
Time bar (total: 7.5s)
| 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 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 4 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 5 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 6 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 7 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 8 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 9 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 10 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 11 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 12 |
Compiled 14 to 11 computations (21.4% saved)
ival-div: 7.0ms (32.2% of total)ival-mult: 6.0ms (27.6% of total)ival-sqrt: 4.0ms (18.4% of total)ival-add: 3.0ms (13.8% of total)const: 1.0ms (4.6% of total)backward-pass: 0.0ms (0% of total)| 856.0ms | 8256× | 0 | valid |
| 170.0ms | 1999× | 0 | invalid |
ival-mult: 312.0ms (49.5% of total)ival-div: 118.0ms (18.7% of total)ival-sqrt: 91.0ms (14.4% of total)ival-add: 85.0ms (13.5% of total)const: 20.0ms (3.2% of total)backward-pass: 4.0ms (0.6% of total)| 2× | egg-herbie |
| 2584× | fnmadd-define |
| 1704× | sum3-define |
| 1646× | fmsub-define |
| 1538× | fnmsub-define |
| 1244× | fmm-def |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 86 |
| 1 | 118 | 72 |
| 2 | 368 | 72 |
| 3 | 818 | 72 |
| 4 | 1868 | 72 |
| 5 | 4169 | 72 |
| 6 | 6307 | 72 |
| 0 | 11 | 8 |
| 1 | 22 | 7 |
| 2 | 37 | 7 |
| 3 | 48 | 7 |
| 0 | 48 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | node limit |
| Inputs |
|---|
(* (/ 1 2) (+ x (* y (sqrt z)))) |
| Outputs |
|---|
(* (/ 1 2) (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| Inputs |
|---|
(* (/ 1 2) (+ x (* y (sqrt z)))) |
(* (/ 1 2) (+ (neg x) (* y (sqrt z)))) |
(* (/ 1 2) (+ x (* (neg y) (sqrt z)))) |
(* (/ 1 2) (+ x (* y (sqrt (neg z))))) |
(neg (* (/ 1 2) (+ (neg x) (* y (sqrt z))))) |
(neg (* (/ 1 2) (+ x (* (neg y) (sqrt z))))) |
(neg (* (/ 1 2) (+ x (* y (sqrt (neg z)))))) |
(* (/ 1 2) (+ y (* x (sqrt z)))) |
(* (/ 1 2) (+ z (* y (sqrt x)))) |
(* (/ 1 2) (+ x (* z (sqrt y)))) |
| Outputs |
|---|
(* (/ 1 2) (+ x (* y (sqrt z)))) |
(* 1/2 (fma y (sqrt z) x)) |
(* (/ 1 2) (+ (neg x) (* y (sqrt z)))) |
(* 1/2 (fmsub y (sqrt z) x)) |
(* (/ 1 2) (+ x (* (neg y) (sqrt z)))) |
(* 1/2 (fnmadd y (sqrt z) x)) |
(* (/ 1 2) (+ x (* y (sqrt (neg z))))) |
(* 1/2 (fma y (sqrt (neg z)) x)) |
(neg (* (/ 1 2) (+ (neg x) (* y (sqrt z))))) |
(* 1/2 (fnmadd y (sqrt z) x)) |
(neg (* (/ 1 2) (+ x (* (neg y) (sqrt z))))) |
(* 1/2 (fmsub y (sqrt z) x)) |
(neg (* (/ 1 2) (+ x (* y (sqrt (neg z)))))) |
(* 1/2 (fnmsub y (sqrt (neg z)) x)) |
(* (/ 1 2) (+ y (* x (sqrt z)))) |
(* 1/2 (fma x (sqrt z) y)) |
(* (/ 1 2) (+ z (* y (sqrt x)))) |
(* 1/2 (fma y (sqrt x) z)) |
(* (/ 1 2) (+ x (* z (sqrt y)))) |
(* 1/2 (fma z (sqrt y) x)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 1 | 0 | - | 0 | - | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (*.f64 y (sqrt.f64 z)) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 0 | 0 | - | 0 | - | (sqrt.f64 z) |
| 0 | 0 | - | 0 | - | z |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
| 71.0ms | 512× | 0 | valid |
Compiled 81 to 32 computations (60.5% saved)
ival-mult: 7.0ms (34.5% of total)ival-div: 4.0ms (19.7% of total)ival-add: 4.0ms (19.7% of total)ival-sqrt: 4.0ms (19.7% of total)const: 1.0ms (4.9% of total)backward-pass: 0.0ms (0% of total)Compiled 11 to 8 computations (27.3% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.5% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
Compiled 11 to 8 computations (27.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 z) |
| ✓ | cost-diff | 0 | (*.f64 y (sqrt.f64 z)) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 32× | *-lowering-*.f32 |
| 32× | *-lowering-*.f64 |
| 20× | fma-lowering-fma.f32 |
| 20× | fma-define |
| 20× | fma-lowering-fma.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 24 |
| 1 | 17 | 22 |
| 2 | 34 | 22 |
| 3 | 44 | 22 |
| 0 | 44 | 22 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
1/2 |
(+ x (* y (sqrt z))) |
x |
(* y (sqrt z)) |
y |
(sqrt z) |
z |
| Outputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
1/2 |
#s(literal 1/2 binary64) |
(+ x (* y (sqrt z))) |
(+.f64 x (*.f64 y (sqrt.f64 z))) |
x |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
y |
(sqrt z) |
(sqrt.f64 z) |
z |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 z) |
| ✓ | accuracy | 100.0% | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ✓ | accuracy | 99.7% | (*.f64 y (sqrt.f64 z)) |
| 29.0ms | 256× | 0 | valid |
Compiled 28 to 9 computations (67.9% saved)
ival-mult: 4.0ms (51.5% of total)ival-sqrt: 2.0ms (25.8% of total)ival-add: 1.0ms (12.9% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (sqrt z)> |
| Outputs |
|---|
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* y (sqrt z))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt x> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt x> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
27 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | z | @ | -inf | (* 1/2 (+ x (* y (sqrt z)))) |
| 1.0ms | x | @ | 0 | (* 1/2 (+ x (* y (sqrt z)))) |
| 1.0ms | z | @ | 0 | (* 1/2 (+ x (* y (sqrt z)))) |
| 1.0ms | y | @ | 0 | (* 1/2 (+ x (* y (sqrt z)))) |
| 0.0ms | x | @ | inf | (* 1/2 (+ x (* y (sqrt z)))) |
| 1× | batch-egg-rewrite |
| 2916× | *-lowering-*.f32 |
| 2916× | *-lowering-*.f64 |
| 2390× | /-lowering-/.f32 |
| 2390× | /-lowering-/.f64 |
| 1382× | pow-lowering-pow.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 20 |
| 1 | 31 | 18 |
| 2 | 243 | 18 |
| 3 | 2445 | 18 |
| 0 | 8453 | 18 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(sqrt z) |
| Outputs |
|---|
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))) |
(+.f64 (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) (/.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x)))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))) |
(fma.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) y (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) x)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) (-.f64 x (*.f64 y (sqrt.f64 z)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) |
(/.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))))) |
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(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (*.f64 y y) z) (-.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 y (sqrt.f64 z)))) (/.f64 (*.f64 (*.f64 y y) z) (-.f64 x (*.f64 y (sqrt.f64 z))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 9/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))) (neg.f64 (-.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (pow.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 y y) z))) #s(literal 3/2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))) (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) (neg.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (*.f64 y (sqrt.f64 z)) x) (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x))) #s(literal -1 binary64)) |
(*.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(*.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 x (*.f64 y (sqrt.f64 z))))) |
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))) |
(*.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(*.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) #s(literal -1 binary64))) |
(*.f64 (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) #s(literal 3 binary64)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) (-.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) (*.f64 x x))))) |
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (+.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 9/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (pow.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 y y) z))) #s(literal 3/2 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))) |
(exp.f64 (log.f64 (*.f64 y (sqrt.f64 z)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 y (sqrt.f64 z))) #s(literal 1 binary64))) |
(pow.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1 binary64)) |
(*.f64 y (sqrt.f64 z)) |
(*.f64 (sqrt.f64 z) y) |
(*.f64 (sqrt.f64 z) (pow.f64 y #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 z) (exp.f64 (log.f64 y))) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y)) |
(*.f64 (*.f64 y (pow.f64 z #s(literal 1/4 binary64))) (pow.f64 z #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y) #s(literal 1 binary64))) |
