
Time bar (total: 9.5s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50% | 50% | 0% | 0% | 0% | 0 |
| 100% | 50% | 0% | 50% | 0% | 0% | 0% | 1 |
Compiled 17 to 12 computations (29.4% saved)
| 801.0ms | 3 206× | 2 | valid |
| 772.0ms | 4 789× | 1 | valid |
| 20.0ms | 261× | 0 | valid |
ival-sqrt: 486.0ms (36.9% of total)adjust: 321.0ms (24.4% of total)ival-sub: 238.0ms (18.1% of total)ival-add: 163.0ms (12.4% of total)ival-<=: 82.0ms (6.2% of total)ival-and: 12.0ms (0.9% of total)exact: 10.0ms (0.8% of total)ival-assert: 3.0ms (0.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 255 | 0 | - | 0 | - | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) x) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) x) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) | cancellation | 255 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 255 | 0 |
| - | 0 | 1 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 255 | 0 | 0 |
| - | 0 | 0 | 1 |
| number | freq |
|---|---|
| 0 | 1 |
| 1 | 255 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 548.0ms | 200× | 2 | valid |
| 34.0ms | 298× | 1 | valid |
| 1.0ms | 14× | 0 | valid |
Compiled 64 to 25 computations (60.9% saved)
ival-sqrt: 17.0ms (34.7% of total)adjust: 13.0ms (26.5% of total)ival-sub: 11.0ms (22.4% of total)ival-add: 6.0ms (12.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
| 92× | lower-fma.f64 |
| 92× | lower-fma.f32 |
| 64× | lower-+.f32 |
| 62× | lower-+.f64 |
| 56× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 21 |
| 1 | 22 | 19 |
| 2 | 52 | 18 |
| 3 | 101 | 18 |
| 4 | 163 | 18 |
| 5 | 237 | 18 |
| 6 | 264 | 18 |
| 7 | 272 | 18 |
| 0 | 7 | 9 |
| 0 | 12 | 9 |
| 1 | 19 | 9 |
| 2 | 26 | 9 |
| 3 | 37 | 9 |
| 4 | 51 | 9 |
| 5 | 74 | 9 |
| 6 | 114 | 9 |
| 7 | 149 | 9 |
| 8 | 196 | 9 |
| 9 | 211 | 9 |
| 10 | 219 | 9 |
| 0 | 219 | 9 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(negabs x)
Compiled 10 to 7 computations (30% saved)
Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 8.0% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
Compiled 10 to 7 computations (30% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (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 (-.f64 #s(literal 1 binary64) x))) |
| 92× | lower-fma.f64 |
| 92× | lower-fma.f32 |
| 64× | lower-+.f32 |
| 62× | lower-+.f64 |
| 56× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 25 |
| 0 | 12 | 25 |
| 1 | 19 | 25 |
| 2 | 26 | 25 |
| 3 | 37 | 25 |
| 4 | 51 | 25 |
| 5 | 74 | 25 |
| 6 | 114 | 25 |
| 7 | 149 | 25 |
| 8 | 196 | 25 |
| 9 | 211 | 25 |
| 10 | 219 | 25 |
| 0 | 219 | 25 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) x) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 #s(literal 1 binary64) x) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.02734375 | (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) | |
| accuracy | 58.89015351628996 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| 77.0ms | 149× | 1 | valid |
| 17.0ms | 100× | 2 | valid |
| 0.0ms | 7× | 0 | valid |
Compiled 27 to 9 computations (66.7% saved)
adjust: 65.0ms (78.4% of total)ival-sqrt: 8.0ms (9.6% of total)ival-sub: 5.0ms (6% of total)ival-add: 3.0ms (3.6% 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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 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)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -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)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (- (sqrt (+ 1 x)) (sqrt (- 1 x))) |
| 1.0ms | x | @ | -inf | (- (sqrt (+ 1 x)) (sqrt (- 1 x))) |
| 0.0ms | x | @ | 0 | (- (sqrt (+ 1 x)) (sqrt (- 1 x))) |
| 0.0ms | x | @ | -inf | (sqrt (+ 1 x)) |
| 0.0ms | x | @ | -inf | (sqrt (- 1 x)) |
| 1× | egg-herbie |
| 21 484× | lower-fma.f64 |
| 21 484× | lower-fma.f32 |
| 4 942× | lower-+.f64 |
| 4 942× | lower-+.f32 |
| 4 596× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 161 | 971 |
| 1 | 493 | 856 |
| 2 | 1729 | 798 |
| 3 | 7219 | 798 |
| 0 | 8083 | 746 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
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))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* -1/8 x) 1/2))) |
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
| Outputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 x (*.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 x (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 x (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(*.f64 x (+.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x)) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(neg.f64 (*.f64 x (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 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))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.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 (* 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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 #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)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (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 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -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))))) |
(*.f64 (-.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))) (neg.f64 x)) |
(* -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)))))) |
(neg.f64 (*.f64 x (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (*.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 (* 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))))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 x)) |
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (- (* -1/8 x) 1/2))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) |
(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 -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 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 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))) |
