
Time bar (total: 10.5s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 0 |
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 1 |
| 50% | 12.5% | 12.5% | 75% | 0% | 0% | 0% | 2 |
| 75% | 18.7% | 6.2% | 75% | 0% | 0% | 0% | 3 |
| 87.5% | 21.9% | 3.1% | 75% | 0% | 0% | 0% | 4 |
| 93.8% | 23.4% | 1.6% | 75% | 0% | 0% | 0% | 5 |
| 96.9% | 24.2% | 0.8% | 75% | 0% | 0% | 0% | 6 |
| 98.4% | 24.6% | 0.4% | 75% | 0% | 0% | 0% | 7 |
| 99.2% | 24.8% | 0.2% | 75% | 0% | 0% | 0% | 8 |
| 99.6% | 24.9% | 0.1% | 75% | 0% | 0% | 0% | 9 |
| 99.8% | 24.9% | 0% | 75% | 0% | 0% | 0% | 10 |
| 99.9% | 25% | 0% | 75% | 0% | 0% | 0% | 11 |
| 100% | 25% | 0% | 75% | 0% | 0% | 0% | 12 |
Compiled 19 to 13 computations (31.6% saved)
| 1.0s | 6 895× | 1 | valid |
| 284.0ms | 1 096× | 2 | valid |
| 19.0ms | 265× | 0 | valid |
ival-sqrt: 303.0ms (27.9% of total)ival-div: 253.0ms (23.3% of total)adjust: 169.0ms (15.6% of total)const: 128.0ms (11.8% of total)ival-sub: 90.0ms (8.3% of total)ival-add: 79.0ms (7.3% of total)ival->: 24.0ms (2.2% of total)ival-<: 18.0ms (1.7% of total)ival-and: 11.0ms (1% of total)exact: 6.0ms (0.6% of total)ival-assert: 3.0ms (0.3% of total)| 1× | egg-herbie |
| 112× | lower-fma.f64 |
| 112× | lower-fma.f32 |
| 80× | lower-*.f64 |
| 80× | lower-*.f32 |
| 52× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 27 |
| 1 | 20 | 25 |
| 2 | 47 | 24 |
| 3 | 89 | 24 |
| 4 | 144 | 24 |
| 5 | 209 | 24 |
| 6 | 245 | 24 |
| 7 | 272 | 24 |
| 8 | 281 | 24 |
| 0 | 8 | 11 |
| 0 | 14 | 11 |
| 1 | 19 | 11 |
| 2 | 27 | 11 |
| 3 | 36 | 11 |
| 4 | 48 | 11 |
| 5 | 68 | 11 |
| 6 | 107 | 11 |
| 7 | 139 | 11 |
| 8 | 195 | 11 |
| 9 | 224 | 11 |
| 10 | 245 | 11 |
| 11 | 247 | 11 |
| 0 | 247 | 11 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Outputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 175 | 1 | (4.2466946299767355e+214) | 0 | - | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 0 | 0 | - | 0 | - | (+.f64 x #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (sqrt.f64 x) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) | cancellation | 176 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 175 | 0 |
| - | 1 | 80 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 175 | 0 | 0 |
| - | 1 | 0 | 80 |
| number | freq |
|---|---|
| 0 | 80 |
| 1 | 176 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 115.0ms | 424× | 1 | valid |
| 14.0ms | 74× | 2 | valid |
| 1.0ms | 14× | 0 | valid |
Compiled 92 to 36 computations (60.9% saved)
ival-sqrt: 76.0ms (69.9% of total)ival-div: 13.0ms (12% of total)adjust: 9.0ms (8.3% of total)ival-add: 5.0ms (4.6% of total)ival-sub: 4.0ms (3.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 39.1% | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 12 to 8 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 112× | lower-fma.f64 |
| 112× | lower-fma.f32 |
| 80× | lower-*.f64 |
| 80× | lower-*.f32 |
| 52× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 32 |
| 0 | 14 | 32 |
| 1 | 19 | 32 |
| 2 | 27 | 32 |
| 3 | 36 | 32 |
| 4 | 48 | 32 |
| 5 | 68 | 32 |
| 6 | 107 | 32 |
| 7 | 139 | 32 |
| 8 | 195 | 32 |
| 9 | 224 | 32 |
| 10 | 245 | 32 |
| 11 | 247 | 32 |
| 0 | 247 | 32 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 x #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | accuracy | 39.3% | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 30.0ms | 212× | 1 | valid |
| 7.0ms | 37× | 2 | valid |
| 0.0ms | 7× | 0 | valid |
Compiled 34 to 10 computations (70.6% saved)
ival-sqrt: 8.0ms (29.8% of total)ival-div: 7.0ms (26% of total)adjust: 5.0ms (18.6% of total)ival-add: 4.0ms (14.9% of total)ival-sub: 2.0ms (7.4% 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (- (* 3/8 x) 1/2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) |
| 1.0ms | x | @ | inf | (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) |
| 1.0ms | x | @ | -inf | (/ 1 (sqrt (+ x 1))) |
| 1.0ms | x | @ | -inf | (/ 1 (sqrt x)) |
| 0.0ms | x | @ | 0 | (/ 1 (sqrt x)) |
| 1× | egg-herbie |
| 23 172× | lower-fma.f64 |
| 23 172× | lower-fma.f32 |
| 4 828× | lower-*.f64 |
| 4 828× | lower-*.f32 |
| 3 424× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 114 | 529 |
| 1 | 303 | 480 |
| 2 | 925 | 455 |
| 3 | 3326 | 445 |
| 0 | 8140 | 416 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (/ 1 x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
| Outputs |
|---|
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(+.f64 (/.f64 (sqrt.f64 x) x) #s(literal -1 binary64)) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (sqrt.f64 x)) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -3/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (sqrt.f64 x)) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(fma.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))) (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 x)) |
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(-.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))) (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| 1× | batch-egg-rewrite |
| 4 400× | lower-fma.f64 |
| 4 400× | lower-fma.f32 |
| 3 040× | lower-*.f64 |
| 3 040× | lower-*.f32 |
| 2 738× | lower-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 23 |
| 0 | 14 | 23 |
| 1 | 66 | 19 |
| 2 | 565 | 19 |
| 3 | 6719 | 19 |
| 0 | 8113 | 19 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(sqrt.f64 x) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| Outputs |
|---|
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(+.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (neg.f64 (sqrt.f64 (/.f64 x (fma.f64 x x x))))) |
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (*.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))))) |
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x)) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) |
(-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(-.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (sqrt.f64 (/.f64 x (fma.f64 x x x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (*.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (neg.f64 (sqrt.f64 (/.f64 x (fma.f64 x x x))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (*.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x)) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x))))) |
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(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x))) |
(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 x))) |
(sqrt.f64 x) |
(neg.f64 (neg.f64 (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(/.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64))) |
(pow.f64 x #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x))) |
(*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))) |
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) |
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
Compiled 7 402 to 705 computations (90.5% saved)
11 alts after pruning (11 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 275 | 11 | 286 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 276 | 11 | 287 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 41.8% | (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| 41.8% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) | |
| ▶ | 39.2% | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
| 41.8% | (/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) | |
| ▶ | 26.9% | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
| 29.7% | (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) | |
| 7.4% | (*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x))) | |
| ▶ | 84.1% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
| 83.2% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) | |
| 68.8% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) | |
| ▶ | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
Compiled 370 to 214 computations (42.2% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) |
| ✓ | cost-diff | 384 | (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
| ✓ | cost-diff | 0 | #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
| ✓ | cost-diff | 0 | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
| 10 320× | lower-fma.f32 |
| 10 314× | lower-fma.f64 |
| 3 388× | lower-*.f32 |
| 3 382× | lower-*.f64 |
| 1 878× | lower-+.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 329 |
| 0 | 63 | 309 |
| 1 | 114 | 301 |
| 2 | 226 | 301 |
| 3 | 443 | 301 |
| 4 | 1046 | 301 |
| 5 | 2369 | 301 |
| 6 | 5369 | 301 |
| 0 | 8157 | 301 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
#s(literal 1/2 binary64) |
(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
#s(literal 1 binary64) |
(*.f64 x (*.f64 x x)) |
x |
(*.f64 x x) |
(fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) |
