sqrt A (should all be same)
Time bar (total: 1.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 1 |
| 100% | 100% | 0% | 0% | 0% | 0% | 0% | 2 |
Compiled 10 to 5 computations (50% saved)
ival-add: 0.0ms (0% of total)ival-mult: 0.0ms (0% of total)const: 0.0ms (0% of total)ival-sqrt: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 382.0ms | 8256× | 0 | valid |
ival-mult: 95.0ms (42.1% of total)ival-sqrt: 73.0ms (32.4% of total)ival-add: 48.0ms (21.3% of total)const: 7.0ms (3.1% of total)backward-pass: 3.0ms (1.3% of total)| 2× | egg-herbie |
| 172× | fmsub-define |
| 168× | fnmadd-define |
| 162× | fnmsub-define |
| 112× | fma-define |
| 80× | sum3-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 10 |
| 1 | 32 | 10 |
| 2 | 80 | 10 |
| 3 | 214 | 10 |
| 4 | 409 | 10 |
| 5 | 627 | 10 |
| 6 | 694 | 10 |
| 7 | 697 | 10 |
| 0 | 4 | 3 |
| 1 | 11 | 3 |
| 2 | 14 | 3 |
| 3 | 17 | 3 |
| 0 | 17 | 3 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(sqrt (+ (* x x) (* x x))) |
| Outputs |
|---|
(sqrt (+ (* x x) (* x x))) |
(hypot.f64 x x) |
| Inputs |
|---|
(sqrt (+ (* x x) (* x x))) |
(sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x)))) |
(neg (sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x))))) |
| Outputs |
|---|
(sqrt (+ (* x x) (* x x))) |
(hypot x x) |
(sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x)))) |
(hypot x x) |
(neg (sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x))))) |
(neg (hypot x x)) |
(abs x)
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 151 | 0 | - | 2 | (5.61989427618999e-158) | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (*.f64 x x) |
| 0 | 0 | - | 0 | - | (+.f64 (*.f64 x x) (*.f64 x x)) |
| 31.0ms | 512× | 0 | valid |
Compiled 51 to 14 computations (72.5% saved)
ival-mult: 7.0ms (47.6% of total)ival-sqrt: 4.0ms (27.2% of total)ival-add: 3.0ms (20.4% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)Compiled 4 to 2 computations (50% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (hypot.f64 x x) |
Compiled 4 to 2 computations (50% saved)
| 1× | egg-herbie |
Found 1 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (hypot.f64 x x) |
| 14× | *-lowering-*.f32 |
| 14× | *-lowering-*.f64 |
| 4× | *-commutative |
| 4× | +-lowering-+.f64 |
| 4× | count-2 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 4 |
| 1 | 11 | 4 |
| 2 | 14 | 4 |
| 3 | 17 | 4 |
| 0 | 17 | 4 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt (+ (* x x) (* x x))) |
x |
| Outputs |
|---|
(sqrt (+ (* x x) (* x x))) |
(hypot.f64 x x) |
x |
Found 1 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (hypot.f64 x x) |
| 16.0ms | 256× | 0 | valid |
Compiled 6 to 3 computations (50% saved)
compiled-spec: 11.0ms (52.6% of total)ival-mult: 6.0ms (28.7% of total)ival-sqrt: 2.0ms (9.6% of total)ival-add: 1.0ms (4.8% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt (+ (* x x) (* x x)))> |
| Outputs |
|---|
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* -1 (* x (sqrt 2)))> |
#<alt (* -1 (* x (sqrt 2)))> |
#<alt (* -1 (* x (sqrt 2)))> |
#<alt (* -1 (* x (sqrt 2)))> |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (sqrt (+ (* x x) (* x x))) |
| 0.0ms | x | @ | inf | (sqrt (+ (* x x) (* x x))) |
| 0.0ms | x | @ | -inf | (sqrt (+ (* x x) (* x x))) |
| 1× | batch-egg-rewrite |
| 66× | *-lowering-*.f32 |
| 66× | *-lowering-*.f64 |
| 34× | /-lowering-/.f32 |
| 34× | /-lowering-/.f64 |
| 32× | pow-lowering-pow.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 3 |
| 1 | 23 | 3 |
| 0 | 172 | 3 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| Inputs |
|---|
(sqrt (+ (* x x) (* x x))) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64))) |
(hypot.f64 x x) |
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)))) |
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64))) |
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 x x))) |
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))) |
| 1× | egg-herbie |
| 88× | sum3-define |
| 76× | fma-define |
| 32× | fma-lowering-fma.f32 |
| 32× | fma-lowering-fma.f64 |
| 24× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 52 |
| 1 | 11 | 52 |
| 2 | 24 | 52 |
| 3 | 28 | 52 |
| 4 | 32 | 52 |
| 5 | 54 | 52 |
| 6 | 86 | 52 |
| 7 | 98 | 52 |
| 8 | 121 | 52 |
| 9 | 188 | 52 |
| 0 | 188 | 52 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* -1 (* x (sqrt 2))) |
(* -1 (* x (sqrt 2))) |
(* -1 (* x (sqrt 2))) |
(* -1 (* x (sqrt 2))) |
| Outputs |
|---|
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* x (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
Compiled 149 to 40 computations (73.2% saved)
2 alts after pruning (1 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 22 | 1 | 23 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 22 | 2 | 24 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 x x) |