| 3 412× | lower-fma.f64 |
| 3 412× | lower-fma.f32 |
| 2 124× | lower-*.f64 |
| 2 124× | lower-*.f32 |
| 1 648× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 20 |
| 0 | 12 | 20 |
| 1 | 51 | 20 |
| 2 | 368 | 20 |
| 3 | 5664 | 20 |
| 0 | 9321 | 20 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))))) |
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(fma.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)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (neg.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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (-.f64 x (+.f64 #s(literal 1 binary64) x)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (-.f64 x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))))) (fma.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (-.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))) (-.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (-.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(fma.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))))) |
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (+.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.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 (+.f64 #s(literal 1 binary64) x))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
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(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 (neg.f64 x) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log1p.f64 x)) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 x)) #s(literal 2 binary64))) |
(fabs.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64)))) |
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.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)) |
(pow.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/8 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.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 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) |
Compiled 9 873 to 1 183 computations (88% saved)
4 alts after pruning (3 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 373 | 3 | 376 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 373 | 4 | 377 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 7.8% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
| ✓ | 8.0% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| ▶ | 99.8% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
| ▶ | 99.7% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
Compiled 54 to 30 computations (44.4% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| 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)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) | |
| cost-diff | 320 | (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 0 | (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) | |
| cost-diff | 0 | (*.f64 x #s(literal 1/8 binary64)) | |
| cost-diff | 0 | (*.f64 x (*.f64 x #s(literal 1/8 binary64))) | |
| cost-diff | 0 | (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
| 21 156× | lower-fma.f32 |
| 21 150× | lower-fma.f64 |
| 3 796× | lower-*.f32 |
| 3 784× | lower-*.f64 |
| 3 584× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 155 |
| 0 | 44 | 155 |
| 1 | 85 | 151 |
| 2 | 165 | 147 |
| 3 | 286 | 147 |
| 4 | 363 | 147 |
| 5 | 452 | 147 |
| 6 | 663 | 147 |
| 7 | 1049 | 147 |
| 8 | 1649 | 147 |
| 9 | 2673 | 147 |
| 10 | 3211 | 147 |
| 11 | 3413 | 147 |
| 12 | 3482 | 147 |
| 13 | 3502 | 147 |
| 14 | 3506 | 147 |
| 15 | 5750 | 147 |
| 16 | 6130 | 147 |
| 17 | 6524 | 147 |
| 18 | 6893 | 147 |
| 19 | 6947 | 147 |
| 20 | 6983 | 147 |
| 0 | 8265 | 143 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) |
x |
(*.f64 x (*.f64 x #s(literal 1/8 binary64))) |
(*.f64 x #s(literal 1/8 binary64)) |
#s(literal 1/8 binary64) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) |
(*.f64 x x) |
x |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) |
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) |
(*.f64 x #s(literal 7/128 binary64)) |
#s(literal 7/128 binary64) |
#s(literal 1/8 binary64) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x 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) |
#s(literal 1 binary64) |
x |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) |
x |
(*.f64 x (*.f64 x #s(literal 1/8 binary64))) |
(*.f64 x #s(literal 1/8 binary64)) |
#s(literal 1/8 binary64) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) |
(*.f64 x x) |
x |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) |
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) |
(*.f64 x #s(literal 7/128 binary64)) |
#s(literal 7/128 binary64) |
#s(literal 1/8 binary64) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.03515625 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 58.89015351628996 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0 | (*.f64 x #s(literal 7/128 binary64)) | |
| accuracy | 0.00390625 | (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) | |
| accuracy | 0.13020408399540429 | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) | |
| accuracy | 0 | (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) | |
| accuracy | 0 | (*.f64 x (*.f64 x #s(literal 1/8 binary64))) | |
| accuracy | 0 | (*.f64 x #s(literal 1/8 binary64)) | |
| accuracy | 0.20140200764955266 | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
| 44.0ms | 100× | 2 | valid |
| 44.0ms | 149× | 1 | valid |
| 4.0ms | 7× | 0 | valid |
Compiled 139 to 27 computations (80.6% saved)
ival-mult: 17.0ms (24.4% of total)adjust: 16.0ms (23% of total)ival-sqrt: 13.0ms (18.7% of total)ival-sub: 11.0ms (15.8% of total)ival-add: 7.0ms (10.1% of total)ival-div: 5.0ms (7.2% 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 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ()) |