(*.f64 (pow.f64 y #s(literal 1 binary64)) (sqrt.f64 z)) |
(*.f64 (pow.f64 (*.f64 y (pow.f64 z #s(literal 1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (exp.f64 (log.f64 y)) (sqrt.f64 z)) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 z #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 z z)) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 z) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (*.f64 (log.f64 z) #s(literal 1/4 binary64)) (*.f64 (log.f64 z) #s(literal 1/4 binary64)))) |
(fabs.f64 (sqrt.f64 z)) |
(sqrt.f64 z) |
(pow.f64 (sqrt.f64 z) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 z #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 z z) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) |
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64)))) |
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))) |
| 1× | egg-herbie |
| 3400× | *-lowering-*.f32 |
| 3400× | *-lowering-*.f64 |
| 1344× | /-lowering-/.f32 |
| 1344× | /-lowering-/.f64 |
| 1232× | fma-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 75 | 622 |
| 1 | 264 | 578 |
| 2 | 891 | 578 |
| 3 | 2789 | 554 |
| 4 | 7950 | 554 |
| 0 | 8118 | 554 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
x |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (+ (sqrt z) (/ x y))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (+ (sqrt z) (/ x y))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (+ (sqrt z) (/ x y))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
Compiled 7917 to 763 computations (90.4% saved)
11 alts after pruning (10 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 311 | 10 | 321 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 311 | 11 | 322 |
| Status | Accuracy | Program |
|---|---|---|
| 47.7% | (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x)) | |
| 26.0% | (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) | |
| ▶ | 99.3% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
| 46.7% | (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) | |
| 99.4% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y)))) | |
| ▶ | 94.6% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
| ▶ | 99.3% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))) |
| 75.7% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64))))) | |
| ▶ | 99.4% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))) |
| ✓ | 99.5% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ▶ | 54.2% | (*.f64 #s(literal 1/2 binary64) x) |
Compiled 329 to 228 computations (30.7% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))) |
| ✓ | cost-diff | 6528 | (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
| ✓ | cost-diff | 0 | (*.f64 y (sqrt.f64 z)) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ✓ | cost-diff | 128 | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))) |
| 270× | *-lowering-*.f32 |
| 270× | *-lowering-*.f64 |
| 168× | fma-define |
| 128× | associate-*r* |
| 120× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 174 |
| 1 | 72 | 165 |
| 2 | 158 | 165 |
| 3 | 303 | 165 |
| 4 | 365 | 165 |
| 0 | 365 | 165 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))) |
1/2 |
(+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))) |
x |
(* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))) |
y |
(* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))) |
(sqrt (pow z 3/4)) |
(pow z 3/4) |
z |
3/4 |
(sqrt (pow z 1/4)) |
(pow z 1/4) |
1/4 |
(* 1/2 x) |
1/2 |
x |
(/ 1/2 (/ 1 (+ x (* y (sqrt z))))) |
1/2 |
(/ 1 (+ x (* y (sqrt z)))) |
1 |
(+ x (* y (sqrt z))) |
x |
(* y (sqrt z)) |
y |
(sqrt z) |
z |
(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z)))) |
1/2 |
(+ x (* (sqrt (/ 1 z)) (* y z))) |
x |
(* (sqrt (/ 1 z)) (* y z)) |
(sqrt (/ 1 z)) |
(/ 1 z) |
1 |
z |
(* y z) |
y |
(* 1/2 (+ x (* y (pow (pow z 1/4) 2)))) |
1/2 |
(+ x (* y (pow (pow z 1/4) 2))) |
x |
(* y (pow (pow z 1/4) 2)) |
y |
(pow (pow z 1/4) 2) |
(pow z 1/4) |
z |
1/4 |
2 |
| Outputs |
|---|
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))) |
1/2 |
#s(literal 1/2 binary64) |
(+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))) |
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))) |
x |
(* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))) |
(*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))) |
y |
(* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))) |
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))) |
(sqrt (pow z 3/4)) |
(sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) |
(pow z 3/4) |
(pow.f64 z #s(literal 3/4 binary64)) |
z |
3/4 |
#s(literal 3/4 binary64) |
(sqrt (pow z 1/4)) |
(sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))) |
(pow z 1/4) |
(pow.f64 z #s(literal 1/4 binary64)) |
1/4 |
#s(literal 1/4 binary64) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
1/2 |
#s(literal 1/2 binary64) |
x |
(/ 1/2 (/ 1 (+ x (* y (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
1/2 |
#s(literal 1/2 binary64) |
(/ 1 (+ x (* y (sqrt z)))) |
(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
1 |
#s(literal 1 binary64) |
(+ x (* y (sqrt z))) |
(+.f64 x (*.f64 y (sqrt.f64 z))) |
x |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
y |
(sqrt z) |
(sqrt.f64 z) |
z |
(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
1/2 |
#s(literal 1/2 binary64) |
(+ x (* (sqrt (/ 1 z)) (* y z))) |
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
x |
(* (sqrt (/ 1 z)) (* y z)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)) |
(sqrt (/ 1 z)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
1 |
#s(literal 1 binary64) |
z |
(* y z) |
(*.f64 y z) |
y |
(* 1/2 (+ x (* y (pow (pow z 1/4) 2)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
1/2 |
#s(literal 1/2 binary64) |
(+ x (* y (pow (pow z 1/4) 2))) |
(+.f64 x (*.f64 y (sqrt.f64 z))) |
x |
(* y (pow (pow z 1/4) 2)) |
(*.f64 y (sqrt.f64 z)) |
y |
(pow (pow z 1/4) 2) |
(sqrt.f64 z) |
(pow z 1/4) |
(pow.f64 z #s(literal 1/4 binary64)) |
z |
1/4 |
#s(literal 1/4 binary64) |
2 |
#s(literal 2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))) |
| ✓ | accuracy | 99.7% | (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.3% | (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
| ✓ | accuracy | 90.6% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)) |
| ✓ | accuracy | 100.0% | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
| ✓ | accuracy | 99.7% | (*.f64 y (sqrt.f64 z)) |
| ✓ | accuracy | 98.7% | (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))) |
| ✓ | accuracy | 99.7% | (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))) |
| ✓ | accuracy | 99.5% | (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))) |
| 167.0ms | 256× | 0 | valid |
Compiled 198 to 33 computations (83.3% saved)
ival-mult: 19.0ms (34.4% of total)ival-pow: 16.0ms (29% of total)ival-sqrt: 8.0ms (14.5% of total)ival-div: 5.0ms (9% of total)ival-add: 5.0ms (9% of total)const: 1.0ms (1.8% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))> |
#<alt (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))> |
#<alt (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))> |
#<alt (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))> |
#<alt (* 1/2 x)> |
#<alt (/ 1/2 (/ 1 (+ x (* y (sqrt z)))))> |
#<alt (/ 1 (+ x (* y (sqrt z))))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))> |
#<alt (+ x (* (sqrt (/ 1 z)) (* y z)))> |
#<alt (* (sqrt (/ 1 z)) (* y z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (pow (pow z 1/4) 2)> |
#<alt (* 1/2 (+ x (* y (pow (pow z 1/4) 2))))> |
#<alt (+ x (* y (pow (pow z 1/4) 2)))> |
#<alt (* y (pow (pow z 1/4) 2))> |
#<alt (sqrt (pow z 3/4))> |
| Outputs |
|---|
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* -1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))))> |
#<alt (* y (sqrt z))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt x> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt x> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))> |
#<alt (* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))> |
#<alt (* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))> |
#<alt (* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1))))> |
#<alt (* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1))))> |
#<alt (* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1))))> |
