
Time bar (total: 28.3s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 100% | 99.9% | 0% | 0.1% | 0% | 0% | 0% | 1 |
Compiled 10 to 5 computations (50% saved)
| 602.0ms | 8 256× | 0 | valid |
ival-hypot: 277.0ms (96.6% of total)ival-true: 6.0ms (2.1% of total)ival-assert: 3.0ms (1% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 135 | 0 | - | 2 | (1.807142125221636e-156 2.1702606633658027e-190) | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 0 | 0 | - | 0 | - | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (*.f64 y y) |
| 0 | 0 | - | 0 | - | (*.f64 x x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
sqrt.f64 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) | oflow-rescue | 112 | 0 |
| ↳ | (*.f64 y y) | overflow | 71 | |
| ↳ | (*.f64 x x) | overflow | 59 | |
| ↳ | (+.f64 (*.f64 x x) (*.f64 y y)) | overflow | 112 | |
sqrt.f64 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) | uflow-rescue | 21 | 0 |
| ↳ | (*.f64 y y) | underflow | 54 | |
| ↳ | (*.f64 x x) | underflow | 79 | |
| ↳ | (+.f64 (*.f64 x x) (*.f64 y y)) | underflow | 21 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 133 | 2 |
| - | 0 | 121 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 133 | 0 | 2 |
| - | 0 | 0 | 121 |
| number | freq |
|---|---|
| 0 | 123 |
| 1 | 133 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 52.0ms | 512× | 0 | valid |
Compiled 58 to 22 computations (62.1% saved)
ival-mult: 29.0ms (72.9% of total)ival-hypot: 8.0ms (20.1% of total)ival-add: 2.0ms (5% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 32× | sub-neg |
| 30× | distribute-lft-neg-in |
| 30× | neg-sub0 |
| 28× | unsub-neg |
| 24× | neg-mul-1 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 42 |
| 1 | 35 | 42 |
| 2 | 77 | 42 |
| 3 | 145 | 42 |
| 4 | 204 | 42 |
| 5 | 217 | 42 |
| 6 | 219 | 42 |
| 0 | 6 | 8 |
| 0 | 10 | 8 |
| 1 | 11 | 8 |
| 0 | 11 | 3 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| Outputs |
|---|
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
(hypot.f64 y x) |
(abs y)
(abs x)
(sort x y)
Compiled 8 to 6 computations (25% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 51.5% | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | -5120 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) | |
| cost-diff | 0 | (*.f64 y y) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 128 | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 4× | lower-hypot.f32 |
| 4× | lower-hypot.f64 |
| 4× | lower-fma.f64 |
| 4× | lift-*.f64 |
| 4× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 23 |
| 0 | 10 | 23 |
| 1 | 11 | 23 |
| 0 | 11 | 17 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
(+.f64 (*.f64 x x) (*.f64 y y)) |
(*.f64 x x) |
x |
(*.f64 y y) |
y |
| Outputs |
|---|
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
(hypot.f64 y x) |
(+.f64 (*.f64 x x) (*.f64 y y)) |
(fma.f64 y y (*.f64 x x)) |
(*.f64 x x) |
x |
(*.f64 y y) |
y |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 y y) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.0078125 | (+.f64 (*.f64 x x) (*.f64 y y)) | |
| accuracy | 31.04734792617676 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 15.0ms | 256× | 0 | valid |
Compiled 25 to 8 computations (68% saved)
ival-hypot: 4.0ms (45.4% of total)ival-mult: 3.0ms (34.1% of total)ival-add: 1.0ms (11.4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt y (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* 1/2 (/ (pow x 2) y))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | y | @ | 0 | ((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y)))) |
| 1.0ms | y | @ | inf | ((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y)))) |
| 1.0ms | x | @ | inf | ((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y)))) |
| 1.0ms | y | @ | -inf | ((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y)))) |
| 1.0ms | x | @ | 0 | ((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y)))) |
| 1× | egg-herbie |
| 18 004× | lower-fma.f64 |
| 18 004× | lower-fma.f32 |
| 5 072× | lower-*.f64 |
| 5 072× | lower-*.f32 |
| 2 260× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 104 | 620 |
| 1 | 296 | 620 |
| 2 | 953 | 618 |
| 3 | 3667 | 584 |
| 4 | 6426 | 582 |
| 0 | 8051 | 530 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(pow x 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(pow y 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
| Outputs |
|---|
(pow x 2) |
(*.f64 x x) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(pow y 2) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))) |
(pow y 2) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(* -1 y) |
(neg.f64 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) x (neg.f64 y)) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) y (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) x (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) y)) |
(pow y 2) |
(*.f64 y y) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) x) x (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x) y) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x) y) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x (*.f64 (/.f64 (*.f64 y y) x) #s(literal 1/2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x)) |
| 5 720× | lower-fma.f64 |
| 5 720× | lower-fma.f32 |
| 4 038× | lower-/.f64 |
| 4 038× | lower-/.f32 |
| 3 184× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 21 |
| 0 | 10 | 21 |
| 1 | 29 | 21 |
| 2 | 196 | 21 |
| 3 | 1788 | 21 |
| 0 | 8624 | 15 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 (*.f64 x x) (*.f64 y y)) |
(*.f64 x x) |
(*.f64 y y) |
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| Outputs |
|---|
(*.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))) |
(*.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) |
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))) |
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))) |
(*.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (*.f64 x x))) |
(*.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (+.f64 y x)) |
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) |
(*.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) |
(*.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 x x))) |
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))) |
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64))) |
(*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) |
(*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 y y (*.f64 x x)) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) |
(*.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 y y (*.f64 x x)) (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x)))) |
(*.f64 (fma.f64 y y (*.f64 x x)) (*.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)))) |
(pow.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)) |
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(/.f64 (hypot.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (sqrt.f64 (*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 y x))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) |
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
(hypot.f64 y x) |
(hypot.f64 x y) |
(exp.f64 (fma.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64)))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 2 binary64))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/2 binary64))) |
Compiled 7 655 to 987 computations (87.1% saved)
7 alts after pruning (7 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 306 | 7 | 313 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 307 | 7 | 314 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (hypot.f64 y x) |
| 51.1% | (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) | |
| ▶ | 51.5% | (sqrt.f64 (fma.f64 y y (*.f64 x x))) |
| ▶ | 51.0% | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
| ▶ | 4.5% | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
| 99.3% | #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) | |
| ▶ | 1.8% | #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
Compiled 96 to 76 computations (20.8% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | -5120 | (sqrt.f64 (fma.f64 y y (*.f64 x x))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (fma.f64 y y (*.f64 x x)) | |
| cost-diff | 0 | (*.f64 y y) | |
| cost-diff | 0 | #s(approx (+ (* x x) (* y y)) (*.f64 y y)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | #s(approx (+ (* x x) (* y y)) (*.f64 x x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) | |
