) |
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2) |
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2) |
(* -1 (+ 1 (sqrt 1/2))) |
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2))) |
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2))) |
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(* -5/32 (pow x 6)) |
(* (pow x 6) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 6) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(* (pow x 6) (- (+ (* 3/16 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(/ 1/2 x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(* -5/32 (pow x 2)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* -5/32 (pow x 4)) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
| Outputs |
|---|
(* -1/4 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/4 binary64)) |
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)) |
(*.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x) |
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x) |
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 35/256 binary64) (*.f64 x x) #s(literal -5/32 binary64)) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x) |
-2 |
#s(literal -2 binary64) |
(- (* 1/8 (pow x 2)) 2) |
(fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -2 binary64)) |
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2) |
(fma.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64)) |
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/4 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) #s(literal 1 binary64))) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (fma.f64 (/.f64 (*.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(* (sqrt 1/2) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(fma.f64 (fma.f64 (/.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/4 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(- 1 (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) #s(literal 1 binary64))) |
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
(fma.f64 (fma.f64 (/.f64 (*.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2))) |
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(sqrt 1/2) |
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1/2 |
#s(literal 1/2 binary64) |
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(sqrt 1/2) |
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1/2 |
#s(literal 1/2 binary64) |
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#s(literal 1/2 binary64) |
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(sqrt 1/2) |
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1/2 |
#s(literal 1/2 binary64) |
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(sqrt 1/2) |
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(/ -1/2 x) |
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(* -5/32 (pow x 2)) |
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(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x))) (sqrt.f64 #s(literal 1/2 binary64))) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2)) |
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) x)) x)) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x)) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(-.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) x)) |
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x)) |
(* -5/32 (pow x 2)) |
(*.f64 #s(literal -5/32 binary64) (*.f64 x x)) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 5/32 binary64)) x) x) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 5/32 binary64)) x) x) |
(* (pow x 2) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 5/32 binary64)) x) x) |
(* -5/32 (pow x 4)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/32 binary64)) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) 5/32)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 5/32 binary64))) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 5/32 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))) |
(* (pow x 4) (- (* 3/16 (/ 1 (pow x 2))) (+ 5/32 (/ 1/4 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 5/32 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))) |
| 5 032× | lower-*.f32 |
| 5 030× | lower-*.f64 |
| 3 770× | lower-/.f32 |
| 3 764× | lower-/.f64 |
| 2 052× | lower-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 277 |
| 0 | 63 | 288 |
| 1 | 282 | 248 |
| 2 | 2216 | 248 |
| 0 | 8596 | 248 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) |
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) |
(fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) |
| Outputs |
|---|
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) |
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))) |
(/.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (pow.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(/.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (*.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) |
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))) |
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64))))) |
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) |
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(literal 1/2 binary64) (neg.f64 (hypot.f64 #s(literal 1 binary64) x))) |
(neg.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64)) (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64)) (pow.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64)))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)) (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64)))) (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 (*.f64 x x) #s(literal -5/32 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)) (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)))) |
(/.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 3/16 binary64) (*.f64 (*.f64 x x) #s(literal -5/32 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal -15/512 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64)))))) |
(/.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64)) (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64))) |
(/.f64 (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal -15/512 binary64))))) |
(/.f64 (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64)) (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)) (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64)))) (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)) (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -9/256 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal -15/512 binary64)))) (fma.f64 #s(literal -125/32768 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27/4096 binary64)))) |
(fma.f64 (*.f64 #s(literal -5/32 binary64) x) x #s(literal 3/16 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) |
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) |
(fma.f64 x (*.f64 #s(literal -5/32 binary64) x) #s(literal 3/16 binary64)) |
(-.f64 (/.f64 (*.f64 #s(literal 25/1024 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal -3/16 binary64)))) |
(+.f64 (*.f64 (*.f64 x x) #s(literal -5/32 binary64)) #s(literal 3/16 binary64)) |
(+.f64 #s(literal 3/16 binary64) (*.f64 (*.f64 x x) #s(literal -5/32 binary64))) |