#<alt (* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1))))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (+ (* -1 (/ x (* (pow y 2) z))) (* (/ 1 y) (sqrt (/ 1 z))))> |
#<alt (+ (* x (- (* (/ x (pow y 3)) (sqrt (/ 1 (pow z 3)))) (/ 1 (* (pow y 2) z)))) (* (/ 1 y) (sqrt (/ 1 z))))> |
#<alt (+ (* x (- (* x (- (* -1 (/ x (* (pow y 4) (pow z 2)))) (* -1 (* (/ 1 (pow y 3)) (sqrt (/ 1 (pow z 3))))))) (/ 1 (* (pow y 2) z)))) (* (/ 1 y) (sqrt (/ 1 z))))> |
#<alt (/ 1 x)> |
#<alt (/ (+ 1 (* -1 (* (/ y x) (sqrt z)))) x)> |
#<alt (/ (- (+ 1 (/ (* (pow y 2) z) (pow x 2))) (* (/ y x) (sqrt z))) x)> |
#<alt (/ (- (+ 1 (* -1 (* (/ (pow y 3) (pow x 3)) (sqrt (pow z 3))))) (+ (* -1 (/ (* (pow y 2) z) (pow x 2))) (* (/ y x) (sqrt z)))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (* (/ y x) (sqrt z)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ (* (pow y 2) z) x) (* y (sqrt z))) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* (pow y 2) z)) x)) (* y (sqrt z))) x)) 1) x))> |
#<alt (/ 1 x)> |
#<alt (+ (* -1 (* (/ y (pow x 2)) (sqrt z))) (/ 1 x))> |
#<alt (+ (* y (- (/ (* y z) (pow x 3)) (* (/ 1 (pow x 2)) (sqrt z)))) (/ 1 x))> |
#<alt (+ (* y (- (* y (- (* -1 (* (/ y (pow x 4)) (sqrt (pow z 3)))) (* -1 (/ z (pow x 3))))) (* (/ 1 (pow x 2)) (sqrt z)))) (/ 1 x))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (/ (+ (sqrt (/ 1 z)) (* -1 (/ x (* y z)))) y)> |
#<alt (/ (- (+ (sqrt (/ 1 z)) (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 (pow z 3))))) (/ x (* y z))) y)> |
#<alt (/ (- (+ (sqrt (/ 1 z)) (* -1 (/ (pow x 3) (* (pow y 3) (pow z 2))))) (+ (* -1 (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 (pow z 3))))) (/ x (* y z)))) y)> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* -1 (/ (+ (* -1 (sqrt (/ 1 z))) (/ x (* y z))) y))> |
#<alt (* -1 (/ (+ (* -1 (sqrt (/ 1 z))) (* -1 (/ (- (* (/ (pow x 2) y) (sqrt (/ 1 (pow z 3)))) (/ x z)) y))) y))> |
#<alt (* -1 (/ (+ (* -1 (sqrt (/ 1 z))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (* y (pow z 2))) (* (pow x 2) (sqrt (/ 1 (pow z 3))))) y)) (/ x z)) y))) y))> |
#<alt (/ 1 (+ x (* y (sqrt z))))> |
#<alt (/ 1 (+ x (* y (sqrt z))))> |
#<alt (/ 1 (+ x (* y (sqrt z))))> |
#<alt (/ 1 (+ x (* y (sqrt z))))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (/ (+ (* -1 (/ x (pow y 2))) (* (/ 1 y) (sqrt z))) z)> |
#<alt (/ (- (+ (* (/ 1 y) (sqrt z)) (* (/ (pow x 2) (pow y 3)) (sqrt (/ 1 z)))) (/ x (pow y 2))) z)> |
#<alt (/ (- (+ (* -1 (/ (pow x 3) (* (pow y 4) z))) (* (/ 1 y) (sqrt z))) (+ (* -1 (* (/ (pow x 2) (pow y 3)) (sqrt (/ 1 z)))) (/ x (pow y 2)))) z)> |
#<alt (* -1 (* (/ 1 y) (sqrt (/ 1 z))))> |
#<alt (* -1 (/ (+ (* -1 (/ x (* (pow y 2) (pow (sqrt -1) 2)))) (* (/ 1 y) (sqrt z))) z))> |
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (* (/ (pow x 2) (* (pow y 3) (pow (sqrt -1) 2))) (sqrt z))) (* -1 (/ (* x z) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* (/ 1 y) (sqrt z))) z))> |
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 3) z) (* (pow y 4) (pow (sqrt -1) 4))) (* -1 (* (/ (pow x 2) (* (pow y 3) (pow (sqrt -1) 2))) (sqrt (pow z 3))))) z)) (* -1 (/ (* x z) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* (/ 1 y) (sqrt z))) z))> |
#<alt (* y (sqrt z))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt x> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt x> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))> |
#<alt (* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))> |
#<alt (* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))> |
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* y (sqrt z))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt x> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* (* y (pow (sqrt -1) 2)) (sqrt z))> |
#<alt (* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z)))))> |
#<alt (* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z)))))> |
#<alt (* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z)))))> |
#<alt x> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* (* y (pow (sqrt -1) 2)) (sqrt z))> |
#<alt (* (* y (pow (sqrt -1) 2)) (sqrt z))> |
#<alt (* (* y (pow (sqrt -1) 2)) (sqrt z))> |
#<alt (* (* y (pow (sqrt -1) 2)) (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (+ x (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* y (sqrt z))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt x> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))> |
#<alt x> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (+ (sqrt z) (/ x y)))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (+ x (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (pow (* 1 (pow z 3)) 1/8)> |
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))> |
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))> |
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))> |
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))> |
120 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 56.0ms | x | @ | 0 | (* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))) |
| 16.0ms | z | @ | 0 | (* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))) |
| 12.0ms | z | @ | -inf | (sqrt (pow z 3/4)) |
| 12.0ms | y | @ | 0 | (* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))) |
| 10.0ms | z | @ | 0 | (sqrt (pow z 3/4)) |
| 1× | batch-egg-rewrite |
| 4716× | *-lowering-*.f32 |
| 4716× | *-lowering-*.f64 |
| 1706× | /-lowering-/.f32 |
| 1706× | /-lowering-/.f64 |
| 904× | +-lowering-+.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 162 |
| 1 | 168 | 82 |
| 2 | 1059 | 82 |
| 0 | 9202 | 82 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))) |
(+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))) |
(* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))) |
(* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))) |
(* 1/2 x) |
(/ 1/2 (/ 1 (+ x (* y (sqrt z))))) |
(/ 1 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z)))) |
(+ x (* (sqrt (/ 1 z)) (* y z))) |
(* (sqrt (/ 1 z)) (* y z)) |
(sqrt (/ 1 z)) |
(pow (pow z 1/4) 2) |
(* 1/2 (+ x (* y (pow (pow z 1/4) 2)))) |
(+ x (* y (pow (pow z 1/4) 2))) |
(* y (pow (pow z 1/4) 2)) |
(sqrt (pow z 3/4)) |
| Outputs |
|---|
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x)) |
(+.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(+.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal -1/2 binary64) (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))) |
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)) (*.f64 (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))) |
(fma.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (sqrt.f64 z) (*.f64 y #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 y (*.f64 z #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 y z) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 y (pow.f64 z #s(literal 3/8 binary64))) (*.f64 (pow.f64 z #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (/.f64 y (sqrt.f64 z)) (*.f64 z #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) y (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal 3/8 binary64))) (pow.f64 z #s(literal 1/8 binary64)) (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (*.f64 y z) (*.f64 #s(literal 1/2 binary64) x)) |
(neg.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64)))) |
(/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) #s(literal 2 binary64)) |
(/.f64 (/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))) |
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal -1 binary64)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (+.f64 (*.f64 z (*.f64 y y)) (*.f64 x (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))) (-.f64 x (*.f64 y (sqrt.f64 z)))) |
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (+.f64 (*.f64 z (*.f64 y y)) (*.f64 x (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64)) (-.f64 x (*.f64 y (sqrt.f64 z)))) |
(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (neg.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))))) (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x))) |
(/.f64 (*.f64 (-.f64 (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) x) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
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(sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) |
(sqrt.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (sqrt.f64 z))) |
(sqrt.f64 (*.f64 (sqrt.f64 z) (pow.f64 z #s(literal 1/4 binary64)))) |
(pow.f64 z #s(literal 3/8 binary64)) |
(pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 z #s(literal 3/8 binary64)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 3/2 binary64)) |
