
Time bar (total: 9.8s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 3 |
| 100% | 99.9% | 0% | 0.1% | 0% | 0% | 0% | 4 |
Compiled 14 to 11 computations (21.4% saved)
| 693.0ms | 8 256× | 0 | valid |
ival-mult: 195.0ms (43.7% of total)ival-add: 181.0ms (40.5% of total)ival-sqrt: 61.0ms (13.7% of total)ival-true: 6.0ms (1.3% of total)ival-assert: 3.0ms (0.7% of total)| 2× | egg-herbie |
| 104× | sub-neg |
| 92× | unsub-neg |
| 66× | neg-sub0 |
| 54× | neg-mul-1 |
| 50× | distribute-lft-neg-in |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 123 |
| 1 | 69 | 123 |
| 2 | 148 | 123 |
| 3 | 291 | 123 |
| 4 | 468 | 123 |
| 5 | 518 | 123 |
| 6 | 520 | 123 |
| 0 | 9 | 12 |
| 1 | 13 | 12 |
| 2 | 20 | 12 |
| 3 | 22 | 12 |
| 0 | 22 | 10 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
| Outputs |
|---|
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) |
| Inputs |
|---|
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z)))) |
(sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z)))) |
(sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z))))) |
(neg (sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z))))) |
(neg (sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z))))) |
(neg (sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z)))))) |
(sqrt (+ (* y y) (+ (* x x) (* z z)))) |
(sqrt (+ (* z z) (+ (* y y) (* x x)))) |
(sqrt (+ (* x x) (+ (* z z) (* y y)))) |
| Outputs |
|---|
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z)))) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z)))) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z))))) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(neg (sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z))))) |
(neg (sqrt (+ (* x x) (+ (* y y) (* z z))))) |
(neg (sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z))))) |
(neg (sqrt (+ (* x x) (+ (* y y) (* z z))))) |
(neg (sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z)))))) |
(neg (sqrt (+ (* x x) (+ (* y y) (* z z))))) |
(sqrt (+ (* y y) (+ (* x x) (* z z)))) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt (+ (* z z) (+ (* y y) (* x x)))) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt (+ (* x x) (+ (* z z) (* y y)))) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(abs x)
(abs y)
(abs z)
(sort x y z)
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 157 | 0 | - | 0 | - | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 0 | 0 | - | 0 | - | (+.f64 (*.f64 y y) (*.f64 z z)) |
| 0 | 0 | - | 0 | - | z |
| 0 | 0 | - | 0 | - | (*.f64 x x) |
| 0 | 0 | - | 0 | - | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) |
| 0 | 0 | - | 0 | - | (*.f64 z z) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (*.f64 y y) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
sqrt.f64 | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) | oflow-rescue | 152 | 0 |
| ↳ | (+.f64 (*.f64 y y) (*.f64 z z)) | overflow | 152 | |
| ↳ | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) | overflow | 152 | |
| ↳ | (*.f64 y y) | overflow | 40 | |
| ↳ | (*.f64 x x) | overflow | 4 | |
| ↳ | (*.f64 z z) | overflow | 152 | |
sqrt.f64 | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) | uflow-rescue | 5 | 0 |
| ↳ | (+.f64 (*.f64 y y) (*.f64 z z)) | underflow | 5 | |
| ↳ | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) | underflow | 5 | |
| ↳ | (*.f64 y y) | underflow | 33 | |
| ↳ | (*.f64 x x) | underflow | 152 | |
| ↳ | (*.f64 z z) | underflow | 5 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 157 | 0 |
| - | 0 | 99 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 157 | 0 | 0 |
| - | 0 | 0 | 99 |
| number | freq |
|---|---|
| 0 | 99 |
| 1 | 157 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 123.0ms | 512× | 0 | valid |
Compiled 118 to 40 computations (66.1% saved)
ival-mult: 98.0ms (91.8% of total)ival-add: 4.0ms (3.7% of total)ival-sqrt: 4.0ms (3.7% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)Compiled 3 to 3 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 43.0% | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
Compiled 15 to 9 computations (40% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| ✓ | cost-diff | 128 | (+.f64 (*.f64 y y) (*.f64 z z)) |
| ✓ | cost-diff | 128 | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) |
| 24× | +-lowering-+.f64 |
| 24× | +-lowering-+.f32 |
| 18× | accelerator-lowering-fma.f32 |
| 18× | accelerator-lowering-fma.f64 |
| 10× | +-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 42 |
| 1 | 13 | 42 |
| 2 | 20 | 42 |
| 3 | 22 | 42 |
| 0 | 22 | 37 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(+ (* x x) (+ (* y y) (* z z))) |
(* x x) |
x |
(+ (* y y) (* z z)) |
(* y y) |
y |
(* z z) |
z |
| Outputs |
|---|
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) |
(+ (* x x) (+ (* y y) (* z z))) |
(fma.f64 x x (fma.f64 y y (*.f64 z z))) |
(* x x) |
(*.f64 x x) |
x |
(+ (* y y) (* z z)) |
(fma.f64 y y (*.f64 z z)) |
(* y y) |
(*.f64 y y) |
y |
(* z z) |
(*.f64 z z) |
z |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 y y) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (+.f64 (*.f64 y y) (*.f64 z z)) |
| ✓ | accuracy | 43.1% | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 37.0ms | 256× | 0 | valid |
Compiled 44 to 11 computations (75% saved)
ival-mult: 25.0ms (85.4% of total)ival-add: 2.0ms (6.8% of total)ival-sqrt: 2.0ms (6.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (+ (* x x) (+ (* y y) (* z z)))> |
#<alt (+ (* y y) (* z z))> |
#<alt (sqrt (+ (* x x) (+ (* y y) (* z z))))> |
#<alt (* x x)> |
#<alt (* y y)> |
| Outputs |
|---|
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (+ (pow x 2) (pow z 2))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (+ (pow x 2) (pow y 2))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (pow z 2)> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (pow y 2)> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (sqrt (+ (pow y 2) (pow z 2)))> |
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))> |
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))))> |
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))> |
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))> |
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))> |
#<alt (sqrt (+ (pow x 2) (pow z 2)))> |
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))> |
#<alt y> |
#<alt (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))> |
#<alt (* -1 y)> |
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))))> |
#<alt (sqrt (+ (pow x 2) (pow y 2)))> |
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))> |
#<alt (* -1 z)> |
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
30 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | z | @ | 0 | (sqrt (+ (* x x) (+ (* y y) (* z z)))) |
| 1.0ms | x | @ | 0 | (+ (* x x) (+ (* y y) (* z z))) |
| 1.0ms | y | @ | inf | (sqrt (+ (* x x) (+ (* y y) (* z z)))) |
| 1.0ms | x | @ | 0 | (sqrt (+ (* x x) (+ (* y y) (* z z)))) |
| 0.0ms | y | @ | 0 | (sqrt (+ (* x x) (+ (* y y) (* z z)))) |
| 1× | batch-egg-rewrite |
| 4 564× | accelerator-lowering-fma.f32 |
| 4 564× | accelerator-lowering-fma.f64 |
| 4 222× | *-lowering-*.f32 |
| 4 222× | *-lowering-*.f64 |
| 2 570× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 36 |
| 1 | 44 | 36 |
| 2 | 405 | 36 |
| 3 | 5921 | 36 |
| 0 | 8215 | 31 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* x x) (+ (* y y) (* z z))) |
(+ (* y y) (* z z)) |
(sqrt (+ (* x x) (+ (* y y) (* z z)))) |
(* x x) |
(* y y) |
| Outputs |
|---|
(+.f64 (*.f64 x x) (fma.f64 y y (*.f64 z z))) |
(+.f64 (*.f64 y y) (fma.f64 x x (*.f64 z z))) |
(+.f64 (*.f64 z z) (fma.f64 x x (*.f64 y y))) |
(+.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x)) |
(+.f64 (fma.f64 x x (*.f64 y y)) (*.f64 z z)) |
(+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))) (neg.f64 (/.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))))) |
(+.f64 (fma.f64 x x (*.f64 z z)) (*.f64 y y)) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))) #s(literal -1 binary64))) |
(-.f64 (/.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (+.f64 y z) (-.f64 y z))) (-.f64 (/.f64 (*.f64 z (*.f64 z (*.f64 z z))) (*.f64 (+.f64 y z) (-.f64 y z))) (*.f64 x x))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))) (/.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))) |
(-.f64 (/.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z))) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x)))) |
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(*.f64 (fma.f64 y y (*.f64 z z)) (/.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 (+.f64 y z) (-.f64 y z)))) |
(*.f64 (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z)))))) |
(*.f64 (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 (fma.f64 y y (*.f64 z z)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z))))))) |
(*.f64 (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z)))) (/.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z)))))) |
(*.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z))))))) |
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))) (*.f64 (+.f64 y z) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 y z) (-.f64 y z))))) |
(*.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 z z))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z))))) (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 y z)))) |
(*.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 z y))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 z y)))) |
(*.f64 (/.f64 (fma.f64 y y (*.f64 z z)) (+.f64 y z)) (+.f64 y z)) |
(*.f64 (/.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 y z))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 y z)))) (fma.f64 y y (*.f64 z z))) |
(*.f64 (/.f64 (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (fma.f64 (*.f64 z (*.f64 z (*.f64 (+.f64 y z) (-.f64 z y)))) (*.f64 (*.f64 z (*.f64 z (*.f64 z z))) (*.f64 (*.f64 (+.f64 y z) (-.f64 z y)) (*.f64 (+.f64 y z) (-.f64 z y)))) (*.f64 (*.f64 y y) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y y) (*.f64 y (*.f64 y (*.f64 y y)))))))) (fma.f64 y (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y (*.f64 y y)))) (*.f64 (*.f64 z (*.f64 z (*.f64 (+.f64 y z) (-.f64 z y)))) (-.f64 (*.f64 z (*.f64 z (*.f64 (+.f64 y z) (-.f64 z y)))) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (*.f64 (fma.f64 (*.f64 y y) (*.f64 (+.f64 y z) (-.f64 y z)) (*.f64 z (*.f64 z (*.f64 z z)))) (fma.f64 y (*.f64 y (*.f64 y y)) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 z y)))))) (fma.f64 y (*.f64 y (*.f64 y y)) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 z y))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (+.f64 y z) (-.f64 y z))) (*.f64 (fma.f64 y (*.f64 y y) (*.f64 z (*.f64 z z))) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 z (*.f64 z z))))) (fma.f64 y (*.f64 y (*.f64 y y)) (*.f64 z (*.f64 z (fma.f64 y y (*.f64 z z)))))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (fma.f64 y y (*.f64 z z))))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))))) #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) |
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z)))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 y y (*.f64 z z)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z)))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))) (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x (neg.f64 x) (fma.f64 y y (*.f64 z z))))) (sqrt.f64 (fma.f64 x (neg.f64 x) (fma.f64 y y (*.f64 z z))))) |
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y))) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))))) (sqrt.f64 (fma.f64 (*.f64 z z) (-.f64 (*.f64 z z) (fma.f64 x x (*.f64 y y))) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x)))) (sqrt.f64 (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (*.f64 (+.f64 y z) (-.f64 y z))))) (sqrt.f64 (fma.f64 x x (*.f64 (+.f64 y z) (-.f64 y z))))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z))))))) (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))))) (neg.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))))) |
(pow.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (fma.f64 y y (*.f64 z z)))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 y y (*.f64 z z))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z))))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))) (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (fma.f64 y y (*.f64 z z)) (fma.f64 y y (*.f64 z z)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 y y (*.f64 z z)) (-.f64 (fma.f64 y y (*.f64 z z)) (*.f64 x x))))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 z z))))))) |