(*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64)) (pow.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64)))) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) x)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64)))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)))) |
(/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) x))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64))) (neg.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64))) (neg.f64 (+.f64 #s(literal 1/16 binary64) (-.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64))))))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64)))))) |
(/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64))) |
(/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64)) (+.f64 #s(literal 1/16 binary64) (-.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64)))))) |
(/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64)) (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64)))) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) (*.f64 x #s(literal -1/4 binary64)))) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/64 binary64)))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) x #s(literal -1/4 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal -1/4 binary64)) |
(fma.f64 x (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) #s(literal -1/4 binary64)) |
(-.f64 (/.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/16 binary64) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)))) |
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) x) #s(literal -1/4 binary64)) |
(+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64)) x) x)) |
Compiled 34 228 to 3 536 computations (89.7% saved)
14 alts after pruning (11 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 210 | 11 | 1 221 |
| Fresh | 8 | 0 | 8 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 220 | 14 | 1 234 |
| Status | Accuracy | Program |
|---|---|---|
| 75.9% | (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))) #s(literal 1 binary64))) | |
| ▶ | 76.6% | (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
| 47.5% | (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) | |
| 47.4% | (/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) | |
| ✓ | 75.9% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| ▶ | 45.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
| ✓ | 46.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
| ✓ | 47.1% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
| ▶ | 31.6% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
| ▶ | 30.5% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
| ▶ | 47.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
| 54.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) | |
| 53.4% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) | |
| 54.7% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
Compiled 336 to 227 computations (32.4% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) | |
| cost-diff | 0 | (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) | |
| cost-diff | 0 | (sqrt.f64 #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) | |
| cost-diff | 0 | #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) | |
| cost-diff | 0 | (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) | |
| cost-diff | 192 | (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 10 328× | lower-fma.f32 |
| 10 326× | lower-fma.f64 |
| 1 998× | lower-*.f32 |
| 1 996× | lower-*.f64 |
| 1 434× | lower-+.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 273 |
| 0 | 66 | 269 |
| 1 | 110 | 269 |
| 2 | 173 | 266 |
| 3 | 284 | 266 |
| 4 | 529 | 266 |
| 5 | 1024 | 266 |
| 6 | 1651 | 266 |
| 7 | 2335 | 266 |
| 8 | 3552 | 266 |
| 9 | 5192 | 266 |
| 10 | 7000 | 266 |
| 0 | 8038 | 266 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
(hypot.f64 #s(literal 1 binary64) x) |
x |
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
#s(literal -1/8 binary64) |
(*.f64 x x) |
x |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
#s(literal 1/2 binary64) |
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
#s(literal 1 binary64) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) |
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) |
#s(literal 1/2 binary64) |
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
#s(literal 1/4 binary64) |
(*.f64 x x) |
x |
| Outputs |
|---|
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
(hypot.f64 #s(literal 1 binary64) x) |
x |
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64)) |
#s(literal -1/8 binary64) |
(*.f64 x x) |
x |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
#s(literal 1/2 binary64) |
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
#s(literal 1 binary64) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) |
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) |
#s(literal 1/2 binary64) |
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
#s(literal 1/4 binary64) |
(*.f64 x x) |
x |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.05078125 | (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) | |
| accuracy | 0.5936424782175677 | (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) | |
| accuracy | 33.966764533507856 | #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) | |
| accuracy | 0 | (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) | |
| accuracy | 0 | (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) | |
| accuracy | 0 | (sqrt.f64 #s(literal 1/2 binary64)) | |
| accuracy | 33.43791773802067 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) | |
| accuracy | 0 | (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) | |
| accuracy | 29.745024254545537 | #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) | |
| accuracy | 15.441387441870212 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) | |
| accuracy | 24.288352818168782 | #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) | |
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) | |
| accuracy | 0.01171875 | (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 0.015625 | (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) | |
| accuracy | 15.020385963245173 | (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 63.0ms | 95× | 2 | valid |
| 25.0ms | 123× | 0 | valid |
| 16.0ms | 38× | 1 | valid |
Compiled 301 to 29 computations (90.4% saved)
ival-div: 16.0ms (20.6% of total)adjust: 13.0ms (16.7% of total)ival-sub: 13.0ms (16.7% of total)ival-hypot: 12.0ms (15.4% of total)ival-sqrt: 10.0ms (12.9% of total)ival-add: 6.0ms (7.7% of total)ival-mult: 5.0ms (6.4% of total)ival-neg: 3.0ms (3.9% of total)exact: 1.0ms (1.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) (patch (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (patch (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (patch (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/4 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/4 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/8 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/8 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