(pow.f64 (pow.f64 z #s(literal 1/8 binary64)) #s(literal 3 binary64)) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow.f64 (pow.f64 z #s(literal 3/16 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 z #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 z z) #s(literal 3/16 binary64)) |
(pow.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (sqrt.f64 z)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (sqrt.f64 z) (pow.f64 z #s(literal 1/4 binary64))) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 z #s(literal 3/8 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 3/8 binary64))) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/8 binary64))) |
(*.f64 (pow.f64 z #s(literal 1/8 binary64)) (pow.f64 z #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 z #s(literal 3/16 binary64)) (pow.f64 z #s(literal 3/16 binary64))) |
(*.f64 (pow.f64 z #s(literal 1/16 binary64)) (*.f64 (pow.f64 z #s(literal 1/16 binary64)) (pow.f64 z #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/8 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 z #s(literal 1/8 binary64)) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/16 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 z #s(literal 1/16 binary64)) #s(literal 3 binary64))) |
(*.f64 (*.f64 (pow.f64 z #s(literal 1/16 binary64)) (pow.f64 z #s(literal 1/8 binary64))) (*.f64 (pow.f64 z #s(literal 1/16 binary64)) (pow.f64 z #s(literal 1/8 binary64)))) |
(*.f64 (*.f64 (pow.f64 z #s(literal 1/8 binary64)) (pow.f64 z #s(literal 1/16 binary64))) (*.f64 (pow.f64 z #s(literal 1/8 binary64)) (pow.f64 z #s(literal 1/16 binary64)))) |
(*.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/16 binary64))) (pow.f64 z #s(literal 1/16 binary64))) |
| 1× | egg-herbie |
| 4492× | *-lowering-*.f32 |
| 4492× | *-lowering-*.f64 |
| 1916× | /-lowering-/.f32 |
| 1916× | /-lowering-/.f64 |
| 1576× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 303 | 3816 |
| 1 | 1045 | 3484 |
| 2 | 3665 | 3429 |
| 0 | 8383 | 3429 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* -1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(+ (* -1 (/ x (* (pow y 2) z))) (* (/ 1 y) (sqrt (/ 1 z)))) |
(+ (* x (- (* (/ x (pow y 3)) (sqrt (/ 1 (pow z 3)))) (/ 1 (* (pow y 2) z)))) (* (/ 1 y) (sqrt (/ 1 z)))) |
(+ (* x (- (* x (- (* -1 (/ x (* (pow y 4) (pow z 2)))) (* -1 (* (/ 1 (pow y 3)) (sqrt (/ 1 (pow z 3))))))) (/ 1 (* (pow y 2) z)))) (* (/ 1 y) (sqrt (/ 1 z)))) |
(/ 1 x) |
(/ (+ 1 (* -1 (* (/ y x) (sqrt z)))) x) |
(/ (- (+ 1 (/ (* (pow y 2) z) (pow x 2))) (* (/ y x) (sqrt z))) x) |
(/ (- (+ 1 (* -1 (* (/ (pow y 3) (pow x 3)) (sqrt (pow z 3))))) (+ (* -1 (/ (* (pow y 2) z) (pow x 2))) (* (/ y x) (sqrt z)))) x) |
(/ 1 x) |
(* -1 (/ (- (* (/ y x) (sqrt z)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ (* (pow y 2) z) x) (* y (sqrt z))) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* (pow y 2) z)) x)) (* y (sqrt z))) x)) 1) x)) |
(/ 1 x) |
(+ (* -1 (* (/ y (pow x 2)) (sqrt z))) (/ 1 x)) |
(+ (* y (- (/ (* y z) (pow x 3)) (* (/ 1 (pow x 2)) (sqrt z)))) (/ 1 x)) |
(+ (* y (- (* y (- (* -1 (* (/ y (pow x 4)) (sqrt (pow z 3)))) (* -1 (/ z (pow x 3))))) (* (/ 1 (pow x 2)) (sqrt z)))) (/ 1 x)) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/ (+ (sqrt (/ 1 z)) (* -1 (/ x (* y z)))) y) |
(/ (- (+ (sqrt (/ 1 z)) (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 (pow z 3))))) (/ x (* y z))) y) |
(/ (- (+ (sqrt (/ 1 z)) (* -1 (/ (pow x 3) (* (pow y 3) (pow z 2))))) (+ (* -1 (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 (pow z 3))))) (/ x (* y z)))) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* -1 (/ (+ (* -1 (sqrt (/ 1 z))) (/ x (* y z))) y)) |
(* -1 (/ (+ (* -1 (sqrt (/ 1 z))) (* -1 (/ (- (* (/ (pow x 2) y) (sqrt (/ 1 (pow z 3)))) (/ x z)) y))) y)) |
(* -1 (/ (+ (* -1 (sqrt (/ 1 z))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (* y (pow z 2))) (* (pow x 2) (sqrt (/ 1 (pow z 3))))) y)) (/ x z)) y))) y)) |
(/ 1 (+ x (* y (sqrt z)))) |
(/ 1 (+ x (* y (sqrt z)))) |
(/ 1 (+ x (* y (sqrt z)))) |
(/ 1 (+ x (* y (sqrt z)))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/ (+ (* -1 (/ x (pow y 2))) (* (/ 1 y) (sqrt z))) z) |
(/ (- (+ (* (/ 1 y) (sqrt z)) (* (/ (pow x 2) (pow y 3)) (sqrt (/ 1 z)))) (/ x (pow y 2))) z) |
(/ (- (+ (* -1 (/ (pow x 3) (* (pow y 4) z))) (* (/ 1 y) (sqrt z))) (+ (* -1 (* (/ (pow x 2) (pow y 3)) (sqrt (/ 1 z)))) (/ x (pow y 2)))) z) |
(* -1 (* (/ 1 y) (sqrt (/ 1 z)))) |
(* -1 (/ (+ (* -1 (/ x (* (pow y 2) (pow (sqrt -1) 2)))) (* (/ 1 y) (sqrt z))) z)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (* (/ (pow x 2) (* (pow y 3) (pow (sqrt -1) 2))) (sqrt z))) (* -1 (/ (* x z) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* (/ 1 y) (sqrt z))) z)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 3) z) (* (pow y 4) (pow (sqrt -1) 4))) (* -1 (* (/ (pow x 2) (* (pow y 3) (pow (sqrt -1) 2))) (sqrt (pow z 3))))) z)) (* -1 (/ (* x z) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* (/ 1 y) (sqrt z))) z)) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* (* y (pow (sqrt -1) 2)) (sqrt z)) |
(* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z))))) |
(* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z))))) |
(* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z))))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* (* y (pow (sqrt -1) 2)) (sqrt z)) |
(* (* y (pow (sqrt -1) 2)) (sqrt z)) |
(* (* y (pow (sqrt -1) 2)) (sqrt z)) |
(* (* y (pow (sqrt -1) 2)) (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(pow (* 1 (pow z 3)) 1/8) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
| Outputs |
|---|
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* -1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(*.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (*.f64 y (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))) |
(*.f64 (+.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) z) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) z)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))) |
(*.f64 (+.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) z) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) z)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))) |
(*.f64 (+.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) z) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))) |
x |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(+ x (* y (sqrt z))) |
(+.f64 (*.f64 y (sqrt.f64 z)) x) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(*.f64 (sqrt.f64 z) (*.f64 (*.f64 y (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))) |
(*.f64 (-.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y (sqrt.f64 #s(literal -1 binary64))))) (/.f64 x z)) (-.f64 #s(literal 0 binary64) z)) |
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))) |
(*.f64 (-.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y (sqrt.f64 #s(literal -1 binary64))))) (/.f64 x z)) (-.f64 #s(literal 0 binary64) z)) |
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))) |
(*.f64 (-.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y (sqrt.f64 #s(literal -1 binary64))))) (/.f64 x z)) (-.f64 #s(literal 0 binary64) z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(*.f64 (sqrt.f64 z) (*.f64 (*.f64 y (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(*.f64 (sqrt.f64 z) (*.f64 (*.f64 y (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(*.f64 (sqrt.f64 z) (*.f64 (*.f64 y (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z)))) |
(*.f64 (sqrt.f64 z) (*.f64 (*.f64 y (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 z) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 z) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 z) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* -1 (* (pow -1 1/4) (* (sqrt z) (sqrt -1)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 z) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
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(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z))) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 y (sqrt.f64 z)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(pow (* 1 (pow z 3)) 1/8) |
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64)) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64))) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64))) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64))) |