#s(literal 1/4 binary64) |
(sqrt.f64 x) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(sqrt.f64 x) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
(*.f64 (-.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) |
#s(literal 1/2 binary64) |
(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(-.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
#s(literal 1 binary64) |
(*.f64 x (*.f64 x x)) |
x |
(*.f64 x x) |
(fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) |
#s(literal 1/4 binary64) |
(sqrt.f64 x) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(sqrt.f64 x) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
#s(literal 1 binary64) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | accuracy | 99.7% | (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 54.2% | (sqrt.f64 (fma.f64 x x x)) |
| ✓ | accuracy | 8.4% | (-.f64 (+.f64 #s(literal 1 binary64) x) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
| ✓ | accuracy | 54.2% | (sqrt.f64 (fma.f64 x x x)) |
| ✓ | accuracy | 6.5% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 98.2% | #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 39.3% | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 99.2% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
| ✓ | accuracy | 84.9% | (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
| ✓ | accuracy | 71.4% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
| 88.0ms | 212× | 1 | valid |
| 54.0ms | 37× | 2 | valid |
| 2.0ms | 7× | 0 | valid |
Compiled 306 to 35 computations (88.6% saved)
ival-div: 21.0ms (26.3% of total)adjust: 17.0ms (21.3% of total)ival-sqrt: 16.0ms (20% of total)ival-add: 9.0ms (11.3% of total)ival-sub: 9.0ms (11.3% of total)ival-mult: 8.0ms (10% 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 #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) (patch (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ()) |
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1 binary64) x) x) (patch (-.f64 (+.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor inf x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) #<representation binary64>) () ())) ()) |
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#s(alt (sqrt (/ 1 (pow x 3))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 (pow x 3))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 (pow x 3))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 (pow x 3))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (patch (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
63 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (/ (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ (* x x) x))) |
| 1.0ms | x | @ | -inf | (/ (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ (* x x) x))) |
| 1.0ms | x | @ | 0 | (/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x)) |
| 1.0ms | x | @ | 0 | (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) |
| 1.0ms | x | @ | -inf | (/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x)) |
| 1× | egg-herbie |
| 16 698× | lower-fma.f64 |
| 16 698× | lower-fma.f32 |
| 5 182× | lower-*.f64 |
| 5 182× | lower-*.f32 |
| 5 074× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 490 | 3730 |
| 1 | 1465 | 3220 |
| 2 | 4803 | 3185 |
| 0 | 8736 | 2997 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (/ 1 x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* 1/2 (sqrt (/ 1 (pow x 7)))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 4)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x) |
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (/ (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 2)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 2)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 2)) |
(* 1/2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) |
(* x (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))))) |
(* x (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(sqrt (/ 1 (pow x 3))) |
(/ (+ (sqrt x) (* x (- (* 1/4 (sqrt x)) (sqrt x)))) (pow x 2)) |
(/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2)) |
(/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2)) |
(sqrt x) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3))))) (sqrt (/ 1 (pow x 3))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(sqrt (/ 1 x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(sqrt (/ 1 x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* (sqrt (/ 1 x)) (- 1 (sqrt x))) |
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(sqrt (/ 1 x)) |
(- (sqrt (/ 1 x)) 1) |
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x)))) |
(/ 1/2 x) |
(/ (- 1/2 (* 1/8 (/ 1 x))) x) |
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x) |
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x) |
-2 |
(* -1 (+ 2 (* 1/2 (/ 1 x)))) |
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2) |
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
| Outputs |
|---|
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(-.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1 binary64)) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (sqrt.f64 x)) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -3/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (sqrt.f64 x)) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (*.f64 x x)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) (*.f64 x x)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/4 binary64) (/.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))) (*.f64 x (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* 1/2 (sqrt (/ 1 (pow x 7)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 4)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4)) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4)) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))) x) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)))) x) |
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(* -1 (/ (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (neg.f64 x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) |
(/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x)) (neg.f64 x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) |
(/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x)) (neg.f64 x)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 2)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 2)) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 x x)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 2)) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 x x)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* x (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))) |
(* x (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))))) |
(*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))))) |
(* x (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))))) |
(*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1 (* x (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(neg.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (neg.f64 x))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (neg.f64 x))))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/ (+ (sqrt x) (* x (- (* 1/4 (sqrt x)) (sqrt x)))) (pow x 2)) |
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#s(literal 1 binary64) |
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#s(literal -2 binary64) |
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(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/8 binary64))))) (sqrt.f64 x)) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(+.f64 x #s(literal 1/2 binary64)) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (+.f64 x #s(literal 1/2 binary64)) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(+.f64 (neg.f64 x) #s(literal -1/2 binary64)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64)))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(fma.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) (neg.f64 x)) |
| 1× | batch-egg-rewrite |
| 5 422× | lower-*.f32 |
| 5 416× | lower-*.f64 |
| 3 468× | lower-/.f32 |
| 3 454× | lower-/.f64 |
| 2 790× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 245 |
| 0 | 63 | 231 |
| 1 | 302 | 188 |
| 2 | 2636 | 183 |
| 0 | 8750 | 180 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(sqrt.f64 x) |
#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(sqrt.f64 (fma.f64 x x x)) |
| Outputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))))) #s(literal -1 binary64))) |
(neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) (*.f64 x (neg.f64 x)))) |
(neg.f64 (/.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64)) (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))))) |