| cost-diff | 0 | (neg.f64 x) | |
| cost-diff | 0 | #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) | |
| cost-diff | 0 | (hypot.f64 y x) |
| 24× | lower-+.f64 |
| 24× | lower-+.f32 |
| 12× | lower-fma.f32 |
| 10× | lower-fma.f64 |
| 8× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 87 |
| 0 | 24 | 78 |
| 1 | 29 | 78 |
| 2 | 31 | 78 |
| 3 | 33 | 78 |
| 4 | 35 | 78 |
| 5 | 39 | 78 |
| 6 | 48 | 78 |
| 7 | 54 | 78 |
| 8 | 58 | 78 |
| 0 | 58 | 78 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(hypot.f64 y x) |
y |
x |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
(neg.f64 x) |
x |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
#s(approx (+ (* x x) (* y y)) (*.f64 x x)) |
(*.f64 x x) |
x |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
#s(approx (+ (* x x) (* y y)) (*.f64 y y)) |
(*.f64 y y) |
y |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
(fma.f64 y y (*.f64 x x)) |
y |
(*.f64 x x) |
x |
| Outputs |
|---|
(hypot.f64 y x) |
(hypot.f64 x y) |
y |
x |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
(neg.f64 x) |
x |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
#s(approx (+ (* x x) (* y y)) (*.f64 x x)) |
(*.f64 x x) |
x |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
#s(approx (+ (* x x) (* y y)) (*.f64 y y)) |
(*.f64 y y) |
y |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
(hypot.f64 x y) |
(fma.f64 y y (*.f64 x x)) |
(fma.f64 x x (*.f64 y y)) |
y |
(*.f64 x x) |
x |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (fma.f64 y y (*.f64 x x)) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 31.04734792617676 | (sqrt.f64 (fma.f64 y y (*.f64 x x))) | |
| accuracy | 0 | (*.f64 y y) | |
| accuracy | 0.3299593409751988 | #s(approx (+ (* x x) (* y y)) (*.f64 y y)) | |
| accuracy | 31.04734792617676 | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 31.04734792617676 | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) | |
| accuracy | 51.99797853203401 | #s(approx (+ (* x x) (* y y)) (*.f64 x x)) | |
| accuracy | 0 | (neg.f64 x) | |
| accuracy | 62.82336435384393 | #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) | |
| accuracy | 0 | (hypot.f64 y x) |
| 25.0ms | 256× | 0 | valid |
Compiled 81 to 11 computations (86.4% saved)
ival-hypot: 9.0ms (61% of total)ival-mult: 3.0ms (20.3% of total)ival-add: 2.0ms (13.6% of total)ival-neg: 1.0ms (6.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ()) |
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ()) |
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ()) |
#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
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#s(alt (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | ((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x)))) |
| 1.0ms | x | @ | -inf | ((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x)))) |
| 1.0ms | y | @ | inf | ((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x)))) |
| 1.0ms | y | @ | -inf | ((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x)))) |
| 0.0ms | y | @ | 0 | ((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x)))) |
| 1× | egg-herbie |
| 18 004× | lower-fma.f64 |
| 18 004× | lower-fma.f32 |
| 5 072× | lower-*.f64 |
| 5 072× | lower-*.f32 |
| 2 260× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 104 | 2548 |
| 1 | 296 | 2548 |
| 2 | 953 | 2538 |
| 3 | 3671 | 2368 |
| 4 | 6433 | 2358 |
| 0 | 8058 | 2134 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(pow x 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(pow x 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow x 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(pow y 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(pow y 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(pow y 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
| Outputs |
|---|
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(pow x 2) |
(*.f64 x x) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(pow x 2) |
(*.f64 x x) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow x 2) |
(*.f64 x x) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
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(fma.f64 (*.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x (*.f64 (/.f64 (*.f64 y y) x) #s(literal 1/2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x (*.f64 (/.f64 (*.f64 y y) x) #s(literal 1/2 binary64))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 x) |
(neg.f64 x) |
(* -1 x) |
(neg.f64 x) |
(* -1 x) |
(neg.f64 x) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 y y (*.f64 x x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x)) |
| 3 958× | lower-fma.f32 |
| 3 956× | lower-fma.f64 |
| 3 618× | lower-*.f32 |
| 3 614× | lower-*.f64 |
| 2 154× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 77 |
| 0 | 24 | 68 |
| 1 | 58 | 68 |
| 2 | 338 | 68 |
| 3 | 3368 | 68 |
| 0 | 8587 | 68 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(hypot.f64 y x) |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
(neg.f64 x) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
#s(approx (+ (* x x) (* y y)) (*.f64 x x)) |
(*.f64 x x) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
#s(approx (+ (* x x) (* y y)) (*.f64 y y)) |
(*.f64 y y) |
(fma.f64 y y (*.f64 x x)) |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (hypot.f64 x y)) |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))) (sqrt.f64 (+.f64 x y))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (hypot.f64 x y)) |
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x y))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 x y)) |
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 x y)) |
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 x y)) |
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (pow.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) |
(*.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) |
(*.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
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(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y)))))) |
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y)))))))) |
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y)))))))) |
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))) |
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y)))))) |
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 x y) (+.f64 x y))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) (*.f64 (-.f64 x y) (+.f64 x y))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64))) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 2 binary64)))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal 2 binary64)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 x y))))) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y))))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) (sqrt.f64 (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64)))))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64)))) (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 x y))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 x y)))) |
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(sqrt.f64 (fma.f64 x x (*.f64 y y))) |
(hypot.f64 x y) |
(hypot.f64 y x) |
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64)))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 2 binary64))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/2 binary64))) |
Compiled 12 517 to 1 138 computations (90.9% saved)
7 alts after pruning (2 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 653 | 1 | 654 |
| Fresh | 1 | 1 | 2 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 0 | 0 |
| Total | 654 | 7 | 661 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 y x) |
| ▶ | 51.1% | (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
| ✓ | 51.5% | (sqrt.f64 (fma.f64 y y (*.f64 x x))) |
| ✓ | 51.0% | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
| ✓ | 4.5% | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
| ▶ | 99.3% | #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
| ✓ | 1.8% | #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
Compiled 48 to 38 computations (20.8% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 y y (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) | |
| cost-diff | 0 | (/.f64 x y) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) | |
| cost-diff | 0 | #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