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z)))))) |
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64))) |
Compiled 37579 to 2270 computations (94% saved)
9 alts after pruning (7 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1908 | 6 | 1914 |
| Fresh | 4 | 1 | 5 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1916 | 9 | 1925 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 94.6% | (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x)) |
| ▶ | 46.6% | (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) |
| ▶ | 46.3% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))) |
| ▶ | 54.0% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
| 88.2% | (*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) | |
| ▶ | 46.7% | (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
| 94.3% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (/.f64 y (sqrt.f64 z)) z))) | |
| ✓ | 99.5% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ✓ | 54.2% | (*.f64 #s(literal 1/2 binary64) x) |
Compiled 175 to 131 computations (25.1% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) z) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
| ✓ | cost-diff | 0 | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) |
| ✓ | cost-diff | 0 | (sqrt.f64 z) |
| ✓ | cost-diff | 0 | (*.f64 y (sqrt.f64 z)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))) |
| ✓ | cost-diff | 128 | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 z) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) |
| ✓ | cost-diff | 0 | (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 128 | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 z) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) y) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) |
| ✓ | cost-diff | 6400 | (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x)) |
| 272× | *-lowering-*.f32 |
| 272× | *-lowering-*.f64 |
| 156× | times-frac |
| 150× | /-lowering-/.f32 |
| 150× | /-lowering-/.f64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 94 |
| 1 | 47 | 94 |
| 2 | 74 | 92 |
| 3 | 113 | 91 |
| 4 | 150 | 91 |
| 5 | 188 | 91 |
| 6 | 245 | 91 |
| 7 | 341 | 91 |
| 8 | 381 | 91 |
| 9 | 439 | 91 |
| 10 | 489 | 91 |
| 11 | 533 | 91 |
| 12 | 534 | 91 |
| 0 | 534 | 91 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x)) |
(/ (* 1/2 y) (sqrt z)) |
(* 1/2 y) |
1/2 |
y |
(sqrt z) |
z |
(* 1/2 x) |
x |
(/ 1/2 (/ 1 x)) |
1/2 |
(/ 1 x) |
1 |
x |
(* y (* 1/2 (sqrt z))) |
y |
(* 1/2 (sqrt z)) |
1/2 |
(sqrt z) |
z |
(/ 1/2 (/ 1 (* y (sqrt z)))) |
1/2 |
(/ 1 (* y (sqrt z))) |
1 |
(* y (sqrt z)) |
y |
(sqrt z) |
z |
(/ 1/2 (/ (sqrt (/ 1 z)) y)) |
1/2 |
(/ (sqrt (/ 1 z)) y) |
(sqrt (/ 1 z)) |
(/ 1 z) |
1 |
z |
y |
| Outputs |
|---|
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x)) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 z (/.f64 (sqrt.f64 z) y)))) |
(/ (* 1/2 y) (sqrt z)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 z) y)) |
(* 1/2 y) |
(*.f64 #s(literal 1/2 binary64) y) |
1/2 |
#s(literal 1/2 binary64) |
y |
(sqrt z) |
(sqrt.f64 z) |
z |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
x |
(/ 1/2 (/ 1 x)) |
(*.f64 #s(literal 1/2 binary64) x) |
1/2 |
#s(literal 1/2 binary64) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
x |
(* y (* 1/2 (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
y |
(* 1/2 (sqrt z)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt z) |
(sqrt.f64 z) |
z |
(/ 1/2 (/ 1 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
1/2 |
#s(literal 1/2 binary64) |
(/ 1 (* y (sqrt z))) |
(/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))) |
1 |
#s(literal 1 binary64) |
(* y (sqrt z)) |
(*.f64 y (sqrt.f64 z)) |
y |
(sqrt z) |
(sqrt.f64 z) |
z |
(/ 1/2 (/ (sqrt (/ 1 z)) y)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) |
1/2 |
#s(literal 1/2 binary64) |
(/ (sqrt (/ 1 z)) y) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(sqrt (/ 1 z)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
1 |
#s(literal 1 binary64) |
z |
y |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) z) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
| ✓ | accuracy | 99.6% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
| ✓ | accuracy | 99.0% | (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 z) |
| ✓ | accuracy | 99.7% | (*.f64 y (sqrt.f64 z)) |
| ✓ | accuracy | 99.0% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))) |
| ✓ | accuracy | 98.5% | (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 z) |
| ✓ | accuracy | 99.7% | (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 z) |
| ✓ | accuracy | 99.7% | (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) |
| ✓ | accuracy | 94.7% | (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x)) |
| 164.0ms | 256× | 0 | valid |
Compiled 108 to 22 computations (79.6% saved)
ival-div: 15.0ms (43% of total)ival-mult: 10.0ms (28.7% of total)ival-sqrt: 4.0ms (11.5% of total)compiled-spec: 4.0ms (11.5% of total)ival-add: 1.0ms (2.9% of total)const: 1.0ms (2.9% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x))> |
#<alt (/ (* 1/2 y) (sqrt z))> |
#<alt (* 1/2 y)> |
#<alt (sqrt z)> |
#<alt (/ 1/2 (/ 1 x))> |
#<alt (/ 1 x)> |
#<alt (* y (* 1/2 (sqrt z)))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (/ 1/2 (/ 1 (* y (sqrt z))))> |
#<alt (/ 1 (* y (sqrt z)))> |
#<alt (* y (sqrt z))> |
#<alt (/ 1/2 (/ (sqrt (/ 1 z)) y))> |
#<alt (/ (sqrt (/ 1 z)) y)> |
#<alt (sqrt (/ 1 z))> |
#<alt (/ 1 z)> |
#<alt (* 1/2 x)> |
| Outputs |
|---|
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))> |
#<alt (* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))> |
#<alt (* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 z))))> |
#<alt (* 1/2 (* y (sqrt (/ 1 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 (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* 1/2 (sqrt z))> |
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* y (sqrt z))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (/ 1 z)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
75 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | y | @ | 0 | (/ (* 1/2 y) (sqrt z)) |
| 1.0ms | z | @ | -inf | (/ 1 (* y (sqrt z))) |
| 1.0ms | z | @ | -inf | (+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x)) |
| 1.0ms | z | @ | -inf | (/ (sqrt (/ 1 z)) y) |
| 1.0ms | z | @ | -inf | (/ (* 1/2 y) (sqrt z)) |
| 1× | batch-egg-rewrite |
| 4668× | *-lowering-*.f32 |
| 4668× | *-lowering-*.f64 |
| 3126× | /-lowering-/.f32 |
| 3126× | /-lowering-/.f64 |
| 958× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 71 |
| 1 | 116 | 68 |
| 2 | 746 | 65 |
| 0 | 8643 | 65 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x)) |
(/ (* 1/2 y) (sqrt z)) |
(* 1/2 y) |
(sqrt z) |
(/ 1/2 (/ 1 x)) |
(/ 1 x) |
(* y (* 1/2 (sqrt z))) |
(* 1/2 (sqrt z)) |
(/ 1/2 (/ 1 (* y (sqrt z)))) |
(/ 1 (* y (sqrt z))) |
(* y (sqrt z)) |
(/ 1/2 (/ (sqrt (/ 1 z)) y)) |
(/ (sqrt (/ 1 z)) y) |
(sqrt (/ 1 z)) |
(/ 1 z) |
(* 1/2 x) |
| Outputs |
|---|
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 x #s(literal 2 binary64))) |
(+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))) |
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) (neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x)))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))) (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))))) |
(fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (/.f64 x #s(literal 2 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (/.f64 x #s(literal 2 binary64))) |
(fma.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 z) y)) (/.f64 x #s(literal 2 binary64))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 z) y)) z (/.f64 x #s(literal 2 binary64))) |
(fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))) |
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)) (/.f64 x #s(literal 2 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) z) (/.f64 y (sqrt.f64 z)) (/.f64 x #s(literal 2 binary64))) |
(neg.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (/.f64 #s(literal 2 binary64) x)))))) |