| ▶ | 99.3% | (*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| 4× | *-lowering-*.f32 |
| 4× | *-lowering-*.f64 |
| 2× | *-commutative |
| 2× | sqrt-lowering-sqrt.f64 |
| 2× | sqrt-lowering-sqrt.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 8 |
| 1 | 5 | 8 |
| 0 | 5 | 8 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x (sqrt 2)) |
x |
(sqrt 2) |
2 |
| Outputs |
|---|
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
x |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 99.3% | (*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| 12.0ms | 256× | 0 | valid |
Compiled 10 to 5 computations (50% saved)
ival-mult: 2.0ms (42% of total)ival-sqrt: 2.0ms (42% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* x (sqrt 2))> |
#<alt (sqrt 2)> |
| Outputs |
|---|
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | -inf | (* x (sqrt 2)) |
| 0.0ms | x | @ | 0 | (* x (sqrt 2)) |
| 0.0ms | x | @ | inf | (* x (sqrt 2)) |
| 1× | batch-egg-rewrite |
| 564× | *-lowering-*.f32 |
| 564× | *-lowering-*.f64 |
| 202× | associate-*r* |
| 150× | associate-*l* |
| 148× | prod-exp |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 6 |
| 1 | 7 | 6 |
| 2 | 14 | 6 |
| 3 | 34 | 6 |
| 4 | 84 | 6 |
| 5 | 220 | 6 |
| 0 | 1024 | 6 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| Inputs |
|---|
(* x (sqrt 2)) |
(sqrt 2) |
| Outputs |
|---|
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))))) |
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) x)) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64))) |
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (*.f64 x (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) |
(*.f64 (*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64))) |
(exp.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) |
(exp.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 4 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) |
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 8 binary64)) |
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 4 binary64))) |
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (exp.f64 #s(literal 1/4 binary64)) (exp.f64 #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64))) |
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))) |
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) |
(*.f64 (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64))) |
| 1× | egg-herbie |
| 4× | *-lowering-*.f32 |
| 4× | *-lowering-*.f64 |
| 2× | *-commutative |
| 2× | sqrt-lowering-sqrt.f64 |
| 2× | sqrt-lowering-sqrt.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 48 |
| 1 | 5 | 48 |
| 0 | 5 | 48 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
| Outputs |
|---|
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
Compiled 562 to 147 computations (73.8% saved)
3 alts after pruning (1 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 66 | 1 | 67 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 1 | 1 |
| Total | 66 | 3 | 69 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 x x) |
| ▶ | 99.1% | (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | 99.3% | (*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
Compiled 17 to 12 computations (29.4% saved)
| 1× | egg-herbie |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) |
| ✓ | cost-diff | 6528 | (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 6528 | (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| 14× | *-lowering-*.f32 |
| 14× | *-lowering-*.f64 |
| 6× | *-commutative |
| 6× | pow-lowering-pow.f64 |
| 6× | pow-lowering-pow.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 1 | 8 | 14 |
| 2 | 16 | 12 |
| 3 | 18 | 12 |
| 0 | 18 | 12 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x (pow (pow 2 1/4) 2)) |
x |
(pow (pow 2 1/4) 2) |
(pow 2 1/4) |
2 |
1/4 |
| Outputs |
|---|
(* x (pow (pow 2 1/4) 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
x |
(pow (pow 2 1/4) 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(pow 2 1/4) |
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) |
2 |
#s(literal 2 binary64) |
1/4 |
#s(literal 1/4 binary64) |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) |
| ✓ | accuracy | 99.3% | (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 98.4% | (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
| 26.0ms | 256× | 0 | valid |
Compiled 20 to 7 computations (65% saved)
ival-pow: 14.0ms (83.6% of total)ival-mult: 2.0ms (11.9% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* x (pow (pow 2 1/4) 2))> |
#<alt (pow (pow 2 1/4) 2)> |
#<alt (pow 2 1/4)> |
| Outputs |
|---|
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
#<alt (* x (sqrt 2))> |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (* x (pow (pow 2 1/4) 2)) |
| 0.0ms | x | @ | inf | (* x (pow (pow 2 1/4) 2)) |
| 0.0ms | x | @ | -inf | (* x (pow (pow 2 1/4) 2)) |
| 1× | batch-egg-rewrite |