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3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | ((- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (* -1/8 (* x x)) 1) (* x x) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/ 1/2 (+ (sqrt 1/2) 1)) (+ (sqrt 1/2) 1) (sqrt 1/2) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (/ 1/4 (* x x)) (/ (- (/ 1/4 (* x x)) 1/2) x)) |
| 2.0ms | x | @ | 0 | ((- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (* -1/8 (* x x)) 1) (* x x) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/ 1/2 (+ (sqrt 1/2) 1)) (+ (sqrt 1/2) 1) (sqrt 1/2) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (/ 1/4 (* x x)) (/ (- (/ 1/4 (* x x)) 1/2) x)) |
| 1.0ms | x | @ | -inf | ((- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (* -1/8 (* x x)) 1) (* x x) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/ 1/2 (+ (sqrt 1/2) 1)) (+ (sqrt 1/2) 1) (sqrt 1/2) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (/ 1/4 (* x x)) (/ (- (/ 1/4 (* x x)) 1/2) x)) |
| 1× | egg-herbie |
| 16 588× | lower-fma.f64 |
| 16 588× | lower-fma.f32 |
| 5 000× | lower-*.f64 |
| 5 000× | lower-*.f32 |
| 4 134× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 294 | 3752 |
| 1 | 889 | 3421 |
| 2 | 2828 | 3346 |
| 0 | 8272 | 3204 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/4 (pow x 2)) |
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
-1/2 |
(- (* 1/4 (pow x 2)) 1/2) |
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* -1/8 (pow x 2))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
-1/2 |
(- (* 1/4 (pow x 2)) 1/2) |
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
2 |
(+ 2 (* -1/8 (pow x 2))) |
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 3)) |
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3)) |
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3)) |
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3)) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x))) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))) |
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(/ -1/2 x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x) |
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x) |
(- 1 (sqrt 1/2)) |
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))) |
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(- 1 (sqrt 1/2)) |
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))) |
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))) |
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))))) |
(- 1 (sqrt 1/2)) |
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))) |
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
(/ -1/2 x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x) |
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(+ 1 (sqrt 1/2)) |
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))) |
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ -1/2 x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x) |
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(/ 1/2 x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(- 1 (sqrt 1/2)) |
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2)) |
(sqrt 1/2) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(/ 1/2 x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(sqrt 1/2) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(+ 1 (sqrt 1/2)) |
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ -1/2 x) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
| Outputs |
|---|
(* 1/4 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (*.f64 x x) #s(literal 5/32 binary64)) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/4 (pow x 2))) |
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/4 (pow x 2)) 1/2) |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2) |
(fma.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(fma.f64 (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -69/1024 binary64) (*.f64 x x) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(fma.f64 (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -69/1024 binary64) (*.f64 x x) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(fma.f64 (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -69/1024 binary64) (*.f64 x x) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/4 (pow x 2))) |
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/4 (pow x 2)) 1/2) |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2) |
(fma.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(fma.f64 (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -69/1024 binary64) (*.f64 x x) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
2 |
#s(literal 2 binary64) |
(+ 2 (* -1/8 (pow x 2))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 2 binary64)) |
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(fma.f64 (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 2 binary64)) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -69/1024 binary64) (*.f64 x x) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 2 binary64)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 3)) |
(/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) |
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))) |
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))) |
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(- 1/2 (* 1/2 (/ 1 x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x))) |
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) |
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/2 binary64))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) x) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))) |
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (-.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) |
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))))) |
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))))) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1/32 binary64) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (/.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/2 (/ 1 x))) |
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1/2 |
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(- 1 (sqrt 1/2)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2)) |
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x))) (sqrt.f64 #s(literal 1/2 binary64))) |
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2)) |
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) x)) x)) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) x)) x)) |
1/2 |
#s(literal 1/2 binary64) |
(- 1/2 (* 1/2 (/ 1 x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) |
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)) |
(/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x)) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) x)) x)) |
(+ 1 (sqrt 1/2)) |
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(-.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))) |
(-.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))) |
(-.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) x)) x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
| 4 802× | lower-*.f32 |