#s(alt (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (patch (*.f64 x (*.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 x #s(literal 1/8 binary64)) (patch (*.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (patch (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.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 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<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>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 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)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -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)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 7/128 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 7/128 binary64)) (patch (*.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#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 (+ 1 (* -1/2 x)) (taylor 0 x) (#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 (+ 1 (* x (- (* 3/8 x) 1/2))) (taylor 0 x) (#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 (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) (taylor 0 x) (#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 (/ 1 x)) (taylor inf x) (#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 (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) (taylor inf x) (#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 (/ 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 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<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 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#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 (+ (* -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 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<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 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<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 #s(literal 1 binary64) x))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
42 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (* x 7/128) |
| 1.0ms | x | @ | 0 | (+ (* x (* x (* x 1/8))) x) |
| 0.0ms | x | @ | -inf | (+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x) |
| 0.0ms | x | @ | -inf | (/ 1 (sqrt (+ 1 x))) |
| 0.0ms | x | @ | inf | (+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x) |
| 1× | egg-herbie |
| 15 950× | lower-fma.f64 |
| 15 950× | lower-fma.f32 |
| 5 620× | lower-+.f64 |
| 5 620× | lower-+.f32 |
| 4 188× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 223 | 2609 |
| 1 | 675 | 2322 |
| 2 | 2206 | 2164 |
| 3 | 6991 | 2164 |
| 0 | 8712 | 2035 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* 1/8 (pow x 3)) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* 1/8 (pow x 3)) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 (pow x 2)) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
(* 1/8 x) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* 7/128 (pow x 5)) |
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
(* 7/128 (pow x 5)) |
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128))) |
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 1/8 x) |
(* x (+ 1/8 (* 7/128 (pow x 2)))) |
(* x (+ 1/8 (* 7/128 (pow x 2)))) |
(* x (+ 1/8 (* 7/128 (pow x 2)))) |
(* 7/128 (pow x 3)) |
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* 7/128 (pow x 3)) |
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* -1/8 x) 1/2))) |
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
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))) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 x) |
(* 7/128 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)))) |
| Outputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 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)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x)) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x)) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.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)))) (*.f64 (sqrt.f64 #s(literal -1 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))))) (neg.f64 x)) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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)))))) (neg.f64 x)) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* 1/8 (pow x 3)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* 1/8 (pow x 3)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 (pow x 2)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
(* 1/8 x) |
(*.f64 x #s(literal 1/8 binary64)) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 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)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
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(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.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)))) (*.f64 (sqrt.f64 #s(literal -1 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))))) (neg.f64 x)) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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)))))) (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 #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)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (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 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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)))))) |
(* -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))))) |
(*.f64 (-.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))) (neg.f64 x)) |
(* -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)))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.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))) (neg.f64 x)) |
(* -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))))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