(/.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64)) (*.f64 x (neg.f64 x))) |
(/.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x)) x) |
(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64))) (neg.f64 (*.f64 x (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)) |
(/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) x) |
(pow.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) |
(*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x))) |
(*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (neg.f64 x)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x)) |
(*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (*.f64 x x)) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) #s(literal -1 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) |
(+.f64 (*.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) |
(fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (*.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))))) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 x))))) (+.f64 (fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (sqrt.f64 x)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))) |
(/.f64 (*.f64 (fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (*.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))))) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 1/2 binary64)) (+.f64 (fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))) (sqrt.f64 x)))) |
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#s(literal 1 binary64) |
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(hypot.f64 (neg.f64 (sqrt.f64 x)) x) |
(hypot.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x)) |
(fabs.f64 (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (*.f64 x x) x) (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 x x (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (sqrt.f64 (-.f64 (*.f64 x x) x))) |
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))))) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x)))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) x)))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 x (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) x)) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) x)) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(pow.f64 (fma.f64 x x x) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (fma.f64 x x x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(*.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) |
Compiled 39 245 to 4 106 computations (89.5% saved)
19 alts after pruning (18 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 525 | 16 | 1 541 |
| Fresh | 4 | 2 | 6 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 533 | 19 | 1 552 |
| Status | Accuracy | Program |
|---|---|---|
| 41.1% | (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| ▶ | 84.8% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ▶ | 38.7% | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| 98.0% | (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| ▶ | 84.1% | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
| 83.2% | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x))) | |
| 84.9% | (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x)))) | |
| 84.9% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) | |
| 7.4% | (*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x))) | |
| 97.9% | #s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)) | |
| 68.8% | #s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) | |
| 83.1% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) | |
| 97.0% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x))))) | |
| ▶ | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| ▶ | 98.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
| 98.6% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x)))) | |
| 83.2% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) | |
| ✓ | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| 26.0% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))))) |
Compiled 642 to 384 computations (40.2% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ✓ | cost-diff | 0 | #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 384 | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| ✓ | cost-diff | 0 | (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) |
| ✓ | cost-diff | 0 | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
| ✓ | cost-diff | 64 | (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) |
| ✓ | cost-diff | 1984 | (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) |
| 10 670× | lower-fma.f32 |
| 10 664× | lower-fma.f64 |
| 3 788× | lower-*.f32 |
| 3 782× | lower-*.f64 |
| 1 404× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 337 |
| 0 | 79 | 337 |
| 1 | 112 | 337 |
| 2 | 138 | 337 |
| 3 | 188 | 337 |
| 4 | 264 | 337 |
| 5 | 486 | 331 |
| 6 | 841 | 331 |
| 7 | 1505 | 329 |
| 8 | 3169 | 326 |
| 9 | 6459 | 326 |
| 0 | 8348 | 324 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
(*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) |
(+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) |
(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) |
(fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) |
x |
#s(literal 1/4 binary64) |
#s(literal 1 binary64) |
(*.f64 x (sqrt.f64 x)) |
(sqrt.f64 x) |
(/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) |
(+.f64 x #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(sqrt.f64 x) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
x |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal -1/8 binary64) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(sqrt.f64 x) |
#s(literal 1/2 binary64) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
| Outputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 x) (*.f64 x x)))) |
(*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 x) (*.f64 x x))) |
(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) |
(+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) (*.f64 x x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x (sqrt.f64 x)))) |
(+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) |
(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) |
(fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) |
x |
#s(literal 1/4 binary64) |
#s(literal 1 binary64) |
(*.f64 x (sqrt.f64 x)) |
(sqrt.f64 x) |
(/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) |
(+.f64 x #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(sqrt.f64 x) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
x |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal -1/8 binary64) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(sqrt.f64 x) |
#s(literal 1/2 binary64) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.6% | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
| ✓ | accuracy | 99.6% | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ✓ | accuracy | 99.3% | #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) |
| ✓ | accuracy | 54.2% | (sqrt.f64 (fma.f64 x x x)) |
| ✓ | accuracy | 100.0% | (+.f64 x (sqrt.f64 (fma.f64 x x x))) |
| ✓ | accuracy | 99.7% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 54.2% | (sqrt.f64 (fma.f64 x x x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.3% | #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
| ✓ | accuracy | 6.5% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| ✓ | accuracy | 99.6% | (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) |
| ✓ | accuracy | 99.2% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
| ✓ | accuracy | 99.2% | (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 66.5% | (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) |
| 117.0ms | 212× | 1 | valid |
| 27.0ms | 37× | 2 | valid |
| 2.0ms | 7× | 0 | valid |
Compiled 293 to 41 computations (86% saved)
ival-div: 35.0ms (31.8% of total)adjust: 20.0ms (18.2% of total)ival-mult: 18.0ms (16.4% of total)ival-add: 17.0ms (15.5% of total)ival-sqrt: 15.0ms (13.6% of total)ival-sub: 4.0ms (3.6% 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 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (patch (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ()) |
#s(alt (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (patch (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) (patch (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ()) |