| 4 800× | lower-*.f64 |
| 4 238× | lower-/.f32 |
| 4 228× | lower-/.f64 |
| 2 026× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 246 |
| 0 | 66 | 242 |
| 1 | 289 | 219 |
| 2 | 2370 | 219 |
| 0 | 8919 | 214 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) |
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) |
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
| Outputs |
|---|
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) |
(*.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (neg.f64 (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (+.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (*.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (*.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) |
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (neg.f64 (hypot.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))) |
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(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) |
(*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (pow.f64 (neg.f64 x) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) x)) |
(pow.f64 (/.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (neg.f64 x)) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)))))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))) (neg.f64 (neg.f64 (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) x))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) x))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) x) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 (neg.f64 x) x)) |
(/.f64 (-.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 x)) (*.f64 (neg.f64 x) #s(literal -1/2 binary64))) (*.f64 (neg.f64 x) (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) (*.f64 (neg.f64 x) #s(literal 1/2 binary64))) (*.f64 (neg.f64 x) x)) |
(/.f64 (-.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 x #s(literal 1/2 binary64))) (*.f64 (neg.f64 x) #s(literal 1 binary64))) (*.f64 (neg.f64 x) (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (neg.f64 x)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) x) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 3 binary64))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) (*.f64 (*.f64 x x) (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal -1/4 binary64) (neg.f64 x)) (*.f64 (*.f64 x (*.f64 (neg.f64 x) x)) #s(literal -1/2 binary64))) (*.f64 (*.f64 x (*.f64 (neg.f64 x) x)) (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 #s(literal -1/4 binary64) x) (*.f64 (*.f64 x (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))) (*.f64 (*.f64 x (*.f64 (neg.f64 x) x)) x)) |
(/.f64 (-.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 x #s(literal 1/2 binary64))) (*.f64 (*.f64 x (*.f64 (neg.f64 x) x)) #s(literal 1 binary64))) (*.f64 (*.f64 x (*.f64 (neg.f64 x) x)) (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (neg.f64 x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (neg.f64 x) x)) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 x #s(literal 1/2 binary64))) (*.f64 x #s(literal 1 binary64))) (*.f64 x (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (neg.f64 x)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 x #s(literal 1/2 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64))) (*.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal 1/2 binary64))) (*.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 1/2 binary64))) (*.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal 1 binary64))) (*.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal -1/2 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 4 binary64))) (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 4 binary64))) x)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 1/2 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 4 binary64))) (/.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) (neg.f64 x)) |
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x))) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (neg.f64 (neg.f64 x))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) #s(literal -1/4 binary64))) (neg.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (neg.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) x)) |
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) x)) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) x) (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) |
(/.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) (*.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64)) (*.f64 x (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (neg.f64 x)) |
(/.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) x) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) x)) |
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) |
(fma.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 x #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) |
(fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal -2 binary64)) x) (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) |
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) |
(exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) #s(literal -1 binary64))) |
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) |
Compiled 28 724 to 3 544 computations (87.7% saved)
14 alts after pruning (7 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 057 | 3 | 1 060 |
| Fresh | 2 | 4 | 6 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 060 | 14 | 1 074 |
| Status | Accuracy | Program |
|---|---|---|
| 75.9% | (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) | |
| ▶ | 47.5% | (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
| ▶ | 76.6% | (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
| 47.4% | (/.f64 #s(approx (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) | |
| ✓ | 75.9% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| ✓ | 45.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
| ✓ | 46.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
| ✓ | 47.1% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
| ✓ | 31.6% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
| ✓ | 30.5% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
| ✓ | 47.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
| ▶ | 54.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
| ▶ | 53.4% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
| ▶ | 54.7% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
Compiled 293 to 195 computations (33.4% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) | |
| cost-diff | 0 | (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) | |
| cost-diff | 0 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) | |
| cost-diff | 0 | (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) | |
| cost-diff | 0 | (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) | |
| cost-diff | 0 | (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) | |
| cost-diff | 0 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) | |
| cost-diff | 0 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) | |
| cost-diff | 0 | (hypot.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
| 14 424× | lower-fma.f32 |