| 132× | associate-*r* |
| 118× | prod-exp |
| 112× | associate-*l* |
| 110× | prod-diff |
| 78× | unpow-prod-down |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 11 |
| 1 | 25 | 8 |
| 2 | 84 | 8 |
| 3 | 276 | 5 |
| 0 | 1622 | 5 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| Inputs |
|---|
(* x (pow (pow 2 1/4) 2)) |
(pow (pow 2 1/4) 2) |
(pow 2 1/4) |
| Outputs |
|---|
(*.f64 x #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) x) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64))) |
(*.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(literal 1 binary64) |
| 1× | egg-herbie |
| 4× | *-lowering-*.f32 |
| 4× | *-lowering-*.f64 |
| 2× | *-commutative |
| 2× | sqrt-lowering-sqrt.f64 |
| 2× | sqrt-lowering-sqrt.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 48 |
| 1 | 5 | 48 |
| 0 | 5 | 48 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
(* x (sqrt 2)) |
| Outputs |
|---|
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 2)) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
Compiled 73 to 11 computations (84.9% saved)
4 alts after pruning (1 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 17 | 1 | 18 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 2 | 2 |
| Total | 17 | 4 | 21 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 x x) |
| ✓ | 99.1% | (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | 99.3% | (*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ▶ | 20.3% | (*.f64 x #s(literal 1 binary64)) |
Compiled 21 to 15 computations (28.6% saved)
| 1× | egg-herbie |
Found 1 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 128 | (*.f64 x #s(literal 1 binary64)) |
| 4× | *-lowering-*.f32 |
| 4× | *-lowering-*.f64 |
| 2× | *-commutative |
| 2× | *-rgt-identity |
| 2× | 1-exp |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 3 | 3 |
| 1 | 6 | 3 |
| 2 | 7 | 3 |
| 0 | 7 | 3 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x 1) |
x |
1 |
| Outputs |
|---|
(* x 1) |
x |
x |
1 |
#s(literal 1 binary64) |
Found 1 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 1 binary64)) |
| 15.0ms | 256× | 0 | valid |
Compiled 7 to 4 computations (42.9% saved)
ival-mult: 2.0ms (83.1% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* x 1)> |
| Outputs |
|---|
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
#<alt x> |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (* x 1) |
| 0.0ms | x | @ | inf | (* x 1) |
| 0.0ms | x | @ | 0 | (* x 1) |
| 1× | batch-egg-rewrite |
| 4× | *-lowering-*.f32 |
| 4× | *-lowering-*.f64 |
| 2× | *-commutative |
| 2× | *-rgt-identity |
| 2× | 1-exp |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 3 | 1 |
| 1 | 6 | 1 |
| 2 | 7 | 1 |
| 0 | 7 | 1 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* x 1) |
| Outputs |
|---|
x |
(*.f64 x #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) x) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 12 |
| 0 | 1 | 12 |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
x |
x |
x |
x |
x |
x |
x |
x |
x |
x |
x |
x |
| Outputs |
|---|
x |
x |
x |
x |
x |
x |
x |
x |
x |
x |
x |
x |
Compiled 20 to 4 computations (80% saved)
4 alts after pruning (1 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 14 | 1 | 15 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 3 | 3 |
| Total | 15 | 4 | 19 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (hypot.f64 x x) |
| ✓ | 99.1% | (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | 99.3% | (*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| 20.3% | x |
Compiled 46 to 27 computations (41.3% saved)
| Inputs |
|---|
x |
(*.f64 x #s(literal 1 binary64)) |
(hypot.f64 x x) |
(*.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) |
(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| Outputs |
|---|
(hypot.f64 x x) |
4 calls:
| 5.0ms | (*.f64 x x) |
| 2.0ms | x |
| 2.0ms | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) |
| 2.0ms | (+.f64 (*.f64 x x) (*.f64 x x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) |
| 100.0% | 1 | (+.f64 (*.f64 x x) (*.f64 x x)) |
| 100.0% | 1 | (*.f64 x x) |
Compiled 23 to 10 computations (56.5% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
x |
(*.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
x |
1 calls:
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 20.3% | 1 | x |
Compiled 2 to 1 computations (50% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 2 | 4 |
| 1× | saturated |
| Inputs |
|---|
(hypot.f64 x x) |
x |
| Outputs |
|---|
(hypot.f64 x x) |
x |
| 564× | *-lowering-*.f32 |
| 564× | *-lowering-*.f64 |
| 202× | associate-*r* |
| 150× | associate-*l* |
| 148× | prod-exp |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 11 |
| 1 | 25 | 8 |
| 2 | 84 | 8 |
| 3 | 276 | 5 |
| 0 | 1622 | 5 |
| 0 | 6 | 52 |
| 1 | 11 | 52 |
| 2 | 24 | 52 |
| 3 | 28 | 52 |
| 4 | 32 | 52 |
| 5 | 54 | 52 |
| 6 | 86