(*.f64 (pow.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64))) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) |
(*.f64 x x) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 y))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 y))) #s(literal 2 binary64))) |
(pow.f64 y #s(literal 2 binary64)) |
(pow.f64 (*.f64 y y) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64)) |
(*.f64 y y) |
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y))) |
| 1× | egg-herbie |
| 11 154× | accelerator-lowering-fma.f32 |
| 11 154× | accelerator-lowering-fma.f64 |
| 4 248× | *-lowering-*.f32 |
| 4 248× | *-lowering-*.f64 |
| 2 568× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 183 | 1644 |
| 1 | 508 | 1644 |
| 2 | 1778 | 1641 |
| 3 | 4736 | 1539 |
| 0 | 8027 | 1308 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (pow y 2) (pow z 2)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(+ (pow x 2) (pow z 2)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(pow y 2) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(pow z 2) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(pow z 2) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(pow z 2) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(pow y 2) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(pow z 2) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(pow z 2) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(sqrt (+ (pow y 2) (pow z 2))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5)))))))))) |
x |
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))) |
(sqrt (+ (pow x 2) (pow z 2))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5)))))))))) |
y |
(* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))) |
(sqrt (+ (pow x 2) (pow y 2))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5)))))))))) |
z |
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(* -1 z) |
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
| Outputs |
|---|
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(*.f64 x (+.f64 x (/.f64 (fma.f64 z z (*.f64 y y)) x))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(*.f64 x (+.f64 x (/.f64 (fma.f64 z z (*.f64 y y)) x))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(*.f64 x (+.f64 x (/.f64 (fma.f64 z z (*.f64 y y)) x))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(*.f64 x (+.f64 x (/.f64 (fma.f64 z z (*.f64 y y)) x))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(*.f64 x (+.f64 x (/.f64 (fma.f64 z z (*.f64 y y)) x))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(*.f64 x (+.f64 x (/.f64 (fma.f64 z z (*.f64 y y)) x))) |
(+ (pow x 2) (pow z 2)) |
(fma.f64 z z (*.f64 x x)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(pow y 2) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(pow y 2) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (pow y 2)) |
(fma.f64 x x (*.f64 y y)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(pow z 2) |
(*.f64 z z) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(pow z 2) |
(*.f64 z z) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(fma.f64 y y (fma.f64 z z (*.f64 x x))) |
(pow z 2) |
(*.f64 z z) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(pow y 2) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(fma.f64 z z (*.f64 y y)) |
(pow y 2) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(fma.f64 z z (*.f64 y y)) |
(pow y 2) |
(*.f64 y y) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 z z (*.f64 y y)) |
(pow z 2) |
(*.f64 z z) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(fma.f64 z z (*.f64 y y)) |
(pow z 2) |
(*.f64 z z) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(fma.f64 z z (*.f64 y y)) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(fma.f64 z z (*.f64 y y)) |
(sqrt (+ (pow y 2) (pow z 2))) |
(sqrt.f64 (fma.f64 z z (*.f64 y y))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))) |
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y))))) (sqrt.f64 (fma.f64 z z (*.f64 y y)))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))) |
(fma.f64 x (*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y)))))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y))))))) (sqrt.f64 (fma.f64 z z (*.f64 y y)))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5)))))))))) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y)))))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y))))))) (sqrt.f64 (fma.f64 z z (*.f64 y y)))) |
x |
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) |
(fma.f64 (fma.f64 z z (*.f64 y y)) (/.f64 #s(literal 1/2 binary64) x) x) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(fma.f64 x (fma.f64 (fma.f64 z z (*.f64 y y)) (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64)) x)) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(fma.f64 x (fma.f64 (fma.f64 z z (*.f64 y y)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y)))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (*.f64 y y)) (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64)) x)) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(-.f64 (*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) x) #s(literal -1/2 binary64)) x) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(fma.f64 x (fma.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) x) #s(literal -1/2 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 x (fma.f64 (fma.f64 z z (*.f64 y y)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y)))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (*.f64 y y)) (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64)) x))) |
(sqrt (+ (pow x 2) (pow z 2))) |
(sqrt.f64 (fma.f64 z z (*.f64 x x))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 x x)))) (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 z z (*.f64 x x)))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))) |
(fma.f64 (*.f64 y y) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 x x)) (*.f64 (fma.f64 z z (*.f64 x x)) (fma.f64 z z (*.f64 x x)))))) (*.f64 (*.f64 y y) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 x x)))))) (sqrt.f64 (fma.f64 z z (*.f64 x x)))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5)))))))))) |
(fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 x x)) (*.f64 (fma.f64 z z (*.f64 x x)) (fma.f64 z z (*.f64 x x)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (*.f64 x x)) #s(literal 5 binary64)))))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 x x)))))) (sqrt.f64 (fma.f64 z z (*.f64 x x)))) |
y |
(* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) |
(fma.f64 (fma.f64 z z (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))) |
(fma.f64 y (fma.f64 (fma.f64 z z (*.f64 x x)) (/.f64 (*.f64 (fma.f64 z z (*.f64 x x)) #s(literal -1/8 binary64)) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (*.f64 x x)) y))) |
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))) |
(fma.f64 y (fma.f64 (fma.f64 z z (*.f64 x x)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (fma.f64 z z (*.f64 x x)) (fma.f64 z z (*.f64 x x)))) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (*.f64 x x)) (/.f64 (*.f64 (fma.f64 z z (*.f64 x x)) #s(literal -1/8 binary64)) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (*.f64 x x)) y))) |
(* -1 y) |
(-.f64 #s(literal 0 binary64) y) |
(* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))) |
(-.f64 (*.f64 (/.f64 (fma.f64 z z (*.f64 x x)) y) #s(literal -1/2 binary64)) y) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))) |
(fma.f64 y (fma.f64 (*.f64 (fma.f64 z z (*.f64 x x)) (/.f64 (fma.f64 z z (*.f64 x x)) (*.f64 (*.f64 y y) (*.f64 y y)))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (*.f64 (/.f64 (fma.f64 z z (*.f64 x x)) y) #s(literal -1/2 binary64))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))) |
(fma.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 (fma.f64 z z (*.f64 x x)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (fma.f64 z z (*.f64 x x)) (fma.f64 z z (*.f64 x x)))) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (*.f64 x x)) (/.f64 (*.f64 (fma.f64 z z (*.f64 x x)) #s(literal -1/8 binary64)) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1 binary64))) (*.f64 (/.f64 (fma.f64 z z (*.f64 x x)) y) #s(literal -1/2 binary64))) |
(sqrt (+ (pow x 2) (pow y 2))) |
(sqrt.f64 (fma.f64 x x (*.f64 y y))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))) (*.f64 (*.f64 z z) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (*.f64 y y)))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))) |
(fma.f64 (*.f64 z z) (fma.f64 z (*.f64 z (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y)))))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))))) (sqrt.f64 (fma.f64 x x (*.f64 y y)))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5)))))))))) |
(fma.f64 (*.f64 z z) (fma.f64 (*.f64 z z) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 5 binary64)))) (*.f64 (*.f64 z z) #s(literal 1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y)))))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))))) (sqrt.f64 (fma.f64 x x (*.f64 y y)))) |
z |
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (*.f64 y y)) z) z) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(fma.f64 z (fma.f64 (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1/8 binary64)) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal 1 binary64)) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64)) z)) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(fma.f64 z (fma.f64 (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y)))) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1/8 binary64)) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64)) z)) |
(* -1 z) |
(-.f64 #s(literal 0 binary64) z) |
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(fma.f64 (/.f64 (fma.f64 x x (*.f64 y y)) z) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) z)) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(fma.f64 z (fma.f64 (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1/2 binary64)) z)) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))) |
(fma.f64 (-.f64 #s(literal 0 binary64) z) (fma.f64 (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y)))) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (fma.f64 x x (*.f64 y y)) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1/8 binary64)) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1/2 binary64)) z)) |
(pow x 2) |
(*.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) |
(pow x 2) |
(*.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) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.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 y 2) |
(*.f64 y y) |
(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 y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
(pow y 2) |
(*.f64 y y) |
Compiled 12 563 to 1 010 computations (92% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 346 | 3 | 349 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 347 | 3 | 350 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 38.6% | (sqrt.f64 (fma.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) (*.f64 x x))) |
| ▶ | 43.1% | (sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| ▶ | 97.9% | z |
Compiled 45 to 23 computations (48.9% saved)
| 1× | egg-herbie |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 z z) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) (*.f64 x x))) |
| ✓ | cost-diff | 384 | (fma.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) (*.f64 x x)) |
| ✓ | cost-diff | 2432 | (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) |
| ✓ | cost-diff | -64 | (*.f64 y y) |
| ✓ | cost-diff | 0 | (fma.f64 z z (*.f64 y y)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| 9 204× | accelerator-lowering-fma.f32 |
| 9 204× | accelerator-lowering-fma.f64 |
| 4 324× | *-lowering-*.f32 |
| 4 324× | *-lowering-*.f64 |
| 1 542× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 88 |
| 1 | 38 | 84 |
| 2 | 88 | 84 |
| 3 | 373 | 84 |
| 4 | 2897 | 84 |
| 5 | 5563 | 84 |
| 0 | 8188 | 73 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
z |
(sqrt (+ (* z z) (* y y))) |
(+ (* z z) (* y y)) |
z |
(* y y) |
y |
(sqrt (+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x))) |
(+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x)) |
(+ (* y y) (* z z)) |
y |
(* z z) |
z |
(* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z)))) |
(* (+ y z) (- y z)) |
(+ y z) |
(- y z) |
(/ 1 (* (+ y z) (- y z))) |