| 48× | lower-*.f32 |
| 42× | lower-*.f64 |
| 20× | lower-fma.f32 |
| 16× | lower-fma.f64 |
| 14× | *-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 88 |
| 0 | 29 | 88 |
| 1 | 39 | 88 |
| 2 | 49 | 88 |
| 3 | 53 | 88 |
| 4 | 56 | 88 |
| 5 | 59 | 88 |
| 0 | 59 | 84 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(/.f64 x y) |
y |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) |
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) |
(fma.f64 y y (*.f64 x x)) |
y |
(*.f64 x x) |
x |
(+.f64 y x) |
(sqrt.f64 (+.f64 y x)) |
| Outputs |
|---|
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(/.f64 x y) |
y |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))) |
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) |
(sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))) |
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) |
(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) |
(fma.f64 y y (*.f64 x x)) |
(fma.f64 x x (*.f64 y y)) |
y |
(*.f64 x x) |
x |
(+.f64 y x) |
(+.f64 x y) |
(sqrt.f64 (+.f64 y x)) |
(sqrt.f64 (+.f64 x y)) |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (sqrt.f64 (+.f64 y x)) | |
| accuracy | 0.0078125 | (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) | |
| accuracy | 0.4921875 | (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) | |
| accuracy | 31.109746689736067 | (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) | |
| accuracy | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) | |
| accuracy | 0 | (/.f64 x y) | |
| accuracy | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| accuracy | 0.4620211082109554 | #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
| 80.0ms | 256× | 0 | valid |
Compiled 87 to 18 computations (79.3% saved)
ival-add: 52.0ms (73.5% of total)ival-mult: 7.0ms (9.9% of total)ival-hypot: 5.0ms (7.1% of total)ival-sqrt: 4.0ms (5.7% of total)ival-div: 3.0ms (4.2% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ()) |
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y))))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3))))))))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 2 (/ y x)) 1))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2)))))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (* x (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (+ 1 (/ (pow x 2) (pow y 2))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y)))) (taylor inf y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (+ 1 (+ (* -1 (/ (* x (- (pow x 2) (* -1 (pow x 2)))) (pow y 3))) (/ (pow x 2) (pow y 2)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y)))) (taylor inf y) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (pow y 2) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
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#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2)))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (* y (- (pow y 2) (* -1 (pow y 2))))))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (- (* -1 (pow y 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (- (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1 (* y (- (* -1 (pow y 2)) (pow y 2)))) (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | y | @ | -inf | ((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x))) |
| 3.0ms | x | @ | -inf | ((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x))) |
| 3.0ms | x | @ | inf | ((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x))) |
| 2.0ms | y | @ | inf | ((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x))) |
| 2.0ms | y | @ | 0 | ((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x))) |
| 1× | egg-herbie |
| 11 852× | lower-fma.f64 |
| 11 852× | lower-fma.f32 |
| 5 482× | lower-*.f64 |
| 5 482× | lower-*.f32 |
| 4 202× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 458 | 2943 |
| 1 | 1451 | 2807 |
| 2 | 4873 | 2721 |
| 0 | 8129 | 2532 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(* 1/2 (/ (pow x 2) y)) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(sqrt x) |
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y))))) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3))))))))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 2 (/ y x)) 1))) |
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1))) |
(pow x 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (* x (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))))))) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (- (+ 1 (/ (pow x 2) (pow y 2))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y)))) |
(* y (- (+ 1 (+ (* -1 (/ (* x (- (pow x 2) (* -1 (pow x 2)))) (pow y 3))) (/ (pow x 2) (pow y 2)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y)))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
y |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/2 (* (sqrt y) (- (* -1 (pow x 2)) (pow x 2)))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1 (* x (- (* -1 (pow x 2)) (pow x 2)))) (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) y)) x) y)) 1))) |
(* -1 (* y (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (- (* -1 (pow x 2)) (pow x 2))) y)) (* -1 (pow x 2))) (pow x 2)) y)) x) y)) 1))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* 1/2 (/ (pow x 2) y))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(sqrt y) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* 7/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -9/16 (* x (sqrt (/ 1 (pow y 5))))) (* 7/8 (sqrt (/ 1 (pow y 3))))))))) |
y |
(+ y (* -1 x)) |
(+ y (* x (- (* 2 (/ x y)) 1))) |
(+ y (* x (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1))) |
(pow y 2) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (pow y 2)) |
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* 1/2 (/ (pow x 2) y)) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2)))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (* y (- (pow y 2) (* -1 (pow y 2))))))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) |
(* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(* 1/2 (/ (pow x 2) y)) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (- (* -1 (pow y 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (- (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1 (* y (- (* -1 (pow y 2)) (pow y 2)))) (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
| Outputs |
|---|
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(* 1/2 (/ (pow x 2) y)) |
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 y y)) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 y y)) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 y y)) y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 7/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -9/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 7/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x)) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 2 (/ y x)) 1))) |
(fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal -1 binary64)) y x) |
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) |
(pow x 2) |
(*.f64 x x) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 y y (*.f64 x x)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
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(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(*.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64))) x) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64)))) x x) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2)))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 y y) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (* y (- (pow y 2) (* -1 (pow y 2))))))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 (*.f64 (*.f64 y y) x) #s(literal 1/4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 y y) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) |
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (*.f64 y y) x) #s(literal -2 binary64) y) #s(literal 1 binary64)) x) |
(* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (*.f64 y y) x) #s(literal -2 binary64) y) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64))))) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 (fma.f64 y (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64)))) x x)) |
(* 1/2 (/ (pow x 2) y)) |