| 14 418× | lower-fma.f64 |
| 2 722× | lower-*.f32 |
| 2 710× | lower-*.f64 |
| 1 856× | lower-+.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 368 |
| 0 | 77 | 368 |
| 1 | 135 | 356 |
| 2 | 222 | 347 |
| 3 | 433 | 347 |
| 4 | 855 | 347 |
| 5 | 1726 | 347 |
| 6 | 2539 | 347 |
| 7 | 3010 | 347 |
| 8 | 3297 | 347 |
| 9 | 4536 | 347 |
| 10 | 5868 | 347 |
| 11 | 6173 | 347 |
| 12 | 6464 | 347 |
| 13 | 6735 | 347 |
| 14 | 6797 | 347 |
| 0 | 8030 | 347 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(hypot.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
#s(literal 1/8 binary64) |
(*.f64 x x) |
x |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
#s(literal -11/128 binary64) |
(*.f64 x x) |
x |
#s(literal 1/8 binary64) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) |
#s(literal 69/1024 binary64) |
(*.f64 x x) |
x |
#s(literal -11/128 binary64) |
#s(literal 1/8 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(hypot.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(sqrt.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
#s(literal -1/2 binary64) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
#s(literal 1/8 binary64) |
(*.f64 x x) |
x |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
#s(literal -11/128 binary64) |
(*.f64 x x) |
x |
#s(literal 1/8 binary64) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) |
#s(literal 69/1024 binary64) |
(*.f64 x x) |
x |
#s(literal -11/128 binary64) |
#s(literal 1/8 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) | |
| accuracy | 0.015625 | (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) | |
| accuracy | 15.020385963245173 | (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) | |
| accuracy | 32.464107603526834 | #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) | |
| accuracy | 0.02734375 | (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) | |
| accuracy | 0.02734375 | (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) | |
| accuracy | 0.0546875 | (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) | |
| accuracy | 28.908522762185093 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) | |
| accuracy | 0.03125 | (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) | |
| accuracy | 0.03125 | (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) | |
| accuracy | 0.06640625 | (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) | |
| accuracy | 29.799683271561943 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0 | (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) | |
| accuracy | 29.011208080925392 | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) | |
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) | |
| accuracy | 0.01171875 | (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 0.015625 | (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) | |
| accuracy | 14.984946734052393 | (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 82.0ms | 95× | 2 | valid |
| 38.0ms | 123× | 0 | valid |
| 23.0ms | 38× | 1 | valid |
Compiled 416 to 42 computations (89.9% saved)
ival-div: 28.0ms (25.5% of total)adjust: 18.0ms (16.4% of total)ival-mult: 16.0ms (14.6% of total)ival-sub: 14.0ms (12.8% of total)ival-hypot: 12.0ms (10.9% of total)ival-add: 12.0ms (10.9% of total)ival-sqrt: 7.0ms (6.4% of total)ival-neg: 2.0ms (1.8% of total)exact: 1.0ms (0.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/4 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt 1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2))))) (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8))))) (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ()) |
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#s(alt (- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 69/1024 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt 1/2) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | -inf | ((/ (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (/ 1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (+ (* 1 1) (* x x))) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* 1/8 (* x x)) (* x x) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) x) x) (* (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) x) (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) (/ (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (+ (* 69/1024 (* x x)) -11/128) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) |
| 4.0ms | x | @ | inf | ((/ (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (/ 1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (+ (* 1 1) (* x x))) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* 1/8 (* x x)) (* x x) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) x) x) (* (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) x) (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) (/ (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (+ (* 69/1024 (* x x)) -11/128) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) |
| 4.0ms | x | @ | 0 | ((/ (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (/ 1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (+ (* 1 1) (* x x))) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* 1/8 (* x x)) (* x x) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) x) x) (* (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) x) (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8) (/ (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (+ (* 69/1024 (* x x)) -11/128) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) |
| 1× | egg-herbie |
| 5 882× | lower-fma.f64 |
| 5 882× | lower-fma.f32 |
| 5 186× | lower-*.f64 |
| 5 186× | lower-*.f32 |
| 3 164× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 511 | 6036 |
| 1 | 1609 | 5663 |
| 2 | 5563 | 5619 |
| 0 | 8270 | 5342 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(* 1/4 (pow x 2)) |
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) |
1/2 |
(+ 1/2 (* -1/4 (pow x 2))) |
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
1 |
(+ 1 (* 1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2))))) |
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8))))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* 1/8 x) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
1/8 |
(+ 1/8 (* -11/128 (pow x 2))) |
(+ 1/8 (* -11/128 (pow x 2))) |
(+ 1/8 (* -11/128 (pow x 2))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(* 1/8 (pow x 2)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* 1/8 x) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
1/8 |
(+ 1/8 (* -11/128 (pow x 2))) |
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))) |
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))) |
(* 1/4 (/ (pow x 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))) |
(* (pow x 2) (+ (* -1 (* (pow x 2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) |
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) |
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (* (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/4 (/ (* (sqrt 1/2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/8 (/ (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 35/256 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))))) (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) |