1 |
(* x x) |
x |
| Outputs |
|---|
z |
(sqrt (+ (* z z) (* y y))) |
(sqrt.f64 (fma.f64 z z (fma.f64 y y #s(literal 0 binary64)))) |
(+ (* z z) (* y y)) |
(fma.f64 z z (fma.f64 y y #s(literal 0 binary64))) |
z |
(* y y) |
(fma.f64 y y #s(literal 0 binary64)) |
y |
(sqrt (+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x))) |
(sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) |
(+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x)) |
(fma.f64 z z (fma.f64 y y (*.f64 x x))) |
(+ (* y y) (* z z)) |
(fma.f64 z z (fma.f64 y y #s(literal 0 binary64))) |
y |
(* z z) |
(*.f64 z z) |
z |
(* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z)))) |
#s(literal 1 binary64) |
(* (+ y z) (- y z)) |
(*.f64 (+.f64 z y) (-.f64 y z)) |
(+ y z) |
(+.f64 z y) |
(- y z) |
(-.f64 y z) |
(/ 1 (* (+ y z) (- y z))) |
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z))) |
1 |
#s(literal 1 binary64) |
(* x x) |
(*.f64 x x) |
x |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 (+.f64 y z) (-.f64 y z)) |
| ✓ | accuracy | 99.2% | (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z))) |
| ✓ | accuracy | 43.1% | (sqrt.f64 (fma.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) (*.f64 x x))) |
| ✓ | accuracy | 40.4% | (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) |
| ✓ | accuracy | 100.0% | (fma.f64 z z (*.f64 y y)) |
| ✓ | accuracy | 100.0% | (*.f64 y y) |
| ✓ | accuracy | 43.1% | (sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| 35.0ms | 256× | 0 | valid |
Compiled 131 to 20 computations (84.7% saved)
ival-mult: 10.0ms (44.9% of total)ival-add: 6.0ms (26.9% of total)ival-sqrt: 3.0ms (13.5% of total)ival-div: 2.0ms (9% of total)ival-sub: 1.0ms (4.5% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt (+ (* z z) (* y y)))> |
#<alt (+ (* z z) (* y y))> |
#<alt (* y y)> |
#<alt (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))> |
#<alt (+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x))> |
#<alt (sqrt (+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x)))> |
#<alt (* z z)> |
#<alt (/ 1 (* (+ y z) (- y z)))> |
#<alt (* (+ y z) (- y z))> |
| Outputs |
|---|
#<alt y> |
#<alt (+ y (* 1/2 (/ (pow z 2) y)))> |
#<alt (+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))> |
#<alt (+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))> |
#<alt (* -1 z)> |
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))> |
#<alt z> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))> |
#<alt (+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))> |
#<alt y> |
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))> |
#<alt (* -1 y)> |
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))> |
#<alt (pow y 2)> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))> |
#<alt (pow z 2)> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt (+ (pow x 2) (pow z 2))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))> |
#<alt (+ (pow x 2) (pow y 2))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (pow z 2)> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))> |
#<alt (+ (pow y 2) (pow z 2))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))> |
#<alt (sqrt (+ (pow x 2) (pow z 2)))> |
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))> |
#<alt y> |
#<alt (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))> |
#<alt (* -1 y)> |
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))))> |
#<alt (sqrt (+ (pow x 2) (pow y 2)))> |
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))))> |
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))> |
#<alt (* -1 z)> |
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))))> |
#<alt (sqrt (+ (pow y 2) (pow z 2)))> |
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))> |
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))))> |
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))> |
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))> |
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (pow z 2)> |
#<alt (/ -1 (pow z 2))> |
#<alt (- (* -1 (/ (pow y 2) (pow z 4))) (/ 1 (pow z 2)))> |
#<alt (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow z 6))) (/ 1 (pow z 4)))) (/ 1 (pow z 2)))> |
#<alt (- (* (pow y 2) (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow z 8))) (/ 1 (pow z 6)))) (/ 1 (pow z 4)))) (/ 1 (pow z 2)))> |
#<alt (/ 1 (pow y 2))> |
#<alt (/ (+ 1 (* -1 (/ (+ z (* -1 z)) y))) (pow y 2))> |
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2))) (pow y 2)))) (+ (* -1 (/ z y)) (/ z y))) (pow y 2))> |
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1 (* (+ z (* -1 z)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2))))) (* (pow z 2) (+ z (* -1 z)))) (pow y 3)))) (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (+ (* -1 (/ (pow (+ z (* -1 z)) 2) (pow y 2))) (/ z y))))) (pow y 2))> |
#<alt (/ 1 (pow y 2))> |
#<alt (/ (+ 1 (* -1 (/ (+ z (* -1 z)) y))) (pow y 2))> |
#<alt (/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow z 2) y)) (* -1 (/ (pow (+ z (* -1 z)) 2) y))) (* -1 (+ z (* -1 z)))) y))) (pow y 2))> |
#<alt (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow z 2) (+ z (* -1 z))) y)) (/ (* (+ z (* -1 z)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2)))) y)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2)))) y)) (* -1 (+ z (* -1 z)))) y))) (pow y 2))> |
#<alt (/ 1 (pow y 2))> |
#<alt (+ (/ 1 (pow y 2)) (/ (pow z 2) (pow y 4)))> |
#<alt (+ (* (pow z 2) (+ (/ 1 (pow y 4)) (/ (pow z 2) (pow y 6)))) (/ 1 (pow y 2)))> |
#<alt (+ (* (pow z 2) (+ (* (pow z 2) (+ (/ 1 (pow y 6)) (/ (pow z 2) (pow y 8)))) (/ 1 (pow y 4)))) (/ 1 (pow y 2)))> |
#<alt (/ -1 (pow z 2))> |
#<alt (/ (- (* -1 (/ (+ y (* -1 y)) z)) 1) (pow z 2))> |
#<alt (/ (- (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) (pow z 2))) (+ 1 (+ (* -1 (/ y z)) (/ y z)))) (pow z 2))> |
#<alt (/ (- (* -1 (/ (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y)))) (pow z 3))) (+ 1 (+ (* -1 (/ y z)) (+ (/ y z) (+ (/ (pow y 2) (pow z 2)) (/ (pow (+ y (* -1 y)) 2) (pow z 2))))))) (pow z 2))> |
#<alt (/ -1 (pow z 2))> |
#<alt (/ (- (+ (* -1 (/ y z)) (/ y z)) 1) (pow z 2))> |
#<alt (/ (- (* -1 (/ (- (+ (/ (pow y 2) z) (/ (pow (+ y (* -1 y)) 2) z)) (+ y (* -1 y))) z)) 1) (pow z 2))> |
#<alt (/ (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) z) (/ (* (pow y 2) (+ y (* -1 y))) z)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) z)) (+ y (* -1 y))) z)) 1) (pow z 2))> |
#<alt (* -1 (pow z 2))> |
#<alt (+ (* -1 (pow z 2)) (* y (+ z (* -1 z))))> |
#<alt (+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z)))))> |
#<alt (+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z)))))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y))))> |
#<alt (* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y)))))> |
#<alt (* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y)))))> |
#<alt (pow y 2)> |
#<alt (* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y))))> |
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y))))> |
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y))))> |
#<alt (pow y 2)> |
#<alt (+ (* z (+ y (* -1 y))) (pow y 2))> |
#<alt (+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2))> |
#<alt (+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2))> |
#<alt (* -1 (pow z 2))> |
#<alt (* (pow z 2) (- (+ (* -1 (/ y z)) (/ y z)) 1))> |
#<alt (* (pow z 2) (- (+ (* -1 (/ y z)) (+ (/ y z) (/ (pow y 2) (pow z 2)))) 1))> |
#<alt (* (pow z 2) (- (+ (* -1 (/ y z)) (+ (/ y z) (/ (pow y 2) (pow z 2)))) 1))> |
#<alt (* -1 (pow z 2))> |
#<alt (* (pow z 2) (- (* -1 (/ (+ y (* -1 y)) z)) 1))> |
#<alt (* (pow z 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) z)))) z)) 1))> |
#<alt (* (pow z 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) z)))) z)) 1))> |
54 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | y | @ | inf | (sqrt (+ (* z z) (* y y))) |
| 1.0ms | y | @ | -inf | (/ 1 (* (+ y z) (- y z))) |
| 1.0ms | z | @ | 0 | (/ 1 (* (+ y z) (- y z))) |
| 1.0ms | y | @ | 0 | (/ 1 (* (+ y z) (- y z))) |
| 1.0ms | y | @ | inf | (/ 1 (* (+ y z) (- y z))) |
| 1× | batch-egg-rewrite |
| 8 928× | accelerator-lowering-fma.f32 |
| 8 928× | accelerator-lowering-fma.f64 |
| 5 846× | *-lowering-*.f32 |
| 5 846× | *-lowering-*.f64 |
| 2 842× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 65 |
| 1 | 100 | 61 |
| 2 | 884 | 61 |
| 0 | 8335 | 51 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (+ (* z z) (* y y))) |
(+ (* z z) (* y y)) |
(* y y) |
(* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z)))) |
(+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x)) |
(sqrt (+ (* (+ (* y y) (* z z)) (* (* (+ y z) (- y z)) (/ 1 (* (+ y z) (- y z))))) (* x x))) |
(* z z) |
(/ 1 (* (+ y z) (- y z))) |
(* (+ y z) (- y z)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (fma.f64 z z (*.f64 y y))) #s(literal 1/2 binary64))) |
(hypot.f64 z y) |
(hypot.f64 z (exp.f64 (log.f64 y))) |
(hypot.f64 y z) |
(hypot.f64 y (-.f64 #s(literal 0 binary64) z)) |
(hypot.f64 y (exp.f64 (log.f64 z))) |
(hypot.f64 (-.f64 #s(literal 0 binary64) z) y) |
(hypot.f64 (-.f64 #s(literal 0 binary64) z) (exp.f64 (log.f64 y))) |
(hypot.f64 (exp.f64 (log.f64 z)) y) |
(hypot.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 y))) |
(hypot.f64 (exp.f64 (log.f64 y)) z) |
(hypot.f64 (exp.f64 (log.f64 y)) (-.f64 #s(literal 0 binary64) z)) |
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 z))) |
(sqrt.f64 (fma.f64 z z (*.f64 y y))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))) (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))) (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))) (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z))) (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))))) |
(/.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z)))))) |
(/.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (sqrt.f64 (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z))) (sqrt.f64 (-.f64 y z))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 z y)) (-.f64 z y)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 z y)) (-.f64 z y)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (-.f64 #s(literal 0 binary64) (fma.f64 z z (*.f64 y y))))) (sqrt.f64 (fma.f64 y (-.f64 #s(literal 0 binary64) y) (*.f64 z z)))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (neg.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z))))) |
(pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.f64 (fma.f64 z z (*.f64 y y)))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 z z (*.f64 y y)))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (sqrt.f64 (fma.f64 z z (*.f64 y y))) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (fma.f64 z z (*.f64 y y))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 z z (*.f64 y y)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z))) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z))))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z)))) (sqrt.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))))) |
(+.f64 (*.f64 z z) (*.f64 y y)) |
(+.f64 (*.f64 y y) (*.f64 z z)) |
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(*.f64 (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (+.f64 z y))) |
(*.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 z y)) (*.f64 (+.f64 z y) (*.f64 (+.f64 z y) (-.f64 y z)))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (+.f64 z y) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (+.f64 z y))) |
(*.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))))) |
(*.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (fma.f64 z z (*.f64 y (-.f64 y z)))))) |
(*.f64 (*.f64 (-.f64 y z) (*.f64 (+.f64 z y) (*.f64 (+.f64 z y) (-.f64 y z)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z)))) |
(*.f64 (*.f64 (-.f64 y z) (*.f64 (+.f64 z y) (*.f64 (+.f64 z y) (-.f64 y z)))) (/.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))))) |
(*.f64 (*.f64 (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (fma.f64 z z (*.f64 y (-.f64 y z)))))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (-.f64 y z) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (-.f64 y z) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (-.f64 y z))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (-.f64 y z) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 y z) (fma.f64 z z (*.f64 y (+.f64 z y)))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 y z)) (-.f64 #s(literal 0 binary64) (+.f64 z y))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 z y)) (-.f64 #s(literal 0 binary64) (-.f64 y z))) |