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64)))) x x)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (- (* -1 (pow y 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (- (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1 (* y (- (* -1 (pow y 2)) (pow y 2)))) (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 (*.f64 y y) x) #s(literal -1 binary64)) #s(literal -1/4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 y y)) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (*.f64 y y) x) #s(literal -2 binary64) y) #s(literal 1 binary64)) x) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1))) |
(*.f64 (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y (+.f64 (fma.f64 (/.f64 (*.f64 y y) x) #s(literal -2 binary64) y) y)) x) y) x) #s(literal 1 binary64)) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
| 7 168× | lower-fma.f32 |
| 7 164× | lower-fma.f64 |
| 5 646× | lower-*.f32 |
| 5 640× | lower-*.f64 |
| 4 016× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 77 |
| 0 | 29 | 76 |
| 1 | 95 | 68 |
| 2 | 679 | 68 |
| 3 | 7993 | 68 |
| 0 | 9166 | 57 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) |
(*.f64 #s(literal 1/2 binary64) x) |
(/.f64 x y) |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) |
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) |
(fma.f64 y y (*.f64 x x)) |
(sqrt.f64 (+.f64 y x)) |
| Outputs |
|---|
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y)) (-.f64 (*.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 y (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x)))))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) (-.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) (*.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)) |
(*.f64 (fma.f64 y y (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y))) |
(*.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))) |
(*.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y))))) |
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(fma.f64 (*.f64 x (pow.f64 (+.f64 x y) #s(literal -1 binary64))) (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (*.f64 y (pow.f64 (+.f64 x y) #s(literal -1 binary64))) (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (*.f64 y (/.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (-.f64 y x))) (-.f64 y x) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (pow.f64 (+.f64 x y) #s(literal -1 binary64)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (pow.f64 (+.f64 x y) #s(literal -1 binary64)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 x y)) (/.f64 y (-.f64 y x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 (/.f64 y (+.f64 x y)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 y x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 (/.f64 (*.f64 y y) (+.f64 x y)) (*.f64 y (/.f64 y (-.f64 y x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 x x)) |
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 y y)) |
(fma.f64 (/.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (-.f64 y x)) (*.f64 (-.f64 y x) y) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (/.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (-.f64 y x)) (*.f64 (-.f64 y x) x) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) x) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) y) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) (*.f64 (fma.f64 x x (*.f64 y y)) x) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) (*.f64 (fma.f64 x x (*.f64 y y)) y) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (/.f64 y (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) y) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) x) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) x (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) y (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) x) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) y) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 x (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 x x (*.f64 y y)) |
(fma.f64 (*.f64 y y) (/.f64 (*.f64 y y) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 y (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(fma.f64 y (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(fma.f64 y y (*.f64 x x)) |
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) y)))) |
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x (*.f64 y y)))) |
(+.f64 (neg.f64 (*.f64 (neg.f64 y) y)) (neg.f64 (*.f64 (neg.f64 x) x))) |
(+.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (*.f64 (neg.f64 y) y))) |
(+.f64 (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(+.f64 (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y))) |
(+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(+.f64 (*.f64 x x) (*.f64 y y)) |
(+.f64 (*.f64 y y) (*.f64 x x)) |
(*.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x y) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 y x)))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(pow.f64 (exp.f64 (log.f64 (+.f64 x y))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (+.f64 x y) (+.f64 x y)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (+.f64 x y) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) (neg.f64 (sqrt.f64 (-.f64 y x)))) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))) |
(/.f64 (sqrt.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (sqrt.f64 (-.f64 x y))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (-.f64 (neg.f64 y) x))) (sqrt.f64 (fma.f64 #s(literal -1 binary64) y x))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))) |
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (-.f64 y x))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x y) #s(literal -1/2 binary64))) |
(sqrt.f64 (+.f64 x y)) |
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64))) |
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/2 binary64))) |
Compiled 21 427 to 2 909 computations (86.4% saved)
9 alts after pruning (2 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 805 | 2 | 807 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 0 | 5 | 5 |
| Total | 805 | 9 | 814 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 y x) |
| ✓ | 51.1% | (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
| ▶ | 47.5% | (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
| ✓ | 51.5% | (sqrt.f64 (fma.f64 y y (*.f64 x x))) |
| ✓ | 51.0% | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
| ✓ | 4.5% | (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
| ✓ | 99.3% | #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
| ▶ | 51.8% | #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
| ✓ | 1.8% | #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
Compiled 87 to 63 computations (27.6% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) | |
| cost-diff | 1152 | (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) | |
| cost-diff | 0 | #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) | |
| cost-diff | 384 | (/.f64 (/.f64 y x) x) | |
| cost-diff | 448 | (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) | |
| cost-diff | 704 | (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
| 7 108× | lower-fma.f32 |
| 7 104× | lower-fma.f64 |
| 2 388× | lower-*.f32 |
| 2 376× | lower-*.f64 |
| 2 220× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 211 |
| 0 | 49 | 210 |
| 1 | 75 | 210 |
| 2 | 119 | 210 |
| 3 | 251 | 210 |
| 4 | 641 | 192 |
| 5 | 1384 | 172 |
| 6 | 3569 | 172 |
| 0 | 8673 | 162 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
#s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) |
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) |
(/.f64 #s(literal 1/2 binary64) y) |
#s(literal 1/2 binary64) |
y |
(/.f64 (/.f64 y x) x) |
(/.f64 y x) |
x |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) |
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) |
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) |
(fma.f64 x x (*.f64 y y)) |
x |
(*.f64 y y) |
y |
(fma.f64 x x (*.f64 (neg.f64 y) y)) |
(*.f64 (neg.f64 y) y) |
(neg.f64 y) |
(-.f64 x y) |
(sqrt.f64 (+.f64 y x)) |
(+.f64 y x) |
| Outputs |
|---|
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))) |
#s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)) |
#s(approx (+ (* (* 1/2 x) (/ x y)) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (/.f64 y x)) |
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) |
(+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) |
(/.f64 #s(literal 1/2 binary64) y) |
#s(literal 1/2 binary64) |
y |
(/.f64 (/.f64 y x) x) |
(/.f64 y (*.f64 x x)) |
(/.f64 y x) |
x |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))) |