(* 1/4 (pow x 2)) |
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) |
1 |
(+ 1 (* -1/4 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/2 x)) x) |
(/ (+ 1/2 (* 1/2 x)) x) |
(/ (+ 1/2 (* 1/2 x)) x) |
1 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
2 |
(+ 2 (* -1/8 (pow x 2))) |
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))) |
-11/128 |
(- (* 69/1024 (pow x 2)) 11/128) |
(- (* 69/1024 (pow x 2)) 11/128) |
(- (* 69/1024 (pow x 2)) 11/128) |
(* (sqrt 1/2) (sqrt 2)) |
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2)))))) |
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2)))))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))) |
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x))) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) |
(/ 1/2 x) |
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x) |
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x) |
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x) |
x |
(* x (+ 1 (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
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(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
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(* -11/128 (pow x 4)) |
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* -11/128 (pow x 3)) |
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* -11/128 (pow x 2)) |
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
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(* 69/1024 (pow x 6)) |
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* 69/1024 (pow x 5)) |
(* (pow x 5) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 5) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 5) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* 69/1024 (pow x 4)) |
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* -1 (/ (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(- (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (pow x 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))) |
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (* -3/32 (/ (sqrt 1/2) (* (pow x 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/16 (/ (sqrt 1/2) (* (pow x 2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/8 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x))) |
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) |
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(+ 1 (sqrt 1/2)) |
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))) |
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) |
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(* 69/1024 (pow x 2)) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))) |
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))) |
(/ -1/2 x) |
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) |
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) |
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) |
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) |
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(* -11/128 (pow x 4)) |
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* -11/128 (pow x 3)) |
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))) |
(* -11/128 (pow x 2)) |
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(* 69/1024 (pow x 6)) |
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* 69/1024 (pow x 5)) |
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))) |
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))) |
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))) |
(* 69/1024 (pow x 4)) |
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) |
(/ 1/2 (+ 1 (sqrt 1/2))) |
(+ (* 1/4 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) |
(+ (* -1 (/ (- (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* x (+ 1 (sqrt 1/2))))) (* -1/16 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ 1 (sqrt 1/2)))) (+ (* -3/32 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/8 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2))))))) x)) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))) |
1/2 |
(- 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
1/2 |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(sqrt 1/2) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(+ 1 (sqrt 1/2)) |
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))) |
(* 69/1024 (pow x 2)) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
| Outputs |
|---|
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/4 (pow x 2)) |
(*.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (*.f64 x x) #s(literal 5/32 binary64)) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 (pow x 2))) |
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) |
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))) |
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) |
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (pow x 2))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
1/8 |
#s(literal 1/8 binary64) |
(+ 1/8 (* -11/128 (pow x 2))) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
(+ 1/8 (* -11/128 (pow x 2))) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
(+ 1/8 (* -11/128 (pow x 2))) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/8 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/8 binary64)) |
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* x (+ 1/8 (* -11/128 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) |
1/8 |
#s(literal 1/8 binary64) |
(+ 1/8 (* -11/128 (pow x 2))) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))) |
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))) |
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(* 1/4 (/ (pow x 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))) |
(*.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) x) x) |
(* (pow x 2) (+ (* -1 (* (pow x 2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) |
(*.f64 (fma.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x)) |
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) |
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 5/32 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 11/256 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) x) x)) |
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (* (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/4 (/ (* (sqrt 1/2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/8 (/ (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 35/256 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))))) (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) |
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(+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ 1 (sqrt 1/2)))) (+ (* -3/32 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/8 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2))))))) x)) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) |
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))) x) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) x) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) x)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) x)) |