(*.f64 (*.f64 (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 z z (*.f64 y (-.f64 y z))) (fma.f64 z z (*.f64 y (+.f64 z y)))))) |
(*.f64 (*.f64 (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (fma.f64 y (*.f64 y (*.f64 y y)) (*.f64 (*.f64 z z) (fma.f64 z z (*.f64 y y)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y))) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 y z)) (*.f64 (+.f64 z y) (*.f64 (-.f64 y z) (-.f64 y z)))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y))))) |
(*.f64 (*.f64 (-.f64 y z) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (-.f64 y z) (-.f64 y z))) (/.f64 #s(literal 1 binary64) (-.f64 y z))) |
(*.f64 (*.f64 (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y (+.f64 z y)))) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y))))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z)) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z)) (/.f64 (+.f64 z y) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (+.f64 z y)) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (+.f64 z y)) (/.f64 (-.f64 y z) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))))) |
(*.f64 (/.f64 (-.f64 y z) (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))))) |
(*.f64 (/.f64 (-.f64 y z) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z))) (/.f64 (-.f64 y z) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1 binary64)) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) #s(literal 1 binary64)) (/.f64 (-.f64 y z) (fma.f64 z z (*.f64 y y)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) #s(literal 1 binary64)) (/.f64 (+.f64 z y) (fma.f64 z z (*.f64 y y)))) |
(*.f64 (/.f64 (+.f64 z y) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))))) |
(*.f64 (/.f64 (+.f64 z y) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (+.f64 z y))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y (+.f64 z y))))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (+.f64 z y))) (/.f64 (+.f64 z y) (fma.f64 z z (*.f64 y (+.f64 z y))))) |
(*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z z (*.f64 y y))) (*.f64 (+.f64 z y) (-.f64 y z))) |
(*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (*.f64 (-.f64 y z) (*.f64 (+.f64 z y) (*.f64 (+.f64 z y) (-.f64 y z))))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))) (/.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (fma.f64 z z (*.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (fma.f64 z z (*.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (/.f64 (fma.f64 z z (*.f64 y y)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (/.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z)))) (/.f64 (-.f64 y z) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) (fma.f64 z z (*.f64 y y))) (-.f64 y z)) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (-.f64 y z) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (-.f64 y z) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (/.f64 (-.f64 y z) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (*.f64 (+.f64 z y) (*.f64 (-.f64 y z) (-.f64 y z)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z)))) (/.f64 (+.f64 z y) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) (fma.f64 z z (*.f64 y y))) (+.f64 z y)) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (+.f64 z y) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z (*.f64 z z)) (*.f64 (*.f64 y y) (*.f64 (+.f64 z y) (-.f64 y z))))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) (fma.f64 z (*.f64 z (*.f64 z (*.f64 z (*.f64 z z)))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (+.f64 z y) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (*.f64 (+.f64 z y) (-.f64 z y)) (*.f64 y (*.f64 y (*.f64 y y))))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) (*.f64 (fma.f64 z z (*.f64 y y)) (*.f64 (+.f64 z y) (-.f64 z y)))) (/.f64 (+.f64 z y) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) (*.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (fma.f64 z z (*.f64 y y)))) (*.f64 (+.f64 z y) (*.f64 (+.f64 z y) (-.f64 y z)))) |
(*.f64 (/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z y)) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))))) (/.f64 (-.f64 y z) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)) (-.f64 y z)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (/.f64 #s(literal 1 binary64) (+.f64 z y)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 z z (*.f64 y (+.f64 z y))) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z)) (-.f64 y z)) (/.f64 (fma.f64 z z (*.f64 y (-.f64 y z))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z))))) |
(*.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z)) #s(literal 1 binary64)) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y)))) |
(*.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 y z)))) (/.f64 (fma.f64 z z (*.f64 y (-.f64 y z))) (-.f64 y z))) |
(*.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (fma.f64 z (*.f64 z z) (*.f64 y (*.f64 y y))))) (/.f64 (fma.f64 z z (*.f64 y (-.f64 y z))) (fma.f64 z z (*.f64 y (-.f64 y z))))) |
(*.f64 (*.f64 (+.f64 z y) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (-.f64 y z)))) (-.f64 y z))) (fma.f64 z z (*.f64 y (-.f64 y z)))) |
(*.f64 (*.f64 (-.f64 y z) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y (+.f64 z y)))) (+.f64 z y))) (fma.f64 z z (*.f64 y (+.f64 z y)))) |
| 1× | egg-herbie |
| 7 310× | accelerator-lowering-fma.f32 |
| 7 310× | accelerator-lowering-fma.f64 |
| 3 748× | *-lowering-*.f32 |
| 3 748× | *-lowering-*.f64 |
| 3 402× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 433 | 2881 |
| 1 | 1294 | 2753 |
| 2 | 5026 | 2726 |
| 0 | 8108 | 2431 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
y |
(+ y (* 1/2 (/ (pow z 2) y))) |
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(* -1 z) |
(* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))) |
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))) |
(pow y 2) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(pow z 2) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(pow z 2) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(pow z 2) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(+ (pow y 2) (pow z 2)) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(pow y 2) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2)))) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(+ (pow x 2) (pow z 2)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(pow y 2) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) |
(+ (pow x 2) (pow y 2)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(pow z 2) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(pow z 2) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) |
(+ (pow y 2) (pow z 2)) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(+ (pow x 2) (+ (pow y 2) (pow z 2))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) |
(sqrt (+ (pow x 2) (pow z 2))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))) |
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5)))))))))) |
y |
(* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))) |
(sqrt (+ (pow x 2) (pow y 2))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))) |
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5)))))))))) |
z |
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(* -1 z) |
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))) |
(sqrt (+ (pow y 2) (pow z 2))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5)))))))))) |
x |
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(pow z 2) |
(/ -1 (pow z 2)) |
(- (* -1 (/ (pow y 2) (pow z 4))) (/ 1 (pow z 2))) |
(- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow z 6))) (/ 1 (pow z 4)))) (/ 1 (pow z 2))) |
(- (* (pow y 2) (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow z 8))) (/ 1 (pow z 6)))) (/ 1 (pow z 4)))) (/ 1 (pow z 2))) |
(/ 1 (pow y 2)) |
(/ (+ 1 (* -1 (/ (+ z (* -1 z)) y))) (pow y 2)) |
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2))) (pow y 2)))) (+ (* -1 (/ z y)) (/ z y))) (pow y 2)) |
(/ (- (+ 1 (* -1 (/ (+ (* -1 (* (+ z (* -1 z)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2))))) (* (pow z 2) (+ z (* -1 z)))) (pow y 3)))) (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (+ (* -1 (/ (pow (+ z (* -1 z)) 2) (pow y 2))) (/ z y))))) (pow y 2)) |
(/ 1 (pow y 2)) |
(/ (+ 1 (* -1 (/ (+ z (* -1 z)) y))) (pow y 2)) |
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow z 2) y)) (* -1 (/ (pow (+ z (* -1 z)) 2) y))) (* -1 (+ z (* -1 z)))) y))) (pow y 2)) |
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow z 2) (+ z (* -1 z))) y)) (/ (* (+ z (* -1 z)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2)))) y)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2)))) y)) (* -1 (+ z (* -1 z)))) y))) (pow y 2)) |
(/ 1 (pow y 2)) |
(+ (/ 1 (pow y 2)) (/ (pow z 2) (pow y 4))) |
(+ (* (pow z 2) (+ (/ 1 (pow y 4)) (/ (pow z 2) (pow y 6)))) (/ 1 (pow y 2))) |
(+ (* (pow z 2) (+ (* (pow z 2) (+ (/ 1 (pow y 6)) (/ (pow z 2) (pow y 8)))) (/ 1 (pow y 4)))) (/ 1 (pow y 2))) |
(/ -1 (pow z 2)) |
(/ (- (* -1 (/ (+ y (* -1 y)) z)) 1) (pow z 2)) |
(/ (- (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) (pow z 2))) (+ 1 (+ (* -1 (/ y z)) (/ y z)))) (pow z 2)) |
(/ (- (* -1 (/ (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y)))) (pow z 3))) (+ 1 (+ (* -1 (/ y z)) (+ (/ y z) (+ (/ (pow y 2) (pow z 2)) (/ (pow (+ y (* -1 y)) 2) (pow z 2))))))) (pow z 2)) |
(/ -1 (pow z 2)) |
(/ (- (+ (* -1 (/ y z)) (/ y z)) 1) (pow z 2)) |
(/ (- (* -1 (/ (- (+ (/ (pow y 2) z) (/ (pow (+ y (* -1 y)) 2) z)) (+ y (* -1 y))) z)) 1) (pow z 2)) |
(/ (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) z) (/ (* (pow y 2) (+ y (* -1 y))) z)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) z)) (+ y (* -1 y))) z)) 1) (pow z 2)) |
(* -1 (pow z 2)) |
(+ (* -1 (pow z 2)) (* y (+ z (* -1 z)))) |
(+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z))))) |
(+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y)))) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y))))) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y))))) |
(pow y 2) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y)))) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y)))) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y)))) |
(pow y 2) |
(+ (* z (+ y (* -1 y))) (pow y 2)) |
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2)) |
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2)) |
(* -1 (pow z 2)) |
(* (pow z 2) (- (+ (* -1 (/ y z)) (/ y z)) 1)) |
(* (pow z 2) (- (+ (* -1 (/ y z)) (+ (/ y z) (/ (pow y 2) (pow z 2)))) 1)) |
(* (pow z 2) (- (+ (* -1 (/ y z)) (+ (/ y z) (/ (pow y 2) (pow z 2)))) 1)) |
(* -1 (pow z 2)) |
(* (pow z 2) (- (* -1 (/ (+ y (* -1 y)) z)) 1)) |
(* (pow z 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) z)))) z)) 1)) |
(* (pow z 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) z)))) z)) 1)) |
| Outputs |
|---|
y |
(+ y (* 1/2 (/ (pow z 2) y))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z #s(literal 0 binary64)) y) y) |
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (fma.f64 z z #s(literal 0 binary64)) (*.f64 y (fma.f64 y y #s(literal 0 binary64)))) (/.f64 #s(literal 1/2 binary64) y)) y) |
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 z z #s(literal 0 binary64)) (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 y (fma.f64 y y #s(literal 0 binary64))))) (/.f64 #s(literal 1/2 binary64) y)) y) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) #s(literal 1 binary64)))) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 z #s(literal 6 binary64))))) z) |
(* -1 z) |
(-.f64 #s(literal 0 binary64) z) |
(* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) z)) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) #s(literal 1 binary64))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 z #s(literal 6 binary64))))) z)) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) z) z) |
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 z (fma.f64 z z #s(literal 0 binary64)))) (/.f64 #s(literal 1/2 binary64) z)) z) |
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z))))) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 #s(literal 1/16 binary64) (*.f64 y (/.f64 y (pow.f64 z #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 z (fma.f64 z z #s(literal 0 binary64))))) (/.f64 #s(literal 1/2 binary64) z)) z) |
y |
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))) |