(* 7/128 x) |
(*.f64 x #s(literal 7/128 binary64)) |
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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (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 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(fma.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) (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))))) (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 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.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 (/ (+ (* -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 (*.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))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (*.f64 x (*.f64 x x)))) |
| 6 238× | lower-fma.f32 |
| 6 232× | lower-fma.f64 |
| 3 986× | lower-/.f32 |
| 3 984× | lower-/.f64 |
| 3 686× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 128 |
| 0 | 44 | 117 |
| 1 | 181 | 105 |
| 2 | 1305 | 105 |
| 0 | 8566 | 101 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) |
(*.f64 x (*.f64 x #s(literal 1/8 binary64))) |
(*.f64 x #s(literal 1/8 binary64)) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) |
(*.f64 x x) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x 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 x #s(literal 7/128 binary64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)) |
(+.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) |
(+.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) |
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))) (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))))) |
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) |
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(fma.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x x) x) |
(fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x x) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/8 binary64)) x) |
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) x) |
(fma.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))))) (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (-.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))) (fma.f64 x (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))) (fma.f64 x x (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))))) (neg.f64 (fma.f64 x (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64))))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))))) (neg.f64 (fma.f64 x x (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64))) (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) (*.f64 (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (*.f64 x x))) (*.f64 (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (-.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)))))) |
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(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x (*.f64 x x)))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))))) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x)) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal 1 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 x #s(literal 7/128 binary64)) |
(*.f64 #s(literal 7/128 binary64) x) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))) |
(-.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 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 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 (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 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 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 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
Compiled 25 324 to 2 293 computations (90.9% saved)
7 alts after pruning (4 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 859 | 4 | 863 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 1 | 1 |
| Total | 860 | 7 | 867 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 8.2% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
| ▶ | 7.9% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
| ✓ | 8.0% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| ▶ | 8.2% | (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
| ✓ | 99.8% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
| ✓ | 99.7% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
| ▶ | 6.3% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
Compiled 99 to 53 computations (46.5% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) | |
| cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 320 | (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) | |
| cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (*.f64 x (*.f64 x x)) | |
| cost-diff | 0 | (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) | |
| cost-diff | 0 | #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
| 9 742× | lower-fma.f64 |
| 9 742× | lower-fma.f32 |
| 2 886× | lower-*.f32 |
| 2 878× | lower-*.f64 |
| 2 770× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 220 |
| 0 | 46 | 214 |
| 1 | 89 | 198 |
| 2 | 162 | 190 |
| 3 | 352 | 190 |
| 4 | 1151 | 190 |
| 5 | 3681 | 190 |
| 6 | 6248 | 190 |
| 0 | 8292 | 188 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) |
#s(literal 1/8 binary64) |
(*.f64 x (*.f64 x x)) |
x |
(*.f64 x x) |
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 #s(literal 1 binary64) x) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 #s(literal 1 binary64) x) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) |
#s(literal 1/8 binary64) |
(*.f64 x (*.f64 x x)) |
x |
(*.f64 x x) |
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (+.f64 x x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(+.f64 x x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 #s(literal 1 binary64) x) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (+.f64 x x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(+.f64 x x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(-.f64 #s(literal 1 binary64) x) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.02734375 | (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) | |