(neg.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 x (*.f64 x #s(literal -1/4 binary64)))) (+.f64 (*.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 z)) (/.f64 x #s(literal 2 binary64))))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (/.f64 #s(literal 2 binary64) x))))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))) (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) x) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) (/.f64 x #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (/.f64 x #s(literal 2 binary64))) (sqrt.f64 z)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 z) x)) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (-.f64 #s(literal 0 binary64) x)) (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal -1/2 binary64) z)) (-.f64 #s(literal 0 binary64) x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) (/.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 z) (/.f64 (*.f64 y (*.f64 #s(literal -1/2 binary64) z)) (*.f64 x #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 z) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal -1/2 binary64) z)) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (/.f64 #s(literal 2 binary64) x)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 x (*.f64 x #s(literal -1/4 binary64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) |
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))) (/.f64 (sqrt.f64 z) x)) |
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (/.f64 x #s(literal 2 binary64))) (sqrt.f64 z)) (/.f64 (sqrt.f64 z) (/.f64 x #s(literal 2 binary64)))) |
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (-.f64 #s(literal 0 binary64) x)) (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 z) x))) |
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal -1/2 binary64) z)) (-.f64 #s(literal 0 binary64) x))) (/.f64 (sqrt.f64 z) x)) |
(/.f64 (+.f64 (sqrt.f64 z) (/.f64 (*.f64 y (*.f64 #s(literal -1/2 binary64) z)) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 (sqrt.f64 z) (/.f64 x #s(literal 2 binary64)))) |
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal -1/2 binary64) z)) x)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 z) x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (/.f64 #s(literal 2 binary64) x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) (+.f64 (*.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 z)) (/.f64 x #s(literal 2 binary64)))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))) |
(/.f64 (+.f64 (*.f64 z (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 (/.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (*.f64 (/.f64 (/.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (+.f64 (*.f64 z (/.f64 #s(literal 2 binary64) x)) (/.f64 (/.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))) (*.f64 (/.f64 (/.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x))) |
(/.f64 (+.f64 (*.f64 z (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) x))) (*.f64 (/.f64 (/.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (/.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) x)))) |
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(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64))) |
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) |
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64))) |
| 1× | egg-herbie |
| 3060× | *-lowering-*.f32 |
| 3060× | *-lowering-*.f64 |
| 2120× | fma-lowering-fma.f32 |
| 2120× | fma-lowering-fma.f64 |
| 2076× | fmsub-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 1601 |
| 1 | 194 | 1521 |
| 2 | 599 | 1497 |
| 3 | 1662 | 1497 |
| 4 | 4972 | 1497 |
| 0 | 8054 | 1497 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(* 1/2 (* y (sqrt (/ 1 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) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* 1/2 (sqrt z)) |
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(/ 1 z) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) (*.f64 y z))) (*.f64 #s(literal 1/2 binary64) x)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) (*.f64 y z))) (*.f64 #s(literal 1/2 binary64) x)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) (*.f64 y z))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) (*.f64 y z))) (*.f64 #s(literal 1/2 binary64) x)) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) (*.f64 y z))) (*.f64 #s(literal 1/2 binary64) x)) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) (*.f64 y z))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (sqrt.f64 z)) x)) (*.f64 x #s(literal -1/2 binary64))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (sqrt.f64 z)) x)) (*.f64 x #s(literal -1/2 binary64))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (sqrt.f64 z)) x)) (*.f64 x #s(literal -1/2 binary64))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (sqrt.f64 z)) x)) (*.f64 x #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (sqrt.f64 z)) x)) (*.f64 x #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (sqrt.f64 z)) x)) (*.f64 x #s(literal -1/2 binary64))) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 #s(literal 1/2 binary64) y)) |
(* 1/2 (* y (sqrt (/ 1 z)))) |
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(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(/ 1 z) |
(/.f64 #s(literal 1 binary64) z) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
Compiled 13920 to 1645 computations (88.2% saved)
9 alts after pruning (4 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1141 | 3 | 1144 |
| Fresh | 1 | 1 | 2 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1144 | 9 | 1153 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 46.7% | (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
| ▶ | 46.6% | (/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
| ▶ | 46.6% | (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
| ✓ | 46.6% | (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) |
| ✓ | 54.0% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
| ▶ | 88.2% | (*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
| ✓ | 46.7% | (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
| ✓ | 99.5% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ✓ | 54.2% | (*.f64 #s(literal 1/2 binary64) x) |
Compiled 87 to 68 computations (21.8% saved)
| 1× | egg-herbie |
Found 13 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (pow.f64 z #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) y) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 2 binary64) y) |
| ✓ | cost-diff | 0 | (sqrt.f64 z) |
| ✓ | cost-diff | 0 | (/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
| ✓ | cost-diff | 0 | (pow.f64 z #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
| ✓ | cost-diff | 0 | (sqrt.f64 z) |
| ✓ | cost-diff | 0 | (+.f64 (sqrt.f64 z) (/.f64 x y)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) y) |
| ✓ | cost-diff | 128 | (*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
| 6268× | *-lowering-*.f32 |
| 6268× | *-lowering-*.f64 |
| 2920× | cube-prod |
| 2396× | pow-lowering-pow.f64 |
| 2396× | pow-lowering-pow.f32 |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 78 |
| 1 | 34 | 78 |
| 2 | 74 | 78 |
| 3 | 132 | 78 |
| 4 | 155 | 77 |
| 5 | 179 | 75 |
| 6 | 242 | 75 |
| 7 | 444 | 75 |
| 8 | 1493 | 75 |
| 9 | 2148 | 75 |
| 10 | 2661 | 75 |
| 11 | 2959 | 75 |
| 12 | 3307 | 75 |
| 13 | 3755 | 75 |
| 14 | 4421 | 75 |
| 15 | 5294 | 75 |
| 16 | 5749 | 75 |
| 17 | 5915 | 75 |
| 18 | 5988 | 75 |
| 19 | 6065 | 75 |
| 20 | 6144 | 75 |
| 21 | 7150 | 75 |
| 22 | 7781 | 75 |
| 23 | 7947 | 75 |
| 0 | 8019 | 75 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* 1/2 y) (+ (sqrt z) (/ x y))) |
(* 1/2 y) |
1/2 |
y |
(+ (sqrt z) (/ x y)) |
(sqrt z) |
z |
(/ x y) |
x |
(/ 1/2 (/ (pow z -1/2) y)) |
1/2 |
(/ (pow z -1/2) y) |
(pow z -1/2) |
z |
-1/2 |
y |
(/ (sqrt z) (/ 2 y)) |
(sqrt z) |
z |
(/ 2 y) |
2 |
y |
(/ (* 1/2 y) (pow z -1/2)) |
(* 1/2 y) |
1/2 |
y |
(pow z -1/2) |
z |
-1/2 |
| Outputs |
|---|
(* (* 1/2 y) (+ (sqrt z) (/ x y))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* 1/2 y) |
(/.f64 y #s(literal 2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
y |
(+ (sqrt z) (/ x y)) |
(+.f64 (sqrt.f64 z) (/.f64 x y)) |
(sqrt z) |
(sqrt.f64 z) |
z |
(/ x y) |
(/.f64 x y) |
x |
(/ 1/2 (/ (pow z -1/2) y)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
1/2 |
#s(literal 1/2 binary64) |
(/ (pow z -1/2) y) |
(/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) |
(pow z -1/2) |
(pow.f64 z #s(literal -1/2 binary64)) |
z |
-1/2 |
#s(literal -1/2 binary64) |
y |
(/ (sqrt z) (/ 2 y)) |
(/.f64 (*.f64 y (sqrt.f64 z)) #s(literal 2 binary64)) |
(sqrt z) |
(sqrt.f64 z) |
z |
(/ 2 y) |
(/.f64 #s(literal 2 binary64) y) |
2 |
#s(literal 2 binary64) |
y |
(/ (* 1/2 y) (pow z -1/2)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