(*.f64 y (fma.f64 #s(literal 1/2 binary64) (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(*.f64 y (fma.f64 #s(literal 1/2 binary64) (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64)))) #s(literal 1 binary64)))) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64)))) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (pow.f64 y #s(literal 6 binary64))))) y) |
(* -1 y) |
(-.f64 #s(literal 0 binary64) y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64)))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) y)) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64)))) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (pow.f64 y #s(literal 6 binary64))))) y)) |
(pow y 2) |
(fma.f64 y y #s(literal 0 binary64)) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) |
(+ (pow y 2) (pow z 2)) |
(fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
(*.f64 z (*.f64 z (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64)))) |
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2)))) |
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(*.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 z z #s(literal 0 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) #s(literal 1 binary64)))) |
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(fma.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 z z #s(literal 0 binary64))) (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (fma.f64 y y (*.f64 x x))) (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x)))) (pow.f64 z #s(literal 6 binary64))))) z) |
(* -1 z) |
(-.f64 #s(literal 0 binary64) z) |
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))) |
(*.f64 (-.f64 #s(literal 0 binary64) z) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 z z #s(literal 0 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) #s(literal 1 binary64))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 z z #s(literal 0 binary64))) (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (fma.f64 y y (*.f64 x x))) (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x)))) (pow.f64 z #s(literal 6 binary64))))) z)) |
(sqrt (+ (pow y 2) (pow z 2))) |
(sqrt.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))))) (sqrt.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))))) (sqrt.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))) |
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5)))))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) #s(literal 5 binary64)))) (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))))) (sqrt.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))) |
x |
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 x x)) #s(literal 1 binary64))) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 x x)) #s(literal 1 binary64)))) |
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(fma.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 x x)) (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))))) x) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))) |
(*.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 x x)) (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))))) x)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(pow z 2) |
(fma.f64 z z #s(literal 0 binary64)) |
(/ -1 (pow z 2)) |
(/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(- (* -1 (/ (pow y 2) (pow z 4))) (/ 1 (pow z 2))) |
(/.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow z 6))) (/ 1 (pow z 4)))) (/ 1 (pow z 2))) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (pow.f64 z #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(- (* (pow y 2) (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow z 8))) (/ 1 (pow z 6)))) (/ 1 (pow z 4)))) (/ 1 (pow z 2))) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 y (pow.f64 z #s(literal 8 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 z #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))))) (/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(/ 1 (pow y 2)) |
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) |
(/ (+ 1 (* -1 (/ (+ z (* -1 z)) y))) (pow y 2)) |
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) |
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2))) (pow y 2)))) (+ (* -1 (/ z y)) (/ z y))) (pow y 2)) |
(/.f64 (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64)) (fma.f64 y y #s(literal 0 binary64))) |
(/ (- (+ 1 (* -1 (/ (+ (* -1 (* (+ z (* -1 z)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2))))) (* (pow z 2) (+ z (* -1 z)))) (pow y 3)))) (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (+ (* -1 (/ (pow (+ z (* -1 z)) 2) (pow y 2))) (/ z y))))) (pow y 2)) |
(/.f64 (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64)) (fma.f64 y y #s(literal 0 binary64))) |
(/ 1 (pow y 2)) |
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) |
(/ (+ 1 (* -1 (/ (+ z (* -1 z)) y))) (pow y 2)) |
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) |
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow z 2) y)) (* -1 (/ (pow (+ z (* -1 z)) 2) y))) (* -1 (+ z (* -1 z)))) y))) (pow y 2)) |
(/.f64 (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64)) (fma.f64 y y #s(literal 0 binary64))) |
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow z 2) (+ z (* -1 z))) y)) (/ (* (+ z (* -1 z)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2)))) y)) (+ (* -1 (pow z 2)) (* -1 (pow (+ z (* -1 z)) 2)))) y)) (* -1 (+ z (* -1 z)))) y))) (pow y 2)) |
(/.f64 (fma.f64 z (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64)) (fma.f64 y y #s(literal 0 binary64))) |
(/ 1 (pow y 2)) |
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) |
(+ (/ 1 (pow y 2)) (/ (pow z 2) (pow y 4))) |
(fma.f64 z (/.f64 z (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))) |
(+ (* (pow z 2) (+ (/ 1 (pow y 4)) (/ (pow z 2) (pow y 6)))) (/ 1 (pow y 2))) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z (/.f64 z (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))) |
(+ (* (pow z 2) (+ (* (pow z 2) (+ (/ 1 (pow y 6)) (/ (pow z 2) (pow y 8)))) (/ 1 (pow y 4)))) (/ 1 (pow y 2))) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z (/.f64 z (pow.f64 y #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))) |
(/ -1 (pow z 2)) |
(/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(/ (- (* -1 (/ (+ y (* -1 y)) z)) 1) (pow z 2)) |
(/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(/ (- (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) (pow z 2))) (+ 1 (+ (* -1 (/ y z)) (/ y z)))) (pow z 2)) |
(/.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(/ (- (* -1 (/ (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y)))) (pow z 3))) (+ 1 (+ (* -1 (/ y z)) (+ (/ y z) (+ (/ (pow y 2) (pow z 2)) (/ (pow (+ y (* -1 y)) 2) (pow z 2))))))) (pow z 2)) |
(/.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(/ -1 (pow z 2)) |
(/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(/ (- (+ (* -1 (/ y z)) (/ y z)) 1) (pow z 2)) |
(/.f64 #s(literal -1 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(/ (- (* -1 (/ (- (+ (/ (pow y 2) z) (/ (pow (+ y (* -1 y)) 2) z)) (+ y (* -1 y))) z)) 1) (pow z 2)) |
(/.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(/ (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) z) (/ (* (pow y 2) (+ y (* -1 y))) z)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) z)) (+ y (* -1 y))) z)) 1) (pow z 2)) |
(/.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(* -1 (pow z 2)) |
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(+ (* -1 (pow z 2)) (* y (+ z (* -1 z)))) |
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z))))) |
(fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)) |
(+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z))))) |
(fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)) |
(pow y 2) |
(fma.f64 y y #s(literal 0 binary64)) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y)))) |
(fma.f64 y y #s(literal 0 binary64)) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y))))) |
(fma.f64 y (*.f64 y (fma.f64 (-.f64 #s(literal 0 binary64) z) (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y))))) |
(fma.f64 y (*.f64 y (fma.f64 (-.f64 #s(literal 0 binary64) z) (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)) |
(pow y 2) |
(fma.f64 y y #s(literal 0 binary64)) |
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y)))) |
(fma.f64 y y #s(literal 0 binary64)) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y)))) |
(fma.f64 y (*.f64 y (fma.f64 (-.f64 #s(literal 0 binary64) z) (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y)))) |
(fma.f64 y (*.f64 y (fma.f64 (-.f64 #s(literal 0 binary64) z) (/.f64 z (fma.f64 y y #s(literal 0 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)) |
(pow y 2) |
(fma.f64 y y #s(literal 0 binary64)) |
(+ (* z (+ y (* -1 y))) (pow y 2)) |
(fma.f64 y y #s(literal 0 binary64)) |
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2)) |
(fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)) |
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2)) |
(fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)) |
(* -1 (pow z 2)) |
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(* (pow z 2) (- (+ (* -1 (/ y z)) (/ y z)) 1)) |
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(* (pow z 2) (- (+ (* -1 (/ y z)) (+ (/ y z) (/ (pow y 2) (pow z 2)))) 1)) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64)) |
(* (pow z 2) (- (+ (* -1 (/ y z)) (+ (/ y z) (/ (pow y 2) (pow z 2)))) 1)) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64)) |
(* -1 (pow z 2)) |
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(* (pow z 2) (- (* -1 (/ (+ y (* -1 y)) z)) 1)) |
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64))) |
(* (pow z 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) z)))) z)) 1)) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64)) |
(* (pow z 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) z)))) z)) 1)) |
(fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64)) |
Compiled 43 474 to 4 012 computations (90.8% saved)
4 alts after pruning (2 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 205 | 2 | 1 207 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 0 | 0 |
| Total | 1 206 | 4 | 1 210 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (hypot.f64 z y) |
| ▶ | 96.3% | (*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
| ✓ | 43.1% | (sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| ✓ | 97.9% | z |
Compiled 37 to 24 computations (35.1% saved)
| 1× | egg-herbie |
Found 5 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 5056 | (hypot.f64 z y) |
| ✓ | cost-diff | 0 | (/.f64 y (fma.f64 z z #s(literal 0 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 704 | (*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
| 5 406× | *-lowering-*.f32 |
| 5 406× | *-lowering-*.f64 |
| 3 082× | /-lowering-/.f32 |
| 3 082× | /-lowering-/.f64 |
| 1 830× | cube-prod |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 54 |
| 1 | 39 | 54 |
| 2 | 83 | 54 |
| 3 | 251 | 54 |
| 4 | 659 | 50 |
| 5 | 1156 | 50 |
| 6 | 1596 | 50 |
| 7 | 2692 | 50 |
| 8 | 3154 | 50 |
| 9 | 3206 | 50 |
| 10 | 3251 | 50 |
| 11 | 3321 | 50 |
| 12 | 3433 | 50 |
| 13 | 4547 | 50 |
| 14 | 4975 | 50 |
| 15 | 5368 | 50 |
| 16 | 5798 | 50 |
| 17 | 6260 | 50 |
| 18 | 6807 | 50 |
| 19 | 7319 | 50 |
| 20 | 7650 | 50 |
| 21 | 7811 | 50 |
| 22 | 7902 | 50 |
| 23 | 7907 | 50 |
| 0 | 8294 | 43 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
z |
(+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1) |
1/2 |
(+ (* y (/ y (+ (* z z) 0))) 0) |
y |
(/ y (+ (* z z) 0)) |
(+ (* z z) 0) |
0 |
1 |
(sqrt (+ (* z z) (* y y))) |
z |
y |
| Outputs |
|---|
(* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
(fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y z) #s(literal 0 binary64)) z) |
z |
(+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ (* y (/ y (+ (* z z) 0))) 0) |
(fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) |
y |
(/ y (+ (* z z) 0)) |
(/.f64 y (fma.f64 z z #s(literal 0 binary64))) |
(+ (* z z) 0) |
(fma.f64 z z #s(literal 0 binary64)) |
0 |
#s(literal 0 binary64) |
1 |
#s(literal 1 binary64) |
(sqrt (+ (* z z) (* y y))) |
(sqrt.f64 (fma.f64 z z (fma.f64 y y #s(literal 0 binary64)))) |
z |
y |
Found 5 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (hypot.f64 z y) |
| ✓ | accuracy | 100.0% | (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
| ✓ | accuracy | 86.2% | (/.f64 y (fma.f64 z z #s(literal 0 binary64))) |
| ✓ | accuracy | 86.0% | (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) |
| 40.0ms | 256× | 0 | valid |
Compiled 57 to 17 computations (70.2% saved)