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) |
(sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))) |
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) |
(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) |
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) |
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x))) |
(fma.f64 x x (*.f64 y y)) |
x |
(*.f64 y y) |
y |
(fma.f64 x x (*.f64 (neg.f64 y) y)) |
(fma.f64 (neg.f64 y) y (*.f64 x x)) |
(*.f64 (neg.f64 y) y) |
(neg.f64 y) |
(-.f64 x y) |
(sqrt.f64 (+.f64 y x)) |
(sqrt.f64 (+.f64 x y)) |
(+.f64 y x) |
(+.f64 x y) |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) | |
| accuracy | 0.0078125 | (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) | |
| accuracy | 0.4921875 | (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) | |
| accuracy | 33.08807501240855 | (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) | |
| accuracy | 0.14453125 | (/.f64 (/.f64 y x) x) | |
| accuracy | 0.4620211082109554 | #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) | |
| accuracy | 14.87336629075456 | (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) | |
| accuracy | 15.074564329206149 | (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) |
| 110.0ms | 256× | 0 | valid |
Compiled 185 to 29 computations (84.3% saved)
ival-div: 32.0ms (40.6% of total)ival-hypot: 23.0ms (29.2% of total)ival-mult: 12.0ms (15.2% of total)ival-add: 5.0ms (6.3% of total)ival-sqrt: 3.0ms (3.8% of total)ival-sub: 1.0ms (1.3% of total)ival-neg: 1.0ms (1.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (/ x y)) (taylor 0 y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 x) (/ (pow y 2) x)) y) (taylor 0 y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 x) (/ (pow y 2) x)) y) (taylor 0 y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/2 x) (/ (pow y 2) x)) y) (taylor 0 y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor 0 y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor 0 y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor 0 y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor 0 y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 2 (/ y x)) 1))) (taylor 0 y) (#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1))) (taylor 0 y) (#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* 1/2 (/ (* y (+ x (* -1 x))) x))) (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)) (* 1/2 (/ (+ x (* -1 x)) x))))) (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (+ (* 1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1 (/ (+ x (* -1 x)) (pow x 2))) (* 1/2 (/ (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2))))) x)) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) x))))))) (taylor 0 y) (#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 y) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y))))) (taylor 0 y) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3))))))))) (taylor 0 y) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y x) (taylor inf y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) (taylor inf y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) (taylor inf y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) (taylor inf y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor inf y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor inf y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor inf y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor inf y) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ()) |
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#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | x | @ | 0 | ((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y)))) |
| 5.0ms | y | @ | 0 | ((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y)))) |
| 3.0ms | x | @ | -inf | ((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y)))) |
| 3.0ms | y | @ | inf | ((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y)))) |
| 3.0ms | x | @ | inf | ((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y)))) |
| 1× | egg-herbie |
| 9 790× | lower-fma.f64 |
| 9 790× | lower-fma.f32 |
| 5 040× | lower-*.f64 |
| 5 040× | lower-*.f32 |
| 3 196× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 635 | 3343 |
| 1 | 2050 | 2746 |
| 2 | 7668 | 2678 |
| 0 | 8092 | 2505 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (/ (pow x 2) y)) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(* 1/2 (/ x y)) |
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y) |
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y) |
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 2 (/ y x)) 1))) |
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1))) |
x |
(+ x (* 1/2 (/ (* y (+ x (* -1 x))) x))) |
(+ x (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)) (* 1/2 (/ (+ x (* -1 x)) x))))) |
(+ x (* y (+ (* 1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1 (/ (+ x (* -1 x)) (pow x 2))) (* 1/2 (/ (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2))))) x)) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) x))))))) |
(sqrt x) |
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y))))) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3))))))))) |
1 |
(+ 1 (* 2 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(/ y x) |
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) |
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) |
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (- (+ 1 (+ (* -1 (/ x y)) (/ (pow x 2) (pow y 2)))) (* -1 (/ (pow x 2) (pow y 2))))) |
(* y (- (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 2) (pow y 2))))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (pow x 3) (pow y 3))))) |
y |
(* y (+ 1 (* -1/2 (/ (+ x (* -1 x)) y)))) |
(* y (+ 1 (+ (* -1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/2 (/ (+ x (* -1 x)) y)) (+ (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 2))) (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 3)) (pow x 3))) (+ (* -1/2 (* (+ x (* -1 x)) (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (* (pow x 2) (+ x (* -1 x))))) (pow y 3))))))) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))) (* 1/2 (* (sqrt (/ 1 (pow y 7))) (- (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))))))) |
-1 |
(- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ (pow x 2) (pow y 2)))) |
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (+ 1 (/ (pow x 2) (pow y 2)))) |
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) (pow y 6))) (+ 1 (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (/ (pow x 2) (pow y 2))))) |
y |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(/ y x) |
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x)))) |
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x)))) |
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x)))) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(* -1 (* y (- (* -1 (/ (+ (* -1 x) (* -1 (/ (- (+ (* -1 (/ (- (* -1 (pow x 3)) (pow x 3)) y)) (* -1 (pow x 2))) (pow x 2)) y))) y)) 1))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))) |
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1/2 (+ x (* -1 x))) (* -1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) y))) y))))) |
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (+ (* -1 (pow x 3)) (pow x 3))) (+ (* -1/2 (* (+ x (* -1 x)) (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (* (pow x 2) (+ x (* -1 x))))) y)) (* 1/2 (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) y)) (* -1/2 (+ x (* -1 x)))) y))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 y)) (- (* -1 (pow x 3)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (* 1/2 (* (sqrt y) (- (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
-1 |
(- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ (pow x 2) (pow y 2)))) |
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (+ 1 (/ (pow x 2) (pow y 2)))) |
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) (pow y 6))) (+ 1 (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (/ (pow x 2) (pow y 2))))) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* 1/2 (/ (pow x 2) y))) |
(/ y x) |
(/ (+ y (* 1/2 (/ (pow x 2) y))) x) |
(/ (+ y (* 1/2 (/ (pow x 2) y))) x) |
(/ (+ y (* 1/2 (/ (pow x 2) y))) x) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
y |
(+ y (* 1/2 (/ (pow x 2) y))) |
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
y |
(+ y (* -1 x)) |
(+ y (* x (- (* 2 (/ x y)) 1))) |