1/2 |
#s(literal 1/2 binary64) |
(- 1/2 (* 1/2 (/ 1 x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))) |
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) |
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (/ 1 x))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x)) |
(+ 1 (sqrt 1/2)) |
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2))))) |
(-.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))) |
(-.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) |
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))) |
(-.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x)) |
(* 69/1024 (pow x 2)) |
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (*.f64 x x))) x) x) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x)) |
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) |
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 3/16 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/8 binary64))) (neg.f64 x))) x)) |
| 5 130× | lower-*.f32 |
| 5 118× | lower-*.f64 |
| 4 408× | lower-/.f32 |
| 4 398× | lower-/.f64 |
| 2 148× | lower--.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 313 |
| 0 | 77 | 303 |
| 1 | 323 | 254 |
| 2 | 2515 | 254 |
| 0 | 9300 | 254 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
(hypot.f64 #s(literal 1 binary64) x) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(*.f64 x x) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) |
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(*.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))) |
(pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
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(pow.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) |
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) |
(fabs.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
(exp.f64 (log.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
Compiled 26 340 to 3 322 computations (87.4% saved)
16 alts after pruning (6 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 982 | 6 | 988 |
| Fresh | 2 | 0 | 2 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 7 | 7 |
| Total | 986 | 16 | 1 002 |
| Status | Accuracy | Program |
|---|---|---|
| 76.6% | (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))) | |
| 40.3% | (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) #s(literal 2 binary64))) | |
| 76.6% | (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) | |
| 47.6% | (/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) | |
| 31.7% | (/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) | |
| ✓ | 75.9% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| ✓ | 45.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
| ✓ | 46.8% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
| ✓ | 47.1% | (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
| ✓ | 31.6% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
| ✓ | 30.5% | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
| ✓ | 47.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
| 54.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) | |
| ✓ | 54.8% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
| ✓ | 53.4% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
| ✓ | 54.7% | #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
Compiled 739 to 310 computations (58.1% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)))))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) #s(literal 2 binary64))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 #s(approx (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))) #s(literal -1 binary64))) |
(fma.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))) |
7 calls:
| 30.0ms | x |
| 24.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 11.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 6.0ms | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 6.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 2 | x |
| 100.0% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 100.0% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 100.0% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 100.0% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 100.0% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 100.0% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)))))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) #s(literal 2 binary64))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
(/.f64 #s(approx (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(/.f64 #s(approx (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
7 calls:
| 26.0ms | x |
| 20.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 9.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 6.0ms | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 6.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 2 | x |
| 99.6% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 99.6% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 99.6% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 99.6% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 99.6% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 99.6% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)))))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (*.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) #s(literal 2 binary64))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
7 calls:
| 22.0ms | x |
| 18.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 9.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 6.0ms | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 5.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 2 | x |
| 99.6% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 99.6% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 99.6% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 99.6% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 99.6% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 99.6% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))) |
7 calls:
| 15.0ms | x |
| 13.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 7.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 5.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 5.0ms | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 2 | x |
| 99.0% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 99.0% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 99.0% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 99.0% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 99.0% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 99.0% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (fma.f64 #s(literal 3/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
7 calls:
| 15.0ms | x |
| 12.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 7.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 6.0ms | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 5.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 2 | x |
| 98.9% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 98.9% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 98.9% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 98.9% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 98.9% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 98.9% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