(* 1/2 y) |
(/.f64 y #s(literal 2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
y |
(pow z -1/2) |
(pow.f64 z #s(literal -1/2 binary64)) |
z |
-1/2 |
#s(literal -1/2 binary64) |
Found 13 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (pow.f64 z #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) y) |
| ✓ | accuracy | 99.7% | (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 2 binary64) y) |
| ✓ | accuracy | 100.0% | (sqrt.f64 z) |
| ✓ | accuracy | 99.5% | (/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
| ✓ | accuracy | 100.0% | (pow.f64 z #s(literal -1/2 binary64)) |
| ✓ | accuracy | 99.6% | (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) |
| ✓ | accuracy | 99.0% | (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) y) |
| ✓ | accuracy | 100.0% | (sqrt.f64 z) |
| ✓ | accuracy | 100.0% | (+.f64 (sqrt.f64 z) (/.f64 x y)) |
| ✓ | accuracy | 88.2% | (*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
| 77.0ms | 256× | 0 | valid |
Compiled 82 to 18 computations (78% saved)
ival-div: 11.0ms (40.4% of total)ival-pow: 6.0ms (22% of total)ival-sqrt: 5.0ms (18.4% of total)ival-mult: 4.0ms (14.7% of total)ival-add: 1.0ms (3.7% of total)const: 1.0ms (3.7% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* (* 1/2 y) (+ (sqrt z) (/ x y)))> |
#<alt (* 1/2 y)> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (sqrt z)> |
#<alt (/ 1/2 (/ (pow z -1/2) y))> |
#<alt (/ (pow z -1/2) y)> |
#<alt (pow z -1/2)> |
#<alt (/ (sqrt z) (/ 2 y))> |
#<alt (/ 2 y)> |
#<alt (/ (* 1/2 y) (pow z -1/2))> |
| Outputs |
|---|
#<alt (* 1/2 x)> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))> |
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))> |
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))> |
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))> |
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))> |
#<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 (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (sqrt z)> |
#<alt (* z (+ (sqrt (/ 1 z)) (/ x (* y z))))> |
#<alt (* z (+ (sqrt (/ 1 z)) (/ x (* y z))))> |
#<alt (* z (+ (sqrt (/ 1 z)) (/ x (* y z))))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))> |
#<alt (sqrt z)> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (/ x y)> |
#<alt (* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))> |
#<alt (* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))> |
#<alt (* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))> |
#<alt (/ x y)> |
#<alt (* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))> |
#<alt (* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))> |
#<alt (* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))> |
#<alt (/ x y)> |
#<alt (/ (+ x (* y (sqrt z))) y)> |
#<alt (/ (+ x (* y (sqrt z))) y)> |
#<alt (/ (+ x (* y (sqrt z))) y)> |
#<alt (sqrt z)> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (sqrt z)> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (+ (sqrt z) (/ x y))> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (sqrt z)> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (* (/ 1 y) (sqrt (/ 1 z)))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (sqrt (/ 1 z))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (/ 2 y)> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* 1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
#<alt (* -1/2 (* y (sqrt z)))> |
54 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 16.0ms | y | @ | -inf | (* (* 1/2 y) (+ (sqrt z) (/ x y))) |
| 1.0ms | z | @ | 0 | (* (* 1/2 y) (+ (sqrt z) (/ x y))) |
| 1.0ms | y | @ | 0 | (* (* 1/2 y) (+ (sqrt z) (/ x y))) |
| 0.0ms | x | @ | inf | (* (* 1/2 y) (+ (sqrt z) (/ x y))) |
| 0.0ms | y | @ | inf | (* (* 1/2 y) (+ (sqrt z) (/ x y))) |
| 1× | batch-egg-rewrite |
| 3730× | *-lowering-*.f32 |
| 3730× | *-lowering-*.f64 |
| 2784× | /-lowering-/.f32 |
| 2784× | /-lowering-/.f64 |
| 826× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 53 |
| 1 | 93 | 50 |
| 2 | 653 | 48 |
| 3 | 7493 | 48 |
| 0 | 8066 | 48 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* 1/2 y) (+ (sqrt z) (/ x y))) |
(* 1/2 y) |
(+ (sqrt z) (/ x y)) |
(sqrt z) |
(/ 1/2 (/ (pow z -1/2) y)) |
(/ (pow z -1/2) y) |
(pow z -1/2) |
(/ (sqrt z) (/ 2 y)) |
(/ 2 y) |
(/ (* 1/2 y) (pow z -1/2)) |
| Outputs |
|---|
(+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y)) |
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(/.f64 (-.f64 (*.f64 z (-.f64 (sqrt.f64 z) (/.f64 x y))) (*.f64 (-.f64 (sqrt.f64 z) (/.f64 x y)) (/.f64 x (/.f64 y (/.f64 x y))))) (*.f64 (-.f64 (sqrt.f64 z) (/.f64 x y)) (-.f64 (sqrt.f64 z) (/.f64 x y)))) |
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(/.f64 (neg.f64 (-.f64 (/.f64 x (/.f64 y (/.f64 x y))) z)) (neg.f64 (-.f64 (/.f64 x y) (sqrt.f64 z)))) |
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(/.f64 (*.f64 (-.f64 z (/.f64 x (/.f64 y (/.f64 x y)))) #s(literal 1 binary64)) (-.f64 (sqrt.f64 z) (/.f64 x y))) |
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(/.f64 (-.f64 #s(literal 0 binary64) y) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal -2 binary64))) |
(/.f64 (-.f64 #s(literal 0 binary64) y) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 #s(literal -2 binary64) y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 z #s(literal -1/4 binary64)) (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))) |
(/.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal 2 binary64)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 1 binary64)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) y)) |
(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal -2 binary64)))) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (pow.f64 z #s(literal -1/4 binary64)) y)) |
(/.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 z #s(literal -1/4 binary64)))) |
(/.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) #s(literal -2 binary64)) |
(/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) y)) |
(/.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (/.f64 #s(literal 2 binary64) y) (pow.f64 z #s(literal -1/4 binary64)))) |
(/.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (pow.f64 z #s(literal -1/4 binary64))) |
(/.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) |
(/.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) y)) |
(/.f64 (neg.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) y)) |
(/.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 y #s(literal 2 binary64))) (pow.f64 z #s(literal -1/4 binary64))) |
(/.f64 (*.f64 (/.f64 y #s(literal -2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) y) (pow.f64 z #s(literal -1/4 binary64))) |
(/.f64 (*.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 z #s(literal -1/4 binary64))) |
(/.f64 (/.f64 (/.f64 y #s(literal -2 binary64)) (pow.f64 z #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))) |
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) y)) |
(/.f64 (/.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (pow.f64 z #s(literal -1/8 binary64))) (pow.f64 z #s(literal -1/8 binary64))) |
(pow.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) |
(*.f64 y (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 y #s(literal 2 binary64)) (sqrt.f64 z)) |
(*.f64 (sqrt.f64 z) (/.f64 y #s(literal 2 binary64))) |
(*.f64 #s(literal -1/2 binary64) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))))) |
(*.f64 (/.f64 y #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) |
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 (sqrt.f64 z) #s(literal -2 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 y #s(literal -2 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))) |
(*.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) y) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 y (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 (/.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) y))) |
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 y #s(literal 2 binary64)))) |
(*.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (pow.f64 z #s(literal 1/4 binary64))) |
(*.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y)) |
(*.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) |
(*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) y)) |
(*.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) y) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) y) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sqrt.f64 z) #s(literal -1 binary64)) (/.f64 y #s(literal -2 binary64))) |