(+ y (* x (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1))) |
y |
(+ y (* -1/2 (/ (* x (+ (* -1 (pow y 3)) (pow y 3))) (pow y 3)))) |
(+ y (* x (+ (* -1/2 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow y 3))) (* 1/2 (/ (* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow y 2)))) (* 1/4 (/ (pow (+ (* -1 (pow y 3)) (pow y 3)) 2) (pow y 6))))) y))))) |
(+ y (* x (+ (* -1/2 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow y 3))) (* x (+ (* 1/2 (/ (* x (- (* -1 (/ (+ y (* -1 y)) (pow y 2))) (* -1/2 (/ (* (+ (* -1 (pow y 3)) (pow y 3)) (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow y 2)))) (* 1/4 (/ (pow (+ (* -1 (pow y 3)) (pow y 3)) 2) (pow y 6))))) (pow y 4))))) y)) (* 1/2 (/ (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow y 2)))) (* 1/4 (/ (pow (+ (* -1 (pow y 3)) (pow y 3)) 2) (pow y 6)))) y))))))) |
(sqrt y) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* 7/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -9/16 (* x (sqrt (/ 1 (pow y 5))))) (* 7/8 (sqrt (/ 1 (pow y 3))))))))) |
-1 |
(- (* -2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (- (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1) |
(* 1/2 (/ (pow x 2) y)) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* 1/2 (/ x y)) |
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
x |
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (- (+ 1 (+ (* -1 (/ y x)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2))))) |
(* x (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 3) (pow x 3))) (/ (pow y 2) (pow x 2))))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ (pow y 3) (pow x 3))))) |
x |
(* x (+ 1 (* 1/2 (/ (+ y (* -1 y)) x)))) |
(* x (+ 1 (+ (* 1/2 (/ (+ y (* -1 y)) x)) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))) (pow x 2)))))) |
(* x (+ 1 (+ (* 1/2 (/ (+ y (* -1 y)) x)) (+ (* 1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))))))) (pow x 3))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))) (pow x 2))))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2)))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))))))) |
1 |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) y)) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) |
(* 1/2 (/ x y)) |
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y))))) |
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y))))) |
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y))))) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (* -1 (/ (- (+ (* -1 y) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)) 1))) |
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (- (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (/ (pow y 3) x)) (* -1 (/ (pow y 3) x))) x))) x)) 1))) |
(* -1 (* x (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1/2 (/ (+ y (* -1 y)) x)) (pow (sqrt -1) 2)))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2)))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (/ (* (+ y (* -1 y)) (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))))) x)) (* 1/2 (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- (pow y 3) (+ (* -1 (pow y 3)) (* -1/4 (* x (pow y 2)))))))) (* 1/2 (* (sqrt x) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2))))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
1 |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2))))) |
| Outputs |
|---|
(* 1/2 (/ (pow x 2) y)) |
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/.f64 (fma.f64 y y (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/.f64 (fma.f64 y y (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) y) |
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) |
(/.f64 (fma.f64 y y (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) y) |
(* 1/2 (/ x y)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x) |
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y) |
(/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 y y) x)) y) |
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y) |
(/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 y y) x)) y) |
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y) |
(/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 y y) x)) y) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
x |
(+ x (* 1/2 (/ (pow y 2) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 2 (/ y x)) 1))) |
(fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal -1 binary64)) y x) |
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) (/.f64 y (*.f64 x x)) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) |
x |
(+ x (* 1/2 (/ (* y (+ x (* -1 x))) x))) |
(+.f64 (/.f64 #s(literal 0 binary64) x) x) |
(+ x (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)) (* 1/2 (/ (+ x (* -1 x)) x))))) |
(fma.f64 (fma.f64 (/.f64 (+.f64 y (/.f64 (/.f64 #s(literal 0 binary64) x) x)) x) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) x)) y x) |
(+ x (* y (+ (* 1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1 (/ (+ x (* -1 x)) (pow x 2))) (* 1/2 (/ (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2))))) x)) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) x))))))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) x) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) x) #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) x)) y (/.f64 #s(literal 0 binary64) x)) y x) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 7/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -9/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 7/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 2 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(/ y x) |
(/.f64 y x) |
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) |
(*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y) |
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) |
(*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y) |
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x))) |
(*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
y |
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(* y (- (+ 1 (+ (* -1 (/ x y)) (/ (pow x 2) (pow y 2)))) (* -1 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 x (/.f64 (/.f64 x y) y) (fma.f64 x (/.f64 (/.f64 x y) y) (-.f64 #s(literal 1 binary64) (/.f64 x y)))) y) |
(* y (- (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 2) (pow y 2))))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (pow x 3) (pow y 3))))) |
(*.f64 (-.f64 (+.f64 (-.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (neg.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)))) (/.f64 x y)) (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64))) (pow.f64 (/.f64 x y) #s(literal 3 binary64))) y) |
y |
(* y (+ 1 (* -1/2 (/ (+ x (* -1 x)) y)))) |
(+.f64 (/.f64 #s(literal 0 binary64) y) y) |
(* y (+ 1 (+ (* -1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 2)))))) |
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) (/.f64 #s(literal 0 binary64) y)) y y) |
(* y (+ 1 (+ (* -1/2 (/ (+ x (* -1 x)) y)) (+ (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 2))) (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 3)) (pow x 3))) (+ (* -1/2 (* (+ x (* -1 x)) (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (* (pow x 2) (+ x (* -1 x))))) (pow y 3))))))) |
(fma.f64 (fma.f64 (fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) y)) y y) |
(sqrt y) |
(sqrt.f64 y) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2)))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))) (* 1/2 (* (sqrt (/ 1 (pow y 7))) (- (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))))))) |
(*.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -2 binary64)) (*.f64 (*.f64 y (*.f64 x x)) #s(literal 1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) #s(literal 1/2 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
-1 |
#s(literal -1 binary64) |
(- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal -2 binary64) #s(literal -1 binary64)) |
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (+ 1 (/ (pow x 2) (pow y 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 x x)) (pow.f64 y #s(literal 4 binary64))) (*.f64 x x) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal -2 binary64) #s(literal -1 binary64))) |
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) (pow y 6))) (+ 1 (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (/ (pow x 2) (pow y 2))))) |