| accuracy | 58.782411101969856 | (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.0078125 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) | |
| accuracy | 0.015625 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 58.91087475425268 | (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) | |
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.02734375 | (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) | |
| accuracy | 58.782411101969856 | (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0 | (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) | |
| accuracy | 0.0625 | (*.f64 x (*.f64 x x)) | |
| accuracy | 0.20140200764955266 | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) | |
| accuracy | 59.980657739436595 | #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) |
| 49.0ms | 152× | 1 | valid |
| 46.0ms | 96× | 2 | valid |
| 1.0ms | 8× | 0 | valid |
Compiled 196 to 26 computations (86.7% saved)
adjust: 15.0ms (21.7% of total)ival-sub: 14.0ms (20.2% of total)ival-sqrt: 12.0ms (17.3% of total)ival-mult: 11.0ms (15.9% of total)ival-div: 10.0ms (14.4% of total)ival-add: 7.0ms (10.1% 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 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (patch (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (patch (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 3)) (taylor inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (pow x 3)) (taylor -inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (patch #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #<representation binary64>) () ())) ()) |
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45 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | inf | (* (- (+ 1 x) (- 1 x)) (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x))))) |
| 2.0ms | x | @ | -inf | (* (- (+ 1 x) (- 1 x)) (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x))))) |
| 1.0ms | x | @ | -inf | (/ (- (+ 1 x) (sqrt (- 1 (* x x)))) (sqrt (+ 1 x))) |
| 1.0ms | x | @ | inf | (/ (- (+ 1 x) (sqrt (- 1 (* x x)))) (sqrt (+ 1 x))) |
| 0.0ms | x | @ | -inf | (+ (sqrt (+ 1 x)) (sqrt (- 1 x))) |
| 1× | egg-herbie |
| 10 248× | lower-fma.f64 |
| 10 248× | lower-fma.f32 |
| 5 162× | lower-*.f64 |
| 5 162× | lower-*.f32 |
| 4 044× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 476 | 4459 |
| 1 | 1518 | 3692 |
| 2 | 5732 | 3636 |
| 0 | 8144 | 3489 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* 1/8 (pow x 3)) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* 1/8 (pow x 3)) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(* 1/8 (pow x 3)) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) |
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(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
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(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (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))) |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(* -1 x) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* -1 x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(* (sqrt x) (- 1 (sqrt -1))) |
(* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (- 1 (sqrt -1))))) |
(* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (- 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (- 1 (sqrt -1))))))) |
(* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (- 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (- 1 (sqrt -1))))))))) |
(* (sqrt x) (* (pow (sqrt -1) 2) (+ 1 (sqrt -1)))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ 1 (sqrt -1))))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ 1 (sqrt -1))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt x) (+ 1 (sqrt -1))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ 1 (sqrt -1))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt x) (+ 1 (sqrt -1))))) x)) (+ (* -1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt x) (+ 1 (sqrt -1)))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))) |
x |
(* x (+ 1 (* 1/2 x))) |
(* x (+ 1 (* x (+ 1/2 (* 1/8 (pow x 2)))))) |
(* x (+ 1 (* x (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))))) |
(* x (- 1 (sqrt -1))) |
(* x (- (+ 1 (/ 1 x)) (sqrt -1))) |
(* x (- (+ 1 (/ 1 x)) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ 1 (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* x (+ 1 (sqrt -1))) |
(* x (+ 1 (+ (sqrt -1) (/ 1 x)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (+ 1 (sqrt -1))))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (+ 1 (sqrt -1))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (* x (sqrt -1))) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) |
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(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* -1/8 x) 1/2))) |
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
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))))))) |
2 |
(+ 2 (* -1/4 (pow x 2))) |
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4))) |
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))) |
| Outputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(fma.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))) (*.f64 x x) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 x (-.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (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)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))))) |
(* 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))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(*.f64 x (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))))) (neg.f64 x)) |