ival-hypot: 19.0ms (63% of total)ival-mult: 6.0ms (19.9% of total)ival-add: 3.0ms (9.9% of total)ival-div: 2.0ms (6.6% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1))> |
#<alt (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)> |
#<alt (+ (* y (/ y (+ (* z z) 0))) 0)> |
#<alt (/ y (+ (* z z) 0))> |
#<alt (sqrt (+ (* z z) (* y y)))> |
| Outputs |
|---|
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt z> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt z> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ (pow y 2) (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt (/ y (pow z 2))> |
#<alt y> |
#<alt (+ y (* 1/2 (/ (pow z 2) y)))> |
#<alt (+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))> |
#<alt (+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))> |
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))> |
#<alt (* -1 z)> |
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))> |
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))> |
#<alt z> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))> |
#<alt (+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))> |
#<alt y> |
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))> |
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))> |
#<alt (* -1 y)> |
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))> |
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))> |
30 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | z | @ | 0 | (* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
| 1.0ms | y | @ | inf | (* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
| 1.0ms | y | @ | 0 | (* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
| 0.0ms | y | @ | inf | (/ y (+ (* z z) 0)) |
| 0.0ms | z | @ | inf | (* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
| 1× | batch-egg-rewrite |
| 12 268× | accelerator-lowering-fma.f32 |
| 12 268× | accelerator-lowering-fma.f64 |
| 6 004× | *-lowering-*.f32 |
| 6 004× | *-lowering-*.f64 |
| 3 850× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 44 |
| 1 | 98 | 44 |
| 2 | 907 | 38 |
| 0 | 9155 | 31 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* z (+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1)) |
(+ (* 1/2 (+ (* y (/ y (+ (* z z) 0))) 0)) 1) |
(+ (* y (/ y (+ (* z z) 0))) 0) |
(/ y (+ (* z z) 0)) |
(sqrt (+ (* z z) (* y y))) |
| Outputs |
|---|
(+.f64 z (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
(+.f64 (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) z) |
(+.f64 (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) z)) |
(+.f64 (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) |
(-.f64 (/.f64 (*.f64 (fma.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (fma.f64 y y #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal -1 binary64)))) (/.f64 (fma.f64 z z #s(literal 0 binary64)) (*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal -1 binary64))))) |
(fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) z) |
(fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 z #s(literal 1 binary64) (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
(fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (fma.f64 z (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) z) |
(fma.f64 #s(literal 1/2 binary64) (fma.f64 z (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 y (*.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 #s(literal 1/2 binary64) z)) z) |
(fma.f64 y (*.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 #s(literal 1/2 binary64) z)) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 y (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 z z #s(literal 0 binary64)))) z) z) |
(fma.f64 y (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 z z #s(literal 0 binary64)))) z) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 #s(literal 1/2 binary64) z)) z) |
(fma.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 #s(literal 1/2 binary64) z)) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (*.f64 y #s(literal 1/2 binary64)) z) z) |
(fma.f64 (/.f64 y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (*.f64 y #s(literal 1/2 binary64)) z) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) (*.f64 #s(literal 1/2 binary64) z) z) |
(fma.f64 (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) (*.f64 #s(literal 1/2 binary64) z) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) z z) |
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) z (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 #s(literal 1 binary64) z (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
(fma.f64 #s(literal 1 binary64) (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) z) |
(fma.f64 #s(literal 1 binary64) (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 #s(literal 1 binary64) (fma.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) |
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64)) z #s(literal 0 binary64)) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z #s(literal 0 binary64))) (*.f64 #s(literal 1/2 binary64) z)) z) |
(fma.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z #s(literal 0 binary64))) (*.f64 #s(literal 1/2 binary64) z)) (+.f64 #s(literal 0 binary64) z)) |
(fma.f64 (fma.f64 (*.f64 y (fma.f64 y y #s(literal 0 binary64))) (/.f64 (*.f64 y (fma.f64 y y #s(literal 0 binary64))) (fma.f64 z (*.f64 z (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) #s(literal 0 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 y y #s(literal 0 binary64)) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) (*.f64 #s(literal 1/2 binary64) z)) z) |
(fma.f64 (fma.f64 (*.f64 y (fma.f64 y y #s(literal 0 binary64))) (/.f64 (*.f64 y (fma.f64 y y #s(literal 0 binary64))) (fma.f64 z (*.f64 z (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) #s(literal 0 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 y y #s(literal 0 binary64)) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) (*.f64 #s(literal 1/2 binary64) z)) (+.f64 #s(literal 0 binary64) z)) |
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(*.f64 (*.f64 (/.f64 y (fma.f64 z (*.f64 z (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) (fma.f64 z z #s(literal 0 binary64))) (fma.f64 z z #s(literal 0 binary64))) |
(*.f64 (*.f64 (/.f64 y (fma.f64 z (*.f64 z (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) z) |
(*.f64 (*.f64 (/.f64 y (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) z) z) |
(*.f64 (*.f64 (/.f64 y (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 z (*.f64 z (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(*.f64 (*.f64 (/.f64 y (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 z z #s(literal 0 binary64)))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) #s(literal 1/2 binary64))) |
(hypot.f64 z y) |
(hypot.f64 z (exp.f64 (log.f64 y))) |
(hypot.f64 y z) |
(hypot.f64 y (-.f64 #s(literal 0 binary64) z)) |
(hypot.f64 y (exp.f64 (log.f64 z))) |
(hypot.f64 y (/.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) |
(hypot.f64 y (/.f64 (fma.f64 z z #s(literal 0 binary64)) z)) |
(hypot.f64 (-.f64 #s(literal 0 binary64) z) y) |
(hypot.f64 (-.f64 #s(literal 0 binary64) z) (exp.f64 (log.f64 y))) |
(hypot.f64 (exp.f64 (log.f64 z)) y) |
(hypot.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 y))) |
(hypot.f64 (exp.f64 (log.f64 y)) z) |
(hypot.f64 (exp.f64 (log.f64 y)) (-.f64 #s(literal 0 binary64) z)) |
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 z))) |
(hypot.f64 (exp.f64 (log.f64 y)) (/.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64)))) |
(hypot.f64 (exp.f64 (log.f64 y)) (/.f64 (fma.f64 z z #s(literal 0 binary64)) z)) |
(hypot.f64 (/.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) y) |
(hypot.f64 (/.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (exp.f64 (log.f64 y))) |
(hypot.f64 (/.f64 (fma.f64 z z #s(literal 0 binary64)) z) y) |
(hypot.f64 (/.f64 (fma.f64 z z #s(literal 0 binary64)) z) (exp.f64 (log.f64 y))) |
(sqrt.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64))))) (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64)))))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))) (sqrt.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y)))))) |
(/.f64 (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64)))))))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)))))) |
(/.f64 (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64)))))))) (sqrt.f64 (fma.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64))) (*.f64 (fma.f64 z z #s(literal 0 binary64)) (*.f64 (+.f64 z y) (-.f64 z y)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y)))) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64))))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64))))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)) #s(literal 0 binary64))) (sqrt.f64 (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64)))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64))))))))) (neg.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64))))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))) |
(pow.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (fma.f64 y y (fma.f64 z z #s(literal 0 binary64)))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 (log.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))))) #s(literal 1/2 binary64)) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64)))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64)))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64))))))) |
(*.f64 (sqrt.f64 (fma.f64 z (*.f64 (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 z z #s(literal 0 binary64))) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (fma.f64 y y #s(literal 0 binary64)))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z z #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) #s(literal 0 binary64))))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y)))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) (*.f64 (+.f64 z y) (-.f64 z y)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))) |
(*.f64 (pow.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 y y (fma.f64 z z #s(literal 0 binary64))) #s(literal 1/4 binary64))) |
| 1× | egg-herbie |
| 22 120× | accelerator-lowering-fma.f32 |
| 22 120× | accelerator-lowering-fma.f64 |
| 4 966× | *-lowering-*.f32 |
| 4 966× | *-lowering-*.f64 |
| 2 570× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 117 | 1178 |
| 1 | 318 | 1178 |
| 2 | 1020 | 1176 |
| 3 | 3843 | 1082 |
| 4 | 7556 | 1082 |
| 0 | 8031 | 1014 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (/ (pow y 2) z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
z |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ (pow y 2) (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
(/ y (pow z 2)) |
y |
(+ y (* 1/2 (/ (pow z 2) y))) |
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(* -1 z) |
(* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))) |
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z))))) |
y |
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(* -1 y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))) |
| Outputs |
|---|
(* 1/2 (/ (pow y 2) z)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) z) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
z |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* 1/2 (/ (pow y 2) z)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* 1/2 (/ (pow y 2) z)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) (*.f64 z z)) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) (*.f64 z z)) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) (*.f64 z z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) (*.f64 z z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) (*.f64 z z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) (*.f64 z z)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ (pow y 2) (pow z 2)) |
(/.f64 (*.f64 y y) (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
(/ y (pow z 2)) |
(/.f64 y (*.f64 z z)) |
y |
(+ y (* 1/2 (/ (pow z 2) y))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 z z) y) y) |
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y))))) |
(fma.f64 (/.f64 (*.f64 z z) y) (fma.f64 #s(literal -1/8 binary64) (*.f64 z (/.f64 z (*.f64 y y))) #s(literal 1/2 binary64)) y) |
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) |
(fma.f64 (*.f64 z z) (fma.f64 (*.f64 z z) (fma.f64 (*.f64 z z) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1/2 binary64) y)) y) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(fma.f64 z (fma.f64 (*.f64 y (*.f64 y (*.f64 y y))) (/.f64 #s(literal -1/8 binary64) (*.f64 z (*.f64 z (*.f64 z z)))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z)) |