#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 (sqrt (/ 1 (pow x 7)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 4)) (taylor 0 x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4)) (taylor 0 x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4)) (taylor 0 x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x) (taylor inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x) (taylor inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x) (taylor inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor -inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* -1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* -1/2 (sqrt (/ 1 x)))) x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* -1/2 (sqrt (/ 1 x)))) x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) (patch (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 (pow x 5))) (taylor 0 x) (#s(alt (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (patch (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (patch (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (patch (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (/ 1 (pow x 3))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/4 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/4 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (patch (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt (pow x 3)) (* -1 (sqrt x))) x) (taylor 0 x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt (pow x 3)) (* -1 (sqrt x))) x) (taylor 0 x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (sqrt (pow x 3)) (* -1 (sqrt x))) x) (taylor 0 x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor -inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) (patch (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (sqrt x)) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 2 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt -1/2 (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/8 (/ 1 x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
66 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | 0 | (/ (+ (* (sqrt (/ 1 x)) -1/8) (* (sqrt x) 1/2)) x) |
| 2.0ms | x | @ | -inf | (* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) x) (/ 1/2 x)) |
| 1.0ms | x | @ | -inf | (/ (+ (* (sqrt (/ 1 x)) -1/8) (* (sqrt x) 1/2)) x) |
| 0.0ms | x | @ | 0 | (* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) x) (/ 1/2 x)) |
| 0.0ms | x | @ | inf | (/ (+ (* (sqrt (/ 1 x)) -1/8) (* (sqrt x) 1/2)) x) |
| 1× | egg-herbie |
| 17 610× | lower-fma.f64 |
| 17 610× | lower-fma.f32 |
| 5 190× | lower-*.f64 |
| 5 190× | lower-*.f32 |
| 5 070× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 495 | 4196 |
| 1 | 1489 | 3738 |
| 2 | 4855 | 3699 |
| 0 | 8663 | 3442 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (sqrt (/ 1 (pow x 7)))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 4)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4)) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* -1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* -1/2 (sqrt (/ 1 x)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* -1/2 (sqrt (/ 1 x)))) x)) |
(sqrt (/ 1 (pow x 5))) |
(/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 3)) |
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3)) |
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3)) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) |
(+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))) |
(+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) |
(+ (sqrt (/ 1 x)) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x))) |
(+ (sqrt (/ 1 x)) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x))) |
(sqrt (/ 1 x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(sqrt (/ 1 (pow x 3))) |
(/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 2)) |
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 2)) |
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 2)) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))) |
(sqrt x) |
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))))) |
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x))))) x))))) |
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x))))) x))))) |
(sqrt (/ 1 x)) |
(/ (+ (sqrt x) (* -1 x)) x) |
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) |
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) |
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) |
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 x)) (- 1 (sqrt x))) |
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* (sqrt (/ 1 x)) (- 1 (sqrt x))) |
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(sqrt (/ 1 (pow x 3))) |
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2)) |
(* 1/4 (sqrt (/ 1 x))) |
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) |
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) |
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) |
(* 1/4 (sqrt (/ 1 x))) |
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) |
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) |
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x)))) |
(* -1 (sqrt (/ 1 x))) |
(/ (+ (sqrt (pow x 3)) (* -1 (sqrt x))) x) |
(/ (+ (sqrt (pow x 3)) (* -1 (sqrt x))) x) |
(/ (+ (sqrt (pow x 3)) (* -1 (sqrt x))) x) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))) |
(sqrt x) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(sqrt x) |
(+ x (sqrt x)) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) |
(* 2 x) |
(* x (+ 2 (* 1/2 (/ 1 x)))) |
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
-1/2 |
(- (* 1/8 (/ 1 x)) 1/2) |
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) |
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) |
| Outputs |
|---|
(* 1/2 (sqrt (/ 1 (pow x 7)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 4)) |
(/.f64 (fma.f64 x (*.f64 (sqrt.f64 x) #s(literal -3/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (sqrt.f64 x) #s(literal -3/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (sqrt.f64 x) #s(literal -3/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -3/8 binary64) x))) x) |
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x) |
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(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
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(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
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(* 1/2 (sqrt (/ 1 x))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
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#s(literal 1 binary64) |
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1 |
#s(literal 1 binary64) |
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x |
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(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal -1/2 binary64) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(fma.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(fma.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (neg.f64 x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x)) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) x) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) x)) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (+.f64 #s(literal 1/2 binary64) x) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal -1/2 binary64) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(fma.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(fma.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (neg.f64 x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ x (sqrt x)) |
(+.f64 x (sqrt.f64 x)) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) #s(literal 1 binary64)) (sqrt.f64 x)) |
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) #s(literal 1 binary64)) (sqrt.f64 x)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* x (+ 2 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64)) |
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))) |
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/8 (/ 1 x)) 1/2) |
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) |
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) |
(+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) |
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) |
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x)) x)) |
| 1× | batch-egg-rewrite |
| 5 508× | lower-/.f32 |
| 5 486× | lower-/.f64 |
| 4 006× | lower-fma.f32 |
| 4 000× | lower-fma.f64 |
| 3 834× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 267 |
| 0 | 79 | 267 |
| 1 | 330 | 250 |
| 2 | 2751 | 250 |
| 0 | 8791 | 236 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
(+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(sqrt.f64 x) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) |
(/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 x x x)) |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x))))) |
(/.f64 (/.f64 (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 2 binary64))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) x)) |