(* -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)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(*.f64 x (neg.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))) |
(* -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))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
(*.f64 (-.f64 (-.f64 (fma.f64 #s(literal 1/8 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)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 #s(literal -1 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))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) (neg.f64 x)) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* 1/8 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(fma.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))) (*.f64 x x) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x) |
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) |
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(-.f64 (/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) |
(-.f64 (-.f64 (/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))))) (/.f64 (+.f64 (/.f64 (*.f64 (neg.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 x)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x)))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))) |
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1 |
#s(literal 1 binary64) |
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1 |
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(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))) |
| 4 848× | lower-*.f32 |
| 4 840× | lower-*.f64 |
| 4 554× | lower-/.f32 |
| 4 548× | lower-/.f64 |
| 3 396× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 153 |
| 0 | 46 | 121 |
| 1 | 185 | 115 |
| 2 | 1498 | 115 |
| 0 | 8711 | 113 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) |
(*.f64 x (*.f64 x x)) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 #s(literal 1 binary64) x) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))) |
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) |
(*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x x)) |
(*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) |
(*.f64 (*.f64 x x) (*.f64 x #s(literal 1/8 binary64))) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal 3/2 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(*.f64 x (*.f64 x x)) |
(*.f64 (*.f64 x x) x) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) |
(*.f64 (*.f64 x (*.f64 x x)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x x))) |
(+.f64 #s(literal 1 binary64) (+.f64 (-.f64 x #s(literal 1 binary64)) x)) |
(+.f64 x (+.f64 x #s(literal 0 binary64))) |
(+.f64 x (+.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 x (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(+.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) |
(+.f64 (+.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) |
(+.f64 (+.f64 x #s(literal 0 binary64)) x) |
(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(-.f64 (+.f64 x #s(literal 0 binary64)) (neg.f64 x)) |
(-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) |
(fma.f64 #s(literal 1 binary64) x (+.f64 x #s(literal 0 binary64))) |
(fma.f64 #s(literal 1 binary64) x (+.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal 1 binary64) x (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 x #s(literal 1 binary64) (+.f64 x #s(literal 0 binary64))) |
(fma.f64 x #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 x #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) |
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64))))))) |
(/.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64))))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64))))) (neg.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 #s(literal 1 binary64) x))))))) |
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(/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) |
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 #s(literal 1 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))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 #s(literal 1 binary64) x)) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) |
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) |
(/.f64 (fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) |
(/.f64 (fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (*.f64 (-.f64 (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 (-.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))) (neg.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))) |
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 x (+.f64 x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(*.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))) |
(*.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 0 binary64))) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 0 binary64))) (+.f64 x (+.f64 x #s(literal 0 binary64)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
Compiled 87 933 to 4 990 computations (94.3% saved)
6 alts after pruning (2 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 440 | 2 | 2 442 |
| Fresh | 0 | 0 | 0 |
| Picked | 3 | 1 | 4 |
| Done | 0 | 3 | 3 |
| Total | 2 443 | 6 | 2 449 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
| ✓ | 8.0% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| ▶ | 100.0% | (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
| ✓ | 99.8% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
| ✓ | 99.7% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
| ✓ | 6.3% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
Compiled 77 to 46 computations (40.3% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) | |
| cost-diff | 0 | (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 128 | (*.f64 x #s(literal 2 binary64)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 0 | #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) | |