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(fma.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 z (*.f64 z (*.f64 z z)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z)) |
(* -1 z) |
(-.f64 #s(literal 0 binary64) z) |
(* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z)) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 z (fma.f64 (*.f64 y (*.f64 y (*.f64 y y))) (/.f64 #s(literal -1/8 binary64) (*.f64 z (*.f64 z (*.f64 z z)))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z))) |
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 z (*.f64 z (*.f64 z z)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y y)) z))) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))) |
(fma.f64 (/.f64 (*.f64 y y) z) (fma.f64 (*.f64 y y) (/.f64 #s(literal -1/8 binary64) (*.f64 z z)) #s(literal 1/2 binary64)) z) |
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z))))) |
(fma.f64 (*.f64 y y) (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 (/.f64 y (pow.f64 z #s(literal 5 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 z (*.f64 z z)))) (/.f64 #s(literal 1/2 binary64) z)) z) |
y |
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 z z) y) y) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(fma.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 z (*.f64 z (*.f64 z z))) (*.f64 y (*.f64 y (*.f64 y y)))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 z z)) y)) |
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(fma.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 z (*.f64 z (*.f64 z z))) (*.f64 y (*.f64 y (*.f64 y y)))) (fma.f64 (pow.f64 z #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 z z)) y)) |
(* -1 y) |
(-.f64 #s(literal 0 binary64) y) |
(* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 z z) y) y)) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 z (*.f64 z (*.f64 z z))) (*.f64 y (*.f64 y (*.f64 y y)))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 z z)) y))) |
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))) |
(-.f64 #s(literal 0 binary64) (fma.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 z (*.f64 z (*.f64 z z))) (*.f64 y (*.f64 y (*.f64 y y)))) (fma.f64 (pow.f64 z #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 z z)) y))) |
Compiled 38 488 to 2 915 computations (92.4% saved)
6 alts after pruning (3 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 999 | 3 | 1 002 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 1 | 2 |
| Done | 0 | 2 | 2 |
| Total | 1 000 | 6 | 1 006 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 98.5% | (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) z) |
| ✓ | 100.0% | (hypot.f64 z y) |
| ▶ | 98.5% | (*.f64 z (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
| ▶ | 81.6% | (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64))) |
| ✓ | 43.1% | (sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| ✓ | 97.9% | z |
Compiled 65 to 40 computations (38.5% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) z) |
| ✓ | cost-diff | 0 | (/.f64 y z) |
| ✓ | cost-diff | 0 | (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) z) |
| ✓ | cost-diff | 1024 | (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 y z) |
| ✓ | cost-diff | 384 | (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 640 | (*.f64 z (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) |
| ✓ | cost-diff | 0 | (*.f64 y y) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 640 | (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64))) |
| 6 030× | *-lowering-*.f32 |
| 6 030× | *-lowering-*.f64 |
| 3 876× | associate-*r/ |
| 2 548× | /-lowering-/.f32 |
| 2 548× | /-lowering-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 104 |
| 1 | 60 | 104 |
| 2 | 150 | 104 |
| 3 | 492 | 88 |
| 4 | 921 | 88 |
| 5 | 1269 | 88 |
| 6 | 1824 | 88 |
| 7 | 2331 | 88 |
| 8 | 2364 | 88 |
| 9 | 2377 | 88 |
| 10 | 2385 | 88 |
| 11 | 2393 | 88 |
| 12 | 2401 | 88 |
| 13 | 2846 | 88 |
| 14 | 2866 | 88 |
| 15 | 2876 | 88 |
| 16 | 2884 | 88 |
| 17 | 2892 | 88 |
| 18 | 2900 | 88 |
| 19 | 2908 | 88 |
| 20 | 2916 | 88 |
| 21 | 6022 | 88 |
| 22 | 6124 | 88 |
| 23 | 6142 | 88 |
| 24 | 6182 | 88 |
| 25 | 6250 | 88 |
| 26 | 6376 | 88 |
| 27 | 7493 | 88 |
| 28 | 7779 | 88 |
| 0 | 8035 | 83 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* z (+ (* (* y y) (/ 1/2 (* z z))) 1)) |
z |
(+ (* (* y y) (/ 1/2 (* z z))) 1) |
(* y y) |
y |
(/ 1/2 (* z z)) |
1/2 |
(* z z) |
1 |
(* z (+ (* (/ y z) (* (/ y z) 1/2)) 1)) |
z |
(+ (* (/ y z) (* (/ y z) 1/2)) 1) |
(/ y z) |
y |
(* (/ y z) 1/2) |
1/2 |
1 |
(+ (* (/ y z) (* (/ y z) (* 1/2 z))) z) |
(/ y z) |
y |
z |
(* (/ y z) (* 1/2 z)) |
(* 1/2 z) |
1/2 |
| Outputs |
|---|
(* z (+ (* (* y y) (/ 1/2 (* z z))) 1)) |
(fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z) |
z |
(+ (* (* y y) (/ 1/2 (* z z))) 1) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(* y y) |
(*.f64 y y) |
y |
(/ 1/2 (* z z)) |
(/.f64 #s(literal 1/2 binary64) (*.f64 z z)) |
1/2 |
#s(literal 1/2 binary64) |
(* z z) |
(*.f64 z z) |
1 |
#s(literal 1 binary64) |
(* z (+ (* (/ y z) (* (/ y z) 1/2)) 1)) |
(fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z) |
z |
(+ (* (/ y z) (* (/ y z) 1/2)) 1) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
(/ y z) |
(/.f64 y z) |
y |
(* (/ y z) 1/2) |
(/.f64 (*.f64 y #s(literal 1/2 binary64)) z) |
1/2 |
#s(literal 1/2 binary64) |
1 |
#s(literal 1 binary64) |
(+ (* (/ y z) (* (/ y z) (* 1/2 z))) z) |
(fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z) |
(/ y z) |
(/.f64 y z) |
y |
z |
(* (/ y z) (* 1/2 z)) |
(*.f64 y #s(literal 1/2 binary64)) |
(* 1/2 z) |
(*.f64 z #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (/.f64 y z) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) z) |
| ✓ | accuracy | 100.0% | (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) z) |
| ✓ | accuracy | 87.7% | (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) |
| ✓ | accuracy | 100.0% | (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (/.f64 y z) |
| ✓ | accuracy | 100.0% | (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 z (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 y y) |
| ✓ | accuracy | 100.0% | (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64))) |
| ✓ | accuracy | 99.2% | (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) |
| ✓ | accuracy | 83.0% | (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64)) |
| 34.0ms | 256× | 0 | valid |
Compiled 101 to 22 computations (78.2% saved)
ival-mult: 15.0ms (67.9% of total)ival-div: 3.0ms (13.6% of total)ival-add: 3.0ms (13.6% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* z (+ (* (* y y) (/ 1/2 (* z z))) 1))> |
#<alt (+ (* (* y y) (/ 1/2 (* z z))) 1)> |
#<alt (* y y)> |
#<alt (/ 1/2 (* z z))> |
#<alt (* z (+ (* (/ y z) (* (/ y z) 1/2)) 1))> |
#<alt (+ (* (/ y z) (* (/ y z) 1/2)) 1)> |
#<alt (/ y z)> |
#<alt (* (/ y z) 1/2)> |
#<alt (* (/ y z) (* 1/2 z))> |
#<alt (+ (* (/ y z) (* (/ y z) (* 1/2 z))) z)> |
#<alt (* 1/2 z)> |
| Outputs |
|---|
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt z> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt z> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (pow y 2)> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (/ 1/2 (pow z 2))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt z> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt z> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))> |
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (/ y z)> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 (/ y z))> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt (* 1/2 y)> |
#<alt z> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (+ z (* 1/2 (/ (pow y 2) z)))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))> |
#<alt (* 1/2 (/ (pow y 2) z))> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)> |
#<alt z> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))> |
#<alt z> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
#<alt (* 1/2 z)> |
57 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | y | @ | inf | (/ y z) |
| 0.0ms | y | @ | inf | (+ (* (/ y z) (* (/ y z) (* 1/2 z))) z) |
| 0.0ms | y | @ | 0 | (/ y z) |
| 0.0ms | y | @ | -inf | (* (/ y z) 1/2) |
| 0.0ms | z | @ | inf | (+ (* (/ y z) (* (/ y z) (* 1/2 z))) z) |
| 1× | batch-egg-rewrite |
| 7 974× | accelerator-lowering-fma.f32 |
| 7 974× | accelerator-lowering-fma.f64 |
| 4 952× | *-lowering-*.f32 |
| 4 952× | *-lowering-*.f64 |
| 2 426× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 87 |
| 1 | 112 | 77 |
| 2 | 965 | 77 |
| 3 | 7936 | 77 |
| 0 | 8978 | 72 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* z (+ (* (* y y) (/ 1/2 (* z z))) 1)) |
(+ (* (* y y) (/ 1/2 (* z z))) 1) |
(* y y) |
(/ 1/2 (* z z)) |
(* z (+ (* (/ y z) (* (/ y z) 1/2)) 1)) |
(+ (* (/ y z) (* (/ y z) 1/2)) 1) |
(/ y z) |
(* (/ y z) 1/2) |
(* (/ y z) (* 1/2 z)) |
(+ (* (/ y z) (* (/ y z) (* 1/2 z))) z) |
(* 1/2 z) |
| Outputs |
|---|
(+.f64 z (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))) |
(+.f64 (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) z) |
(+.f64 (/.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 z z) (*.f64 (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1/4 binary64)))) (*.f64 (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))) (*.f64 z z))) (neg.f64 (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))))))) |
(-.f64 (/.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 z z) (*.f64 (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1/4 binary64)))) (*.f64 (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))) (*.f64 z z))) (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))))) |
(-.f64 (/.f64 (*.f64 z z) (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))) (/.f64 (*.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z)))) (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64))))) |
(fma.f64 z (/.f64 (*.f64 y y) (*.f64 z (*.f64 z #s(literal 2 binary64)))) z) |
(fma.f64 z #s(literal 1 binary64) (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))) |
(fma.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))) z) |
(fma.f64 y (/.f64 (/.f64 (*.f64 z #s(literal 1/2 binary64)) z) (/.f64 z y)) z) |
(fma.f64 (*.f64 y y) (*.f64 z (/.f64 #s(literal 1/2 binary64) (*.f64 z z))) z) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 z (/.f64 (*.f64 y y) (*.f64 z z))) z) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 z (/.f64 y z)) (/.f64 z y)) z) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) (*.f64 z (*.f64 y y)) z) |
(fma.f64 (/.f64 (*.f64 y y) (*.f64 z (*.f64 z #s(literal 2 binary64)))) z z) |
(fma.f64 #s(literal 1 binary64) z (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))) |
(fma.f64 #s(literal 1 binary64) (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) z) |
(fma.f64 (/.f64 y z) (*.f64 z (*.f64 #s(literal 1/2 binary64) (/.f64 y z))) z) |
(fma.f64 (/.f64 y z) (/.f64 (*.f64 (*.f64 (/.f64 (*.f64 y (*.f64 y y)) (*.f64 z (*.f64 z z))) (*.f64 z #s(literal 1/2 binary64))) (*.f64 z #s(literal 1/2 binary64))) (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))) (neg.f64 (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y z)) (*.f64 z (/.f64 y z)) z) |
(fma.f64 (*.f64 z #s(literal 1/2 binary64)) (/.f64 (*.f64 y y) (*.f64 z z)) z) |
(fma.f64 (*.f64 z (*.f64 #s(literal 1/2 binary64) (/.f64 y z))) (/.f64 y z) z) |
(fma.f64 (*.f64 z (*.f64 #s(literal 1/2 binary64) (/.f64 y z))) (/.f64 (*.f64 (/.f64 (*.f64 y (*.f64 y y)) (*.f64 z (*.f64 z z))) (*.f64 z #s(literal 1/2 binary64))) (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))) (neg.f64 (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))))))) |
(fma.f64 (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) #s(literal 1 binary64) z) |
(fma.f64 (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) (/.f64 (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))) (neg.f64 (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))))))) |
(fma.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 (*.f64 z (*.f64 #s(literal 1/2 binary64) (/.f64 y z))) (-.f64 #s(literal 0 binary64) z)) z) |
(fma.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 (*.f64 z (*.f64 y #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 z z))) z) |
(fma.f64 (*.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z)))) (/.f64 #s(literal 1 binary64) (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))) (neg.f64 (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) z) (*.f64 z (/.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) z)) z) |