(/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)))) |
(/.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) (neg.f64 x)))) |
(/.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (neg.f64 x) (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x))))) |
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x))) |
(/.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x x)) |
(/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) (neg.f64 x))) |
(/.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 x) (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)))) |
(/.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) x))) |
(/.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 x (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x))))) |
(/.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x))) x) |
(/.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) |
(/.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64)) (*.f64 x (neg.f64 x))) |
(/.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal 1 binary64)) (*.f64 (neg.f64 x) (*.f64 x #s(literal 2 binary64)))) |
(/.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal 1/2 binary64)) (*.f64 (neg.f64 x) x)) |
(/.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal -1/2 binary64)) (*.f64 x x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) (*.f64 (*.f64 x #s(literal 2 binary64)) x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) (*.f64 (*.f64 x #s(literal 2 binary64)) (neg.f64 x))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) (*.f64 x (neg.f64 x))) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) (*.f64 (neg.f64 x) x)) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) (*.f64 x x)) |
(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 x x))) |
(/.f64 (neg.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x)))) (neg.f64 x)) |
(/.f64 (*.f64 (/.f64 (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) (*.f64 x (*.f64 x x))) #s(literal -1/2 binary64)) (neg.f64 x)) |
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x))) |
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) (neg.f64 x)) |
(/.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 x)) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) (*.f64 x (*.f64 x x)))) (neg.f64 x)) |
(/.f64 (neg.f64 (/.f64 (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) (*.f64 x (*.f64 x x)))) (neg.f64 (*.f64 x #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1 binary64))) (neg.f64 (*.f64 x (*.f64 x #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64))) (neg.f64 (*.f64 x (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal 1 binary64))) (neg.f64 (*.f64 (neg.f64 x) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (neg.f64 x) x))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))) #s(literal -1/2 binary64))) (neg.f64 (*.f64 x x))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))))) (neg.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) x))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))))) (neg.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))))) (neg.f64 (*.f64 x (neg.f64 x)))) |
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(pow.f64 (/.f64 (/.f64 (-.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) x) (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) (-.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) x))) #s(literal -1 binary64)) |
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#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x))) |
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(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x)))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) #s(literal -1 binary64)) |
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) |
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(sqrt.f64 x) |
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(neg.f64 (/.f64 (neg.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
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(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
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(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 x #s(literal 1 binary64))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))) (neg.f64 (*.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))) (neg.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 x))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))) (neg.f64 (neg.f64 (sqrt.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (neg.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (neg.f64 (+.f64 x #s(literal 1 binary64)))) |
(pow.f64 (/.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) |
(*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x x)))) |
(hypot.f64 x (sqrt.f64 x)) |
(hypot.f64 x (neg.f64 (sqrt.f64 x))) |
(hypot.f64 (sqrt.f64 x) x) |
(hypot.f64 (sqrt.f64 x) (neg.f64 x)) |
(hypot.f64 (neg.f64 x) (sqrt.f64 x)) |
(hypot.f64 (neg.f64 x) (neg.f64 (sqrt.f64 x))) |
(hypot.f64 (neg.f64 (sqrt.f64 x)) x) |
(hypot.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x)) |
(fabs.f64 (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (*.f64 x x) x) (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))))) |
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (fma.f64 x x (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (sqrt.f64 (-.f64 (*.f64 x x) x))) |
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x)))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) x)))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 x (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) x)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) x)) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (neg.f64 (sqrt.f64 (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x)))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)))) |
(pow.f64 (fma.f64 x x x) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (fma.f64 x x x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(*.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(+.f64 (sqrt.f64 (fma.f64 x x x)) x) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 (fma.f64 x x x) (-.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(-.f64 (/.f64 (fma.f64 x x x) (-.f64 (sqrt.f64 (fma.f64 x x x)) x)) (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 (fma.f64 x x x)) x))) |
(fma.f64 x #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 #s(literal 1 binary64) x (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x) |
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/2 binary64)) x) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) x) |
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)) #s(literal 1/2 binary64)) x) |
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x))) x) |
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) x) |
(fma.f64 (pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (*.f64 x (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x)))) (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (*.f64 x x) (fma.f64 x x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x)))) (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (*.f64 x x) (fma.f64 x x x))))) |
(/.f64 (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x))) (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x))) (+.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x x)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (neg.f64 (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x)))) (neg.f64 (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (neg.f64 (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x)))) (neg.f64 (+.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (fma.f64 x x x))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x x))) (neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (-.f64 (fma.f64 x x x) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x x)) x)) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x x)))) (neg.f64 (neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (neg.f64 (-.f64 (fma.f64 x x x) (*.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (fma.f64 x x x)) x))) |
(pow.f64 (/.f64 (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x)))) (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (*.f64 x x) (fma.f64 x x x))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x (fma.f64 x x x)) (*.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(*.f64 (-.f64 (*.f64 x x) (fma.f64 x x x)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x x))))) |
Compiled 39 659 to 4 400 computations (88.9% saved)
18 alts after pruning (14 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 532 | 9 | 1 541 |