7 calls:
| 12.0ms | x |
| 10.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 5.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 4.0ms | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 4.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 2 | x |
| 98.9% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 98.9% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 98.9% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 98.9% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 98.9% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 98.9% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) |
7 calls:
| 11.0ms | x |
| 9.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 6.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 4.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 4.0ms | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 2 | x |
| 98.7% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 98.7% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 98.7% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 98.7% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 98.7% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 98.7% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
7 calls:
| 10.0ms | x |
| 9.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 6.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 4.0ms | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 4.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 2 | x |
| 98.5% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 98.5% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 98.5% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 98.5% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 98.5% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 98.5% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
7 calls:
| 9.0ms | x |
| 8.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 7.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 4.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 3.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 2 | x |
| 97.9% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 97.9% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 97.9% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 97.9% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 97.9% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 97.9% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) |
7 calls:
| 9.0ms | x |
| 7.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 5.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 4.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 4.0ms | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.5% | 2 | x |
| 97.5% | 2 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 97.5% | 2 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 97.5% | 2 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 97.5% | 2 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 97.5% | 2 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 97.5% | 2 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
| Outputs |
|---|
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
7 calls:
| 4.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 3.0ms | x |
| 2.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 2.0ms | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 2.0ms | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 54.7% | 1 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 54.7% | 1 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 54.7% | 1 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 54.7% | 1 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 54.7% | 1 | x |
| 54.7% | 1 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 54.7% | 1 | (hypot.f64 #s(literal 1 binary64) x) |
Compiled 47 to 37 computations (21.3% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
7 calls:
| 3.0ms | x |
| 3.0ms | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
| 2.0ms | (hypot.f64 #s(literal 1 binary64) x) |
| 2.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 2.0ms | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 30.5% | 1 | x |
| 30.5% | 1 | (hypot.f64 #s(literal 1 binary64) x) |
| 30.5% | 1 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) |
| 30.5% | 1 | (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) |
| 30.5% | 1 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) |
| 30.5% | 1 | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) |
| 30.5% | 1 | (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) |
Compiled 47 to 37 computations (21.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.000002125703755 | 1.3580932555790084 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.3580932555790084 | 1422.460167590609 |
Compiled 15 to 14 computations (6.7% saved)
| 1× | egg-herbie |
| 58× | +-commutative-binary64-+.f64 |
| 48× | sub-neg-binary64-neg.f64-+.f64--.f64 |
| 40× | *-commutative-binary64-*.f64 |
| 28× | neg-sub0-binary64--.f64-neg.f64 |
| 28× | neg-mul-1-binary64-*.f64-neg.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 93 | 758 |
| 1 | 127 | 758 |
| 2 | 170 | 758 |
| 3 | 198 | 758 |
| 4 | 216 | 758 |
| 5 | 220 | 758 |
| 1× | saturated |
| Inputs |
|---|
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 5404319552844595/4503599627370496 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64)))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 #s(approx (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
| Outputs |
|---|
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 5404319552844595/4503599627370496 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64)))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 #s(approx (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))) |
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))) |
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))) |
| 18 030× | lower-fma.f64 |
| 18 030× | lower-fma.f32 |
| 16 588× | lower-fma.f64 |
| 16 588× | lower-fma.f32 |
| 12 740× | lower-fma.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 246 |
| 0 | 66 | 242 |
| 1 | 289 | 219 |
| 2 | 2370 | 219 |
| 0 | 8919 | 214 |
| 0 | 48 | 313 |
| 0 | 77 | 303 |
| 1 | 323 | 254 |
| 2 | 2515 | 254 |
| 0 | 9300 | 254 |
| 0 | 415 | 3886 |
| 1 | 1292 | 3534 |
| 2 | 3999 | 3396 |
| 0 | 8520 | 3235 |
| 0 | 294 | 3752 |
| 1 | 889 | 3421 |
| 2 | 2828 | 3346 |
| 0 | 8272 | 3204 |
| 0 | 38 | 277 |
| 0 | 63 | 288 |
| 1 | 282 | 248 |
| 2 | 2216 | 248 |
| 0 | 8596 | 248 |
| 0 | 511 | 6036 |
| 1 | 1609 | 5663 |
| 2 | 5563 | 5619 |
| 0 | 8270 | 5342 |
| 0 | 206 | 855 |
| 1 | 592 | 781 |
| 2 | 1621 | 742 |
| 3 | 4409 | 701 |
| 0 | 8156 | 662 |
| 0 | 9 | 43 |
| 0 | 18 | 43 |
| 1 | 78 | 37 |
| 2 | 562 | 37 |
| 3 | 5209 | 37 |
| 0 | 8824 | 37 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 772 to 373 computations (51.7% saved)
(abs x)
Compiled 742 to 222 computations (70.1% saved)
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