(fma.f64 (/.f64 #s(literal 1 binary64) z) (/.f64 (*.f64 z (*.f64 #s(literal 1/2 binary64) (/.f64 y z))) (/.f64 #s(literal 1 binary64) y)) z) |
(fma.f64 (/.f64 (*.f64 y y) (*.f64 z z)) (*.f64 z #s(literal 1/2 binary64)) z) |
(fma.f64 (/.f64 (*.f64 y y) (*.f64 z z)) (/.f64 (*.f64 z #s(literal 1/2 binary64)) #s(literal 1 binary64)) z) |
(fma.f64 (/.f64 (*.f64 y y) (*.f64 z z)) (/.f64 (*.f64 (*.f64 z z) (*.f64 (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1/4 binary64))) (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))) (neg.f64 (*.f64 z (/.f64 z (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))))))) |
(fma.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))) (*.f64 z y) z) |
(fma.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))) (/.f64 z (/.f64 #s(literal 1 binary64) y)) z) |
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (*.f64 z z)) z) |
(fma.f64 (*.f64 z (*.f64 y #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 z z)) y) z) |
(fma.f64 (*.f64 z (*.f64 y #s(literal 1/2 binary64))) (/.f64 (/.f64 y z) z) z) |
(fma.f64 (*.f64 z (*.f64 y #s(literal 1/2 binary64))) (/.f64 y (*.f64 z z)) z) |
(fma.f64 (*.f64 z (*.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 z (/.f64 z y))) z) |
(fma.f64 (*.f64 z (*.f64 y #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 z z))) z) |
(fma.f64 (*.f64 z (/.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) z)) (/.f64 #s(literal 1 binary64) z) z) |
(fma.f64 (/.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) z) (/.f64 z z) z) |
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(*.f64 (*.f64 z (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) (-.f64 #s(literal 0 binary64) (*.f64 z z))) (fma.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) (-.f64 #s(literal 0 binary64) (*.f64 z z)))) (*.f64 z (fma.f64 y (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1/8 binary64)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))) (fma.f64 (*.f64 z (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))) (*.f64 (*.f64 z z) (*.f64 (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64))) (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64))))) (pow.f64 (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) #s(literal 6 binary64)))) (fma.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1/8 binary64)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (*.f64 z (*.f64 z z))) (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) (*.f64 (*.f64 z (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))) (-.f64 (*.f64 z (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))) (*.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z)))))))) |
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1/8 binary64)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))) (*.f64 (fma.f64 (*.f64 y (*.f64 z (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))))) (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal -1 binary64))) (*.f64 z z)) (-.f64 (*.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z)))) (*.f64 z (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64))))))) (-.f64 (*.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z)))) (*.f64 z (*.f64 z (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) (-.f64 #s(literal 0 binary64) (*.f64 z z))) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1/8 binary64)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (*.f64 z (*.f64 z z)) (neg.f64 (*.f64 z (*.f64 z z))))) (fma.f64 z (*.f64 z (fma.f64 y (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))) #s(literal 1 binary64))) (*.f64 (*.f64 z z) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z)))))) |
(*.f64 (/.f64 (*.f64 z (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))))) #s(literal 1 binary64))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64))) (pow.f64 (/.f64 (*.f64 y y) (*.f64 z (*.f64 z #s(literal 2 binary64)))) #s(literal 6 binary64)))) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 y y) (*.f64 y y))) #s(literal 1/8 binary64)) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z)))) (/.f64 (*.f64 y y) (*.f64 z (*.f64 z #s(literal 2 binary64)))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))))))) |
(*.f64 (/.f64 (*.f64 z (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))))) #s(literal 1 binary64))) (*.f64 (fma.f64 (/.f64 (*.f64 y y) (*.f64 z z)) (-.f64 (*.f64 (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64))))) (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (*.f64 z (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal -1 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal -1 binary64))) (fma.f64 y (*.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 z z))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (*.f64 z (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 y y) (*.f64 y y))) (*.f64 (*.f64 z z) (*.f64 z z))) #s(literal -1 binary64))) (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 z (*.f64 z z)) (*.f64 z (*.f64 z z))))) #s(literal -1 binary64))) (fma.f64 (/.f64 (*.f64 y y) (*.f64 z z)) (fma.f64 (/.f64 (*.f64 y y) (*.f64 z z)) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 z #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) z) |
(*.f64 #s(literal 1 binary64) (*.f64 z #s(literal 1/2 binary64))) |
(*.f64 (*.f64 z #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| 1× | egg-herbie |
| 3 204× | *-lowering-*.f32 |
| 3 204× | *-lowering-*.f64 |
| 2 418× | accelerator-lowering-fma.f32 |
| 2 418× | accelerator-lowering-fma.f64 |
| 2 132× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 1620 |
| 1 | 92 | 1620 |
| 2 | 210 | 1620 |
| 3 | 663 | 1440 |
| 4 | 2328 | 1440 |
| 5 | 5490 | 1440 |
| 0 | 8413 | 1350 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (/ (pow y 2) z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
z |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(pow y 2) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(/ 1/2 (pow z 2)) |
(* 1/2 (/ (pow y 2) z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
z |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))) |
(* 1/2 (/ (pow y 2) (pow z 2))) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) (pow z 2)) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
1 |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 (/ y z)) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* 1/2 (/ (pow y 2) z)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(* 1/2 (/ (pow y 2) z)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
z |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
(* 1/2 z) |
| Outputs |
|---|
(* 1/2 (/ (pow y 2) z)) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) z) #s(literal 0 binary64)) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) z) |
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) (*.f64 z z)) z) |
z |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
z |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
z |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(+ z (* 1/2 (/ (pow y 2) z))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* 1/2 (/ (pow y 2) z)) |
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) z) #s(literal 0 binary64)) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2)))) |
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(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
(* 1/2 z) |
(*.f64 #s(literal 1/2 binary64) z) |
Compiled 29 968 to 1 323 computations (95.6% saved)
6 alts after pruning (1 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 187 | 1 | 1 188 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 3 | 3 |
| Total | 1 188 | 6 | 1 194 |
| Status | Accuracy | Program |
|---|---|---|
| 98.5% | (fma.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) y) z) | |
| ✓ | 100.0% | (hypot.f64 z y) |
| ✓ | 98.5% | (*.f64 z (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
| ✓ | 81.6% | (*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64))) |
| ✓ | 43.1% | (sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| ✓ | 97.9% | z |
Compiled 173 to 79 computations (54.3% saved)
| Inputs |
|---|
z |
(sqrt.f64 (fma.f64 z z (*.f64 y y))) |
(fma.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) y) z) |
(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
(*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64))) |
(*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
(*.f64 z (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) z) |
(sqrt.f64 (fma.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) (*.f64 x x))) |
(hypot.f64 z y) |
| Outputs |
|---|
(hypot.f64 z y) |
9 calls:
| 4.0ms | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) |
| 4.0ms | z |
| 3.0ms | y |
| 3.0ms | x |
| 3.0ms | (*.f64 y y) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | z |
| 100.0% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 100.0% | 1 | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) |
| 100.0% | 1 | (*.f64 x x) |
| 100.0% | 1 | (+.f64 (*.f64 y y) (*.f64 z z)) |
| 100.0% | 1 | (*.f64 y y) |
| 100.0% | 1 | (*.f64 z z) |
Compiled 69 to 44 computations (36.2% saved)
| Inputs |
|---|
z |
(sqrt.f64 (fma.f64 z z (*.f64 y y))) |
(fma.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) y) z) |
(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
(*.f64 z (fma.f64 (*.f64 y y) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)) #s(literal 1 binary64))) |
(*.f64 z (fma.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 y (fma.f64 z z #s(literal 0 binary64))) #s(literal 0 binary64)) #s(literal 1 binary64))) |
(*.f64 z (fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 (/.f64 y z) (*.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) z) |
(sqrt.f64 (fma.f64 (fma.f64 y y (*.f64 z z)) (*.f64 (*.f64 (+.f64 y z) (-.f64 y z)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y z) (-.f64 y z)))) (*.f64 x x))) |
| Outputs |
|---|
(fma.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) y) z) |
9 calls:
| 4.0ms | y |
| 3.0ms | (*.f64 z z) |
| 3.0ms | x |
| 3.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 3.0ms | z |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | y |
| 98.5% | 1 | z |
| 98.5% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 98.5% | 1 | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) |
| 98.5% | 1 | (*.f64 x x) |
| 98.5% | 1 | (+.f64 (*.f64 y y) (*.f64 z z)) |
| 98.5% | 1 | (*.f64 y y) |
| 98.5% | 1 | (*.f64 z z) |
Compiled 69 to 44 computations (36.2% saved)
Total -35.8b remaining (-2639.2%)
Threshold costs -35.8b (-2639.2%)
| Inputs |
|---|
z |
(sqrt.f64 (fma.f64 z z (*.f64 y y))) |
| Outputs |
|---|
z |
9 calls:
| 2.0ms | y |
| 1.0ms | x |
| 1.0ms | z |
| 1.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 1.0ms | (+.f64 (*.f64 y y) (*.f64 z z)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | x |
| 97.9% | 1 | y |
| 97.9% | 1 | z |
| 97.9% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z)))) |
| 97.9% | 1 | (+.f64 (*.f64 x x) (+.f64 (*.f64 y y) (*.f64 z z))) |
| 97.9% | 1 | (*.f64 x x) |
| 97.9% | 1 | (+.f64 (*.f64 y y) (*.f64 z z)) |
| 97.9% | 1 | (*.f64 y y) |
| 97.9% | 1 | (*.f64 z z) |
Compiled 69 to 44 computations (36.2% saved)
| 1× | egg-herbie |
| 2× | *-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 12 |
| 1 | 8 | 12 |
| 1× | saturated |
| Inputs |
|---|
(hypot.f64 z y) |
(fma.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) y) z) |
z |
| Outputs |
|---|
(hypot.f64 z y) |
(fma.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) y) z) |
(fma.f64 (/.f64 y z) (*.f64 y #s(literal 1/2 binary64)) z) |
z |
| 12 268× | accelerator-lowering-fma.f32 |
| 12 268× | accelerator-lowering-fma.f64 |
| 11 154× | accelerator-lowering-fma.f32 |
| 11 154× | accelerator-lowering-fma.f64 |
| 8 928× | accelerator-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 433 | 2881 |
| 1 | 1294 | 2753 |
| 2 | 5026 | 2726 |
| 0 | 8108 | 2431 |
| 0 | 18 | 65 |
| 1 | 100 | 61 |
| 2 | 884 | 61 |
| 0 | 8335 | 51 |
| 0 | 16 | 44 |
| 1 | 98 | 44 |
| 2 | 907 | 38 |
| 0 | 9155 | 31 |
| 0 | 183 | 1644 |
| 1 | 508 | 1644 |
| 2 | 1778 | 1641 |
| 3 | 4736 | 1539 |
| 0 | 8027 | 1308 |
| 0 | 39 | 1620 |
| 1 | 92 | 1620 |
| 2 | 210 | 1620 |
| 3 | 663 | 1440 |
| 4 | 2328 | 1440 |
| 5 | 5490 | 1440 |
| 0 | 8413 | 1350 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 88 to 53 computations (39.8% saved)
Compiled 172 to 108 computations (37.2% saved)
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