| Fresh | 8 | 5 | 13 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 542 | 18 | 1 560 |
| Status | Accuracy | Program |
|---|---|---|
| 41.1% | (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| ✓ | 84.8% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ▶ | 98.9% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
| 97.9% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64)))) | |
| ✓ | 38.7% | (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ▶ | 3.2% | (/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ▶ | 98.0% | (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| 38.8% | (/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) | |
| ▶ | 97.9% | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| 84.9% | (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x)))) | |
| ▶ | 84.9% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
| 84.8% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) | |
| 68.8% | #s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) | |
| 83.1% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) | |
| ✓ | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| 41.6% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) x))) | |
| 97.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x))) | |
| ✓ | 5.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
Compiled 438 to 268 computations (38.8% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) x) |
| ✓ | cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 384 | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
| 12 560× | lower-fma.f32 |
| 12 558× | lower-fma.f64 |
| 2 614× | lower--.f32 |
| 2 612× | lower--.f64 |
| 2 372× | lower-*.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 277 |
| 0 | 66 | 277 |
| 1 | 109 | 269 |
| 2 | 137 | 269 |
| 3 | 177 | 269 |
| 4 | 232 | 269 |
| 5 | 396 | 269 |
| 6 | 744 | 269 |
| 7 | 2295 | 269 |
| 8 | 4844 | 269 |
| 9 | 7752 | 269 |
| 0 | 8070 | 269 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
x |
(+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) |
(+.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 x #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
| Outputs |
|---|
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
x |
(+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) |
(+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 #s(literal 1/2 binary64) x) |
(+.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(literal 1/2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(+.f64 x #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 x #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) x) |
x |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x (sqrt.f64 (fma.f64 x x x))) |
| ✓ | accuracy | 99.6% | (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | accuracy | 98.0% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
| ✓ | accuracy | 54.2% | (sqrt.f64 (fma.f64 x x x)) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.3% | #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
| ✓ | accuracy | 98.3% | #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.7% | (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 98.3% | #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) |
| ✓ | accuracy | 99.6% | (/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.3% | #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
| ✓ | accuracy | 7.0% | #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
| ✓ | accuracy | 6.5% | (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) |
| ✓ | accuracy | 99.7% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 99.3% | #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) |
| 103.0ms | 248× | 1 | valid |
| 2.0ms | 8× | 0 | valid |
Compiled 237 to 29 computations (87.8% saved)
ival-div: 20.0ms (32.1% of total)adjust: 12.0ms (19.3% of total)ival-sqrt: 11.0ms (17.7% of total)ival-add: 9.0ms (14.5% of total)ival-sub: 4.0ms (6.4% of total)ival-mult: 4.0ms (6.4% 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (patch (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ()) |
#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ()) |
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#s(alt (+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) (taylor 0 x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 2 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt -1/2 (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/8 (/ 1 x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (sqrt x)) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 2 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt -1/2 (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/8 (/ 1 x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (fma.f64 x x x))) (patch (+.f64 x (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())) ()) |
72 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | (* (sqrt (+ x 1)) (+ x (sqrt (+ (* x x) x)))) |
| 0.0ms | x | @ | -inf | (* (sqrt (+ x 1)) (+ x (sqrt (+ (* x x) x)))) |
| 0.0ms | x | @ | 0 | (/ 1/2 x) |
| 0.0ms | x | @ | 0 | (* (sqrt (+ x 1)) (+ x (sqrt (+ (* x x) x)))) |
| 0.0ms | x | @ | -inf | (* 1/2 (sqrt (/ 1 x))) |
| 1× | egg-herbie |
| 17 920× | lower-fma.f64 |
| 17 920× | lower-fma.f32 |
| 5 688× | lower-+.f64 |
| 5 688× | lower-+.f32 |
| 4 642× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 464 | 4625 |
| 1 | 1388 | 3965 |
| 2 | 4531 | 3865 |
| 0 | 8162 | 3609 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* (sqrt (/ 1 x)) (- 1 (sqrt x))) |
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(sqrt (/ 1 x)) |
(- (sqrt (/ 1 x)) 1) |
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x)))) |
(/ 1/2 x) |
(/ (- 1/2 (* 1/8 (/ 1 x))) x) |
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x) |
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x) |
-2 |
(* -1 (+ 2 (* 1/2 (/ 1 x)))) |
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2) |
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(* (sqrt (/ 1 x)) (- 1 (sqrt x))) |
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(sqrt x) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))))) |
(+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (+ (* 1/2 (sqrt (/ 1 x))) (* x (- (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) 1/8)))))))))) |
(* 2 (sqrt (pow x 3))) |
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))) |
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (sqrt x)) (* -5/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(sqrt x) |
(+ x (sqrt x)) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) |
(* 2 x) |
(* x (+ 2 (* 1/2 (/ 1 x)))) |
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
-1/2 |
(- (* 1/8 (/ 1 x)) 1/2) |
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) |
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(sqrt x) |
(+ x (sqrt x)) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) |
(* 2 x) |
(* x (+ 2 (* 1/2 (/ 1 x)))) |
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
-1/2 |
(- (* 1/8 (/ 1 x)) 1/2) |
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) |
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) |
| Outputs |
|---|
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x)))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))) |
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x)))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 x (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))) (*.f64 x (+.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -5/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))))) (/.f64 #s(literal -3/8 binary64) x)))) #s(literal 1/2 binary64))) #s(literal -1 binary64))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -3/8 binary64) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) x) |
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -3/8 binary64) (fma.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 3/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))) x) |
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (sqrt.f64 x)) (neg.f64 x))) x)) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/16 binary64) (*.f64 #s(literal 3/4 binary64) (sqrt.f64 x))) x)) x)) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 x)) |
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(fma.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(-.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(fma.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
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(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
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(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
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(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