(-.f64 (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 x x)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)))) (fma.f64 (/.f64 x y) (/.f64 x y) (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 x x)) (pow.f64 y #s(literal 4 binary64))))) |
y |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal -1/2 binary64) #s(literal -1 binary64)) (neg.f64 y)) |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal -1/2 binary64) #s(literal -1 binary64)) (neg.f64 y)) |
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal -1/2 binary64) #s(literal -1 binary64)) (neg.f64 y)) |
(/ y x) |
(/.f64 y x) |
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 x y) (/.f64 #s(literal -1 binary64) x)) (neg.f64 y)) |
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 x y) (/.f64 #s(literal -1 binary64) x)) (neg.f64 y)) |
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 x y) (/.f64 #s(literal -1 binary64) x)) (neg.f64 y)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(* -1 y) |
(neg.f64 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 y)) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) |
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 y)) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) |
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y)) |
y |
(* -1 (* y (- (/ x y) 1))) |
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) (neg.f64 y)) |
(* -1 (* y (- (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) y) x) y) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 y)) |
(* -1 (* y (- (* -1 (/ (+ (* -1 x) (* -1 (/ (- (+ (* -1 (/ (- (* -1 (pow x 3)) (pow x 3)) y)) (* -1 (pow x 2))) (pow x 2)) y))) y)) 1))) |
(*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (*.f64 #s(literal -2 binary64) x) x (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -2 binary64)) (neg.f64 y))) (neg.f64 y)) x) y) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 y)) |
(* -1 y) |
(neg.f64 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))) |
(neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1/2 (+ x (* -1 x))) (* -1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) y))) y))))) |
(neg.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x (/.f64 x y) #s(literal 0 binary64))) y) y y)) |
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (+ (* -1 (pow x 3)) (pow x 3))) (+ (* -1/2 (* (+ x (* -1 x)) (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (* (pow x 2) (+ x (* -1 x))))) y)) (* 1/2 (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) y)) (* -1/2 (+ x (* -1 x)))) y))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (/.f64 #s(literal 0 binary64) y)) (neg.f64 y)) y)) (neg.f64 y)) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
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x |
(* -1 (* x (+ (* -1/2 (/ (+ y (* -1 y)) x)) (pow (sqrt -1) 2)))) |
(fma.f64 (/.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) x) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2)))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 y) y) x) #s(literal -1/2 binary64) #s(literal 0 binary64)) x)) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (/ (* (+ y (* -1 y)) (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))))) x)) (* 1/2 (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2)))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) x)) (neg.f64 x)) x)) (neg.f64 x)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- (pow y 3) (+ (* -1 (pow y 3)) (* -1/4 (* x (pow y 2)))))))) (* 1/2 (* (sqrt x) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2))))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)))) (sqrt.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 (*.f64 (*.f64 y y) (fma.f64 #s(literal 1/4 binary64) x y)))) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) (*.f64 y y) #s(literal 1 binary64)) |
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (*.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64)))) (*.f64 y (/.f64 y (*.f64 x x)))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)))) |
| 5 612× | lower-/.f32 |
| 5 604× | lower-/.f64 |
| 4 854× | lower-fma.f32 |
| 4 850× | lower-fma.f64 |
| 3 604× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 136 |
| 0 | 49 | 134 |
| 1 | 187 | 134 |
| 2 | 1758 | 116 |
| 0 | 8445 | 103 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) |
(/.f64 (/.f64 y x) x) |
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) |
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) |
| Outputs |
|---|
(*.f64 (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x) (*.f64 (/.f64 x y) x)) |
(*.f64 (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) y) (/.f64 (*.f64 x x) x)) |
(*.f64 (*.f64 x x) (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y))) |
(*.f64 (*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) x) x) |
(*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x)) |
(*.f64 x (*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) x)) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) (*.f64 x x))) (neg.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) (*.f64 x x))) (neg.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))) (neg.f64 (*.f64 x y))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) (*.f64 x x)) (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y))))) |
(/.f64 (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) (*.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))) (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))) |
(*.f64 (/.f64 x x) (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) y)) |
(*.f64 (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x) (/.f64 x y)) |
(*.f64 (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) y) (/.f64 x x)) |
(*.f64 (/.f64 x y) (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x)) |
(*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) x) |
(*.f64 x (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 (/.f64 y x) x) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (/.f64 y x) x) x) (*.f64 (/.f64 (/.f64 y x) x) x) (-.f64 (*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (*.f64 (*.f64 (/.f64 (/.f64 y x) x) x) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 (/.f64 y x) x) x) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (*.f64 (*.f64 (/.f64 (/.f64 y x) x) x) (*.f64 (/.f64 (/.f64 y x) x) x)) (*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (*.f64 (/.f64 (/.f64 y x) x) x))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 x (/.f64 (/.f64 y x) x)) #s(literal 3 binary64)) (pow.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64))) (fma.f64 (*.f64 x (/.f64 (/.f64 y x) x)) (*.f64 x (/.f64 (/.f64 y x) x)) (-.f64 (*.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x (/.f64 #s(literal 1/2 binary64) y))) (*.f64 (*.f64 x (/.f64 (/.f64 y x) x)) (*.f64 x (/.f64 #s(literal 1/2 binary64) y)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64)) (pow.f64 (*.f64 x (/.f64 (/.f64 y x) x)) #s(literal 3 binary64))) (fma.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) (-.f64 (*.f64 (*.f64 x (/.f64 (/.f64 y x) x)) (*.f64 x (/.f64 (/.f64 y x) x))) (*.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x (/.f64 (/.f64 y x) x)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) x)) (neg.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) x)) (neg.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x)) (neg.f64 (*.f64 x y))) |
(/.f64 (neg.f64 (*.f64 x (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))))) (neg.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))))) (neg.f64 (*.f64 x y))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) x) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) x) (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y))))) |
(/.f64 (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x) (*.f64 x y)) |
(/.f64 (*.f64 x (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x))) |
(/.f64 (*.f64 x (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64)))) (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y))))) |
(/.f64 (*.f64 x (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))) (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) (*.f64 x (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))) (*.f64 x (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) (*.f64 x (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64)))))) |
(fma.f64 (/.f64 (/.f64 y x) x) x (*.f64 (/.f64 #s(literal 1/2 binary64) y) x)) |