| cost-diff | 128 | (*.f64 x #s(literal 2 binary64)) | |
| cost-diff | 320 | (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
| 10 480× | lower-fma.f64 |
| 10 480× | lower-fma.f32 |
| 4 664× | associate--l+ |
| 4 406× | lower-+.f32 |
| 4 402× | lower-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 135 |
| 0 | 24 | 145 |
| 1 | 40 | 129 |
| 2 | 67 | 117 |
| 3 | 136 | 117 |
| 4 | 375 | 117 |
| 5 | 1153 | 117 |
| 6 | 1973 | 117 |
| 7 | 2249 | 117 |
| 8 | 2393 | 117 |
| 9 | 2459 | 117 |
| 10 | 2472 | 117 |
| 11 | 3478 | 117 |
| 12 | 5512 | 117 |
| 13 | 5789 | 117 |
| 14 | 5950 | 117 |
| 15 | 5987 | 117 |
| 16 | 5991 | 117 |
| 17 | 5991 | 117 |
| 18 | 6311 | 117 |
| 19 | 6419 | 117 |
| 20 | 6429 | 117 |
| 21 | 6439 | 117 |
| 22 | 6487 | 117 |
| 23 | 6501 | 117 |
| 24 | 6501 | 117 |
| 0 | 9102 | 117 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
#s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) |
(*.f64 x #s(literal 2 binary64)) |
x |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) x) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) |
(*.f64 x #s(literal 2 binary64)) |
x |
#s(literal 2 binary64) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) x) |
| Outputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (+.f64 x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) |
#s(approx (- (+ 1 x) (- 1 x)) (+.f64 x x)) |
(*.f64 x #s(literal 2 binary64)) |
(+.f64 x x) |
x |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) x) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (+.f64 x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) |
#s(approx (- (+ 1 x) (- 1 x)) (+.f64 x x)) |
(*.f64 x #s(literal 2 binary64)) |
(+.f64 x x) |
x |
#s(literal 2 binary64) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) x) |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) | |
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.02734375 | (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0 | #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) | |
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.02734375 | (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
| 31.0ms | 157× | 1 | valid |
| 25.0ms | 88× | 2 | valid |
| 1.0ms | 11× | 0 | valid |
Compiled 121 to 15 computations (87.6% saved)
ival-div: 8.0ms (21% of total)adjust: 8.0ms (21% of total)ival-sqrt: 7.0ms (18.4% of total)ival-add: 6.0ms (15.7% of total)ival-sub: 5.0ms (13.1% of total)ival-mult: 4.0ms (10.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ()) |
#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (taylor inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))) (taylor inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) (taylor -inf x) (#s(alt (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
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24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) |
| 2.0ms | x | @ | 0 | (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) |
| 2.0ms | x | @ | -inf | (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) |
| 0.0ms | x | @ | inf | (* x 2) |
| 0.0ms | x | @ | -inf | (* x 2) |
| 1× | egg-herbie |
| 9 158× | lower-fma.f64 |
| 9 158× | lower-fma.f32 |
| 6 212× | lower-*.f64 |
| 6 212× | lower-*.f32 |
| 3 872× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 446 | 4604 |
| 1 | 1422 | 3650 |
| 2 | 5777 | 3609 |
| 0 | 8296 | 3506 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))) |
(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
1/2 |
(+ 1/2 (* 1/16 (pow x 2))) |
(+ 1/2 (* (pow x 2) (+ 1/16 (* 7/256 (pow x 2))))) |
(+ 1/2 (* (pow x 2) (+ 1/16 (* (pow x 2) (+ 7/256 (* 33/2048 (pow x 2))))))) |
(/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(/ (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 2))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) x) |
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 3) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) (pow x 4))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) x) |
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 3) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (+ (* -1 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (+ (* 1/16 (* (sqrt (pow x 5)) (/ 1 (* (pow (sqrt -1) 5) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))) (pow x 6))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))) (* (pow x 4) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 3) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))))) x) |
(/ -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (/ (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (pow x 4))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 1/16 (* (sqrt (pow x 5)) (/ 1 (* (pow (sqrt -1) 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* 1/16 (* (sqrt (pow x 5)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))))) (pow x 6))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (* (pow x 4) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))))))) x)) |
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) |
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))) |
(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
2 |
(+ 2 (* -1/4 (pow x 2))) |
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))) |
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4))) |
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))) |
1 |
(+ 1 (* -1/2 x)) |
(+ 1 (* x (- (* -1/8 x) 1/2))) |
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
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))))))) |
| Outputs |
|---|
x |
(* x (+ 1 (* 1/8 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) |