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1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* (sqrt (/ 1 x)) (- 1 (sqrt x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) |
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(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) |
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(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
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(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2)) |
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(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) |
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
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(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2)) |
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(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
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(* -1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (neg.f64 x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(/.f64 (fma.f64 #s(literal -5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
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(/ 1/2 x) |
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(/ 1/2 x) |
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(/ 1/2 x) |
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
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(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
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(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) |
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(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x) |
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(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x) |
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(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))) |
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) |
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (sqrt.f64 x)) (neg.f64 x))) x)) |
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(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/16 binary64) (*.f64 #s(literal 3/4 binary64) (sqrt.f64 x))) x)) x)) x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+.f64 x (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) |
(+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))))) |
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(+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (+ (* 1/2 (sqrt (/ 1 x))) (* x (- (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) 1/8)))))))))) |
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(* 2 (sqrt (pow x 3))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) |
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
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(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
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(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))) |
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(* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
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(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
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(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (sqrt x)) (* -5/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
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(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
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(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
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1 |
#s(literal 1 binary64) |
(+ 1 x) |
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(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
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(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/2 binary64)))) (sqrt.f64 x)) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(+.f64 x #s(literal 1/2 binary64)) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64))) |
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(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
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(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64)))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
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(sqrt x) |
(sqrt.f64 x) |
(+ x (sqrt x)) |
(+.f64 x (sqrt.f64 x)) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+.f64 x (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) |
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) |
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(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* x (+ 2 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64)) |
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))) |
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/8 (/ 1 x)) 1/2) |
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) |
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) |
(+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) |
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) |
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x)) x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/2 binary64)))) (sqrt.f64 x)) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(+.f64 x #s(literal 1/2 binary64)) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (+.f64 x #s(literal 1/2 binary64)) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal -1/2 binary64) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64)))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 1 binary64)) x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/2 binary64)))) (sqrt.f64 x)) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(+.f64 x #s(literal 1/2 binary64)) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (+.f64 x #s(literal 1/2 binary64)) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal -1/2 binary64) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64)))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 1 binary64)) x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ x (sqrt x)) |
(+.f64 x (sqrt.f64 x)) |
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x))))) |
(+.f64 x (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) |
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (sqrt.f64 x)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* x (+ 2 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64)) |
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))) |
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(+.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/8 (/ 1 x)) 1/2) |
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) |
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) |
(+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) |
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) |
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x)) x)) |
| 1× | batch-egg-rewrite |
| 4 922× | lower-/.f32 |
| 4 906× | lower-/.f64 |
| 4 612× | lower-*.f32 |
| 4 608× | lower-*.f64 |
| 4 384× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 231 |
| 0 | 66 | 231 |
| 1 | 280 | 213 |
| 2 | 1861 | 213 |
| 0 | 8940 | 201 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
(sqrt.f64 x) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 #s(literal 1/2 binary64) x) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) |
(+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))) |
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 x x x)) |
(+.f64 x (sqrt.f64 (fma.f64 x x x))) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))))) |
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(/.f64 #s(literal -1 binary64) (*.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64)))) |
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (neg.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(pow.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (*.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x) (*.f64 x x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (*.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x) (*.f64 x x))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (*.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x) (*.f64 x x))))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (*.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x) (*.f64 x x))))) |
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(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x)))))) x) |