(fma.f64 x (/.f64 (/.f64 y x) x) (*.f64 x (/.f64 #s(literal 1/2 binary64) y))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 (/.f64 y x) x))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (*.f64 (/.f64 (/.f64 y x) x) x)) |
(+.f64 (*.f64 (/.f64 (/.f64 y x) x) x) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x)) |
(+.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (*.f64 (/.f64 (/.f64 y x) x) x)) |
(+.f64 (*.f64 x (/.f64 (/.f64 y x) x)) (*.f64 x (/.f64 #s(literal 1/2 binary64) y))) |
(+.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x (/.f64 (/.f64 y x) x))) |
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (neg.f64 y) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 y) #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 x))) |
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) x)) |
(*.f64 (pow.f64 (/.f64 (neg.f64 x) y) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (neg.f64 y) #s(literal -1 binary64)))) |
(*.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1 binary64)) x)) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 y x)) |
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 y x) x)) |
(*.f64 (/.f64 (neg.f64 y) x) (pow.f64 (neg.f64 x) #s(literal -1 binary64))) |
(*.f64 (/.f64 y x) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 y (/.f64 (pow.f64 x #s(literal -1 binary64)) x)) |
(*.f64 y (pow.f64 x #s(literal -2 binary64))) |
(pow.f64 (*.f64 (/.f64 x y) x) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64))) (neg.f64 (*.f64 (neg.f64 x) x))) |
(/.f64 (neg.f64 (*.f64 (/.f64 y x) #s(literal 1 binary64))) (neg.f64 x)) |
(/.f64 (neg.f64 (*.f64 y #s(literal 1 binary64))) (neg.f64 (*.f64 x x))) |
(/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 x y))) |
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 (*.f64 x x)))) |
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (*.f64 x (neg.f64 x)))) |
(/.f64 (*.f64 (/.f64 y x) #s(literal 1 binary64)) x) |
(/.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (*.f64 (neg.f64 x) x)) |
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(*.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 x x (*.f64 y y))) |
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(*.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (pow.f64 (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (*.f64 (+.f64 x y) (-.f64 y x)))) |
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(*.f64 (fma.f64 x x (*.f64 y y)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64)))) (neg.f64 (*.f64 (+.f64 x y) (-.f64 y x)))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x x (*.f64 y y))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))) (*.f64 (+.f64 x y) (-.f64 y x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) |
(/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x (*.f64 y y)))) (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x)))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y)))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(neg.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x))))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) (/.f64 (fma.f64 x x (*.f64 y y)) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(-.f64 (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (+.f64 x y) (-.f64 y x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (+.f64 x y) (-.f64 y x))) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(-.f64 (/.f64 (*.f64 x x) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 y) y) (fma.f64 (neg.f64 y) y (*.f64 x x)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y)))) #s(literal -1 binary64))) |
Compiled 15 429 to 2 438 computations (84.2% saved)
9 alts after pruning (3 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 542 | 3 | 545 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 3 | 4 | 7 |
| Total | 545 | 9 | 554 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 y x) |
| ✓ | 51.1% | (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
| ✓ | 47.5% | (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
| ✓ | 51.5% | (sqrt.f64 (fma.f64 y y (*.f64 x x))) |
| 98.8% | #s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) | |
| 4.9% | #s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) | |
| ✓ | 99.3% | #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
| ✓ | 51.8% | #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
| 75.9% | #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 #s(approx (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y)) x))) |
Compiled 228 to 128 computations (43.9% saved)
| Inputs |
|---|
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 #s(approx (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y)) x))) |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
(hypot.f64 y x) |
| Outputs |
|---|
(hypot.f64 y x) |
6 calls:
| 8.0ms | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 6.0ms | x |
| 5.0ms | y |
| 4.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 4.0ms | (*.f64 y y) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 100.0% | 1 | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 100.0% | 1 | (*.f64 x x) |
| 100.0% | 1 | (*.f64 y y) |
Compiled 23 to 21 computations (8.7% saved)
| Inputs |
|---|
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) |
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 #s(approx (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y)) x))) |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) |
| Outputs |
|---|
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
6 calls:
| 5.0ms | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 4.0ms | y |
| 4.0ms | x |
| 4.0ms | (*.f64 y y) |
| 4.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | x |
| 99.3% | 1 | y |
| 99.3% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 99.3% | 1 | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 99.3% | 1 | (*.f64 x x) |
| 99.3% | 1 | (*.f64 y y) |
Compiled 23 to 21 computations (8.7% saved)
| Inputs |
|---|
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) |
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) |
(sqrt.f64 (fma.f64 y y (*.f64 x x))) |
| Outputs |
|---|
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
6 calls:
| 25.0ms | x |
| 3.0ms | y |
| 2.0ms | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 2.0ms | (*.f64 y y) |
| 2.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 1 | x |
| 98.8% | 1 | y |
| 98.8% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 98.8% | 1 | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 98.8% | 1 | (*.f64 x x) |
| 98.8% | 1 | (*.f64 y y) |
Compiled 23 to 21 computations (8.7% saved)
Total -2.0b remaining (-3.2%)
Threshold costs -2b (-3.2%)
| Inputs |
|---|
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) |
| Outputs |
|---|
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
6 calls:
| 5.0ms | y |
| 2.0ms | x |
| 1.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 1.0ms | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 1.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.9% | 1 | x |
| 4.9% | 1 | y |
| 4.9% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) |
| 4.9% | 1 | (+.f64 (*.f64 x x) (*.f64 y y)) |
| 4.9% | 1 | (*.f64 x x) |
| 4.9% | 1 | (*.f64 y y) |
Compiled 23 to 21 computations (8.7% saved)
| 1× | egg-herbie |
| 2× | *-commutative-binary64-*.f64 |
| 2× | +-commutative-binary64-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 80 |
| 1 | 29 | 80 |
| 1× | saturated |
| Inputs |
|---|
(hypot.f64 y x) |
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
| Outputs |
|---|
(hypot.f64 y x) |
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y)) |
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x) |
| 18 004× | lower-fma.f64 |
| 18 004× | lower-fma.f32 |
| 9 790× | lower-fma.f64 |
| 9 790× | lower-fma.f32 |
| 7 168× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 635 | 3343 |
| 1 | 2050 | 2746 |
| 2 | 7668 | 2678 |
| 0 | 8092 | 2505 |
| 0 | 18 | 77 |
| 0 | 29 | 76 |
| 1 | 95 | 68 |
| 2 | 679 | 68 |
| 3 | 7993 | 68 |
| 0 | 9166 | 57 |
| 0 | 104 | 620 |
| 1 | 296 | 620 |
| 2 | 953 | 618 |
| 3 | 3667 | 584 |
| 4 | 6426 | 582 |
| 0 | 8051 | 530 |
| 0 | 6 | 21 |
| 0 | 10 | 21 |
| 1 | 29 | 21 |
| 2 | 196 | 21 |
| 3 | 1788 | 21 |
| 0 | 8624 | 15 |
| 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× | iter limit |
| 1× | node limit |
Compiled 141 to 83 computations (41.1% saved)
(sort x y)
(abs x)
(abs y)
Compiled 112 to 82 computations (26.8% saved)
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