(*.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64))))) |
(*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64))))) |
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) y))) |
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal -2 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) y))) |
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) y)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) y))) |
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64))))) |
(*.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 y (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) y)) |
(*.f64 (*.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) #s(literal -1 binary64)) y) |
(*.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1 binary64)) y) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal 1 binary64)) (/.f64 y #s(literal -2 binary64))) |
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1 binary64)) y) |
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y)) |
| 1× | egg-herbie |
| 4746× | *-lowering-*.f32 |
| 4746× | *-lowering-*.f64 |
| 1484× | times-frac |
| 1466× | fnmadd-define |
| 1334× | /-lowering-/.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 1260 |
| 1 | 269 | 1185 |
| 2 | 863 | 1177 |
| 3 | 2682 | 1159 |
| 0 | 8824 | 1159 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (* y (+ (sqrt z) (/ x y)))) |
(* 1/2 (* y (+ (sqrt z) (/ x y)))) |
(* 1/2 (* y (+ (sqrt z) (/ x y)))) |
(* 1/2 (* y (+ (sqrt z) (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 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) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(sqrt z) |
(* z (+ (sqrt (/ 1 z)) (/ x (* y z)))) |
(* z (+ (sqrt (/ 1 z)) (/ x (* y z)))) |
(* z (+ (sqrt (/ 1 z)) (/ x (* y z)))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))))) |
(sqrt z) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(/ x y) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(/ x y) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(/ x y) |
(/ (+ x (* y (sqrt z))) y) |
(/ (+ x (* y (sqrt z))) y) |
(/ (+ x (* y (sqrt z))) y) |
(sqrt z) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(sqrt z) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2)) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(/ 2 y) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
(* -1/2 (* y (sqrt z))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
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(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* 1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(* -1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))) |
(* -1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))) |
(* -1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))) |
(* -1/2 (* y (sqrt z))) |
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64))) |
Compiled 13602 to 1500 computations (89% saved)
10 alts after pruning (1 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 995 | 1 | 996 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 4 | 4 |
| Done | 0 | 5 | 5 |
| Total | 995 | 10 | 1005 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 46.7% | (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
| ✓ | 46.6% | (/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
| ✓ | 46.6% | (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
| ✓ | 46.6% | (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) |
| ✓ | 54.0% | (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
| 42.5% | (*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y)) | |
| ✓ | 88.2% | (*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
| ✓ | 46.7% | (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
| ✓ | 99.5% | (*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| ✓ | 54.2% | (*.f64 #s(literal 1/2 binary64) x) |
Compiled 326 to 162 computations (50.3% saved)
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) x) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y)) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (/.f64 y (sqrt.f64 z)) z))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y))) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x)) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))) |
| Outputs |
|---|
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
7 calls:
| 7.0ms | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 7.0ms | (sqrt.f64 z) |
| 7.0ms | z |
| 6.0ms | x |
| 6.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | y |
| 99.5% | 1 | z |
| 99.5% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 99.5% | 1 | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 99.5% | 1 | (*.f64 y (sqrt.f64 z)) |
| 99.5% | 1 | (sqrt.f64 z) |
Compiled 46 to 34 computations (26.1% saved)
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) x) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y)) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
| Outputs |
|---|
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
4 calls:
| 3.0ms | x |
| 3.0ms | (sqrt.f64 z) |
| 3.0ms | z |
| 3.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 74.8% | 3 | x |
| 77.4% | 3 | y |
| 63.1% | 4 | z |
| 63.1% | 4 | (sqrt.f64 z) |
Compiled 17 to 13 computations (23.5% saved)
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) x) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y)) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) |
| Outputs |
|---|
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) |
1 calls:
| 3.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 77.4% | 3 | y |
Compiled 4 to 3 computations (25% saved)
Total -7.6b remaining (-25.8%)
Threshold costs -7.6b (-25.8%)
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) x) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y)) |
| Outputs |
|---|
(*.f64 #s(literal 1/2 binary64) x) |
3 calls:
| 2.0ms | x |
| 2.0ms | y |
| 2.0ms | z |
| Accuracy | Segments | Branch |
|---|---|---|
| 54.2% | 1 | z |
| 54.2% | 1 | x |
| 54.2% | 1 | y |
Compiled 12 to 9 computations (25% saved)
| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.025349932504715e+22 | 1.0700200736056834e+22 |
| 16.0ms | -1.0773809055121578e+52 | -3.1065192583820855e+49 |
| 11.0ms | 128× | 0 | valid |
Compiled 163 to 135 computations (17.2% saved)
ival-mult: 4.0ms (60.9% of total)ival-div: 1.0ms (15.2% of total)ival-add: 1.0ms (15.2% of total)ival-sqrt: 1.0ms (15.2% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.025349932504715e+22 | 1.0700200736056834e+22 |
| 15.0ms | -1.0773809055121578e+52 | -3.1065192583820855e+49 |
| 10.0ms | 128× | 0 | valid |
Compiled 155 to 127 computations (18.1% saved)
ival-mult: 2.0ms (42.5% of total)ival-div: 1.0ms (21.2% of total)ival-add: 1.0ms (21.2% of total)ival-sqrt: 1.0ms (21.2% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | egg-herbie |
| 12× | *-commutative_binary64 |
| 2× | +-commutative_binary64 |
| 2× | if-if-or-not_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 53 |
| 1 | 34 | 53 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(if (<=.f64 y #s(literal -32000000000000001403066977442438315348289524858880 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))))) |
(if (<=.f64 y #s(literal -41000000000000000012827519726777094232637840556032 binary64)) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))))) |
(*.f64 #s(literal 1/2 binary64) x) |
| Outputs |
|---|
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(if (<=.f64 y #s(literal -32000000000000001403066977442438315348289524858880 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))))) |
(if (<=.f64 y #s(literal -41000000000000000012827519726777094232637840556032 binary64)) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))))) |
(*.f64 #s(literal 1/2 binary64) x) |
| 4668× | *-lowering-*.f32 |
| 4668× | *-lowering-*.f64 |
| 3400× | *-lowering-*.f32 |
| 3400× | *-lowering-*.f64 |
| 3126× | /-lowering-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 71 |
| 1 | 116 | 68 |
| 2 | 746 | 65 |
| 0 | 8643 | 65 |
| 0 | 75 | 622 |
| 1 | 264 | 578 |
| 2 | 891 | 578 |
| 3 | 2789 | 554 |
| 4 | 7950 | 554 |
| 0 | 8118 | 554 |
| 0 | 11 | 8 |
| 1 | 22 | 7 |
| 2 | 37 | 7 |
| 3 | 48 | 7 |
| 0 | 48 | 7 |
| 1× | fuel |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 193 to 124 computations (35.8% saved)
Compiled 148 to 68 computations (54.1% saved)
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