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)) #s(literal 1/2 binary64)) x) |
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x))) x) |
(fma.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) x) |
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x)))) (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (*.f64 x x) (fma.f64 x x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x)))) (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (*.f64 x x) (fma.f64 x x x))))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x))) (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x))) (+.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x x)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x)))) (neg.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x)))) (neg.f64 (+.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (fma.f64 x x x))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x x))) (neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (-.f64 (fma.f64 x x x) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x x)) x)) |
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) x)) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 (*.f64 x x) x)))) |
(/.f64 (fma.f64 x (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))))) |
(/.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) x)) (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) x)))) |
(/.f64 (fma.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))))) |
(/.f64 (fma.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) x)))) |
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) #s(literal 1 binary64) (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) x)) (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) #s(literal -1 binary64) (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) (neg.f64 x))) (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 x x))))) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) #s(literal 1 binary64) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) x)) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x))) #s(literal -1 binary64) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (neg.f64 x))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) #s(literal -1 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fma.f64 x x x)))) (*.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (fma.f64 x x x))) (*.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x))))) (neg.f64 (neg.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x x)))) (neg.f64 (neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (neg.f64 (-.f64 (fma.f64 x x x) (*.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (fma.f64 x x x)) x))) |
(pow.f64 (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x)))) (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (*.f64 x x) (fma.f64 x x x))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 x x x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x x))) (*.f64 x (sqrt.f64 (fma.f64 x x x)))))) |
(*.f64 (-.f64 (*.f64 x x) (fma.f64 x x x)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x x))))) |
Compiled 25 225 to 2 935 computations (88.4% saved)
15 alts after pruning (12 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 144 | 9 | 1 153 |
| Fresh | 6 | 3 | 9 |
| Picked | 3 | 2 | 5 |
| Done | 3 | 1 | 4 |
| Total | 1 156 | 15 | 1 171 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 84.8% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| ✓ | 98.9% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
| 38.8% | (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) | |
| 97.9% | (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) | |
| 8.0% | (/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) | |
| 97.9% | (/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) | |
| 70.5% | (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))))) | |
| 70.5% | (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))))) | |
| ✓ | 84.9% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
| 97.2% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) | |
| 96.2% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64))))) | |
| 68.7% | (/.f64 #s(literal 1 binary64) #s(approx (* (sqrt (+ x 1)) (+ x (sqrt (+ (* x x) x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))) | |
| 83.1% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) | |
| 41.6% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) x))) | |
| 97.7% | #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x))) |
Compiled 887 to 257 computations (71% saved)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt (+ x 1)) (+ x (sqrt (+ (* x x) x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x))) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)) |
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)) (sqrt.f64 (fma.f64 x x x))) |
(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 (sqrt.f64 x) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 x x)) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x))))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))))) |
| Outputs |
|---|
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
2 calls:
| 13.0ms | x |
| 10.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 14 to 9 computations (35.7% saved)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt (+ x 1)) (+ x (sqrt (+ (* x x) x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64)))) |
| Outputs |
|---|
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
2 calls:
| 7.0ms | x |
| 4.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 1 | x |
| 98.0% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 14 to 9 computations (35.7% saved)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
2 calls:
| 4.0ms | x |
| 3.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 97.9% | 1 | x |
Compiled 14 to 9 computations (35.7% saved)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(approx (+ x (sqrt (+ (* x x) x))) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) |
| Outputs |
|---|
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
2 calls:
| 4.0ms | x |
| 3.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 97.9% | 1 | x |
Compiled 14 to 9 computations (35.7% saved)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
| Outputs |
|---|
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 83.1% | 1 | x |
| 83.1% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 14 to 9 computations (35.7% saved)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) |
| Outputs |
|---|
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
2 calls:
| 3.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 38.8% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 38.8% | 1 | x |
Compiled 14 to 9 computations (35.7% saved)
Total -3.1b remaining (-5.3%)
Threshold costs -3.1b (-5.3%)
| Inputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
2 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 8.0% | 1 | x |
| 8.0% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 14 to 9 computations (35.7% saved)
| 1× | egg-herbie |
| 6× | +-commutative_binary64 |
| 2× | *-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | 1-exp_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 58 | 183 |
| 1 | 65 | 183 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
| Outputs |
|---|
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x))) |
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x))) |
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) |
(/.f64 #s(approx (/ 1 (sqrt (+ 1 x))) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) |
| 23 172× | lower-fma.f64 |
| 23 172× | lower-fma.f32 |
| 17 920× | lower-fma.f64 |
| 17 920× | lower-fma.f32 |
| 17 610× | lower-fma.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 495 | 4196 |
| 1 | 1489 | 3738 |
| 2 | 4855 | 3699 |
| 0 | 8663 | 3442 |
| 0 | 114 | 529 |
| 1 | 303 | 480 |
| 2 | 925 | 455 |
| 3 | 3326 | 445 |
| 0 | 8140 | 416 |
| 0 | 490 | 3730 |
| 1 | 1465 | 3220 |
| 2 | 4803 | 3185 |
| 0 | 8736 | 2997 |
| 0 | 8 | 23 |
| 0 | 14 | 23 |
| 1 | 66 | 19 |
| 2 | 565 | 19 |
| 3 | 6719 | 19 |
| 0 | 8113 | 19 |
| 0 | 464 | 4625 |
| 1 | 1388 | 3965 |
| 2 | 4531 | 3865 |
| 0 | 8162 | 3609 |
| 0 | 41 | 231 |
| 0 | 66 | 231 |
| 1 | 280 | 213 |
| 2 | 1861 | 213 |
| 0 | 8940 | 201 |
| 0 | 37 | 245 |
| 0 | 63 | 231 |
| 1 | 302 | 188 |
| 2 | 2636 | 183 |
| 0 | 8750 | 180 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter 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× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 266 to 135 computations (49.2% saved)
Compiled 216 to 90 computations (58.3% saved)
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