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(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 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)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (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 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (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))))) |
(* -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))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
(* -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)))))) |
(*.f64 (fma.f64 #s(literal 1/8 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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x)) |
(* -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))))))) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x)) |
| 8 250× | lower-fma.f64 |
| 8 250× | lower-fma.f32 |
| 4 126× | lower-/.f32 |
| 4 122× | lower-/.f64 |
| 3 746× | lower-*.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 86 |
| 0 | 24 | 84 |
| 1 | 96 | 78 |
| 2 | 742 | 72 |
| 0 | 8755 | 72 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 x #s(literal 2 binary64)) |
#s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
(+.f64 (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.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 (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) |
(+.f64 (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))) (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))) |
(+.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))) |
(+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x))) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)))) |
(fma.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))) |
(fma.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.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 (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(neg.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) |
(/.f64 (neg.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (neg.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x x)) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64))) |
(*.f64 x #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) x) |
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) |
(neg.f64 (neg.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) |
#s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) |
(*.f64 #s(literal 1 binary64) #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64)))) |
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))))) |
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(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 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) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.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 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) |
Compiled 18 143 to 1 430 computations (92.1% saved)
6 alts after pruning (1 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 565 | 1 | 566 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 1 | 3 | 4 |
| Total | 566 | 6 | 572 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
| ✓ | 8.0% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| ✓ | 100.0% | (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
| 99.2% | (*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) | |
| ✓ | 99.8% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
| ✓ | 99.7% | #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
Compiled 223 to 83 computations (62.8% saved)
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
| Outputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
2 calls:
| 3.0ms | x |
| 3.0ms | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
Compiled 12 to 8 computations (33.3% saved)
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
| Outputs |
|---|
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
Compiled 12 to 8 computations (33.3% saved)
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
2 calls:
| 4.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
Compiled 12 to 8 computations (33.3% saved)
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
| Outputs |
|---|
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
2 calls:
| 2.0ms | x |
| 1.0ms | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
Compiled 12 to 8 computations (33.3% saved)
Total -59.5b remaining (-12172.6%)
Threshold costs -59.5b (-12172.6%)
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) |
| Outputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
2 calls:
| 1.0ms | x |
| 1.0ms | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
Compiled 12 to 8 computations (33.3% saved)
| 1× | egg-herbie |
| 16× | *-commutative_binary64 |
| 8× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 110 |
| 1 | 50 | 110 |
| 2 | 54 | 110 |
| 3 | 56 | 110 |
| 4 | 57 | 110 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
| Outputs |
|---|
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) |
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) |
(*.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) #s(approx (/ 1 (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) #s(literal 1/2 binary64))) |
| 21 484× | lower-fma.f64 |
| 21 484× | lower-fma.f32 |
| 10 248× | lower-fma.f64 |
| 10 248× | lower-fma.f32 |
| 9 158× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 476 | 4459 |
| 1 | 1518 | 3692 |
| 2 | 5732 | 3636 |
| 0 | 8144 | 3489 |
| 0 | 26 | 128 |
| 0 | 44 | 117 |
| 1 | 181 | 105 |
| 2 | 1305 | 105 |
| 0 | 8566 | 101 |
| 0 | 161 | 971 |
| 1 | 493 | 856 |
| 2 | 1729 | 798 |
| 3 | 7219 | 798 |
| 0 | 8083 | 746 |
| 0 | 446 | 4604 |
| 1 | 1422 | 3650 |
| 2 | 5777 | 3609 |
| 0 | 8296 | 3506 |
| 0 | 7 | 20 |
| 0 | 12 | 20 |
| 1 | 51 | 20 |
| 2 | 368 | 20 |
| 3 | 5664 | 20 |
| 0 | 9321 | 20 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 278 to 143 computations (48.6% saved)
(negabs x)
Compiled 204 to 104 computations (49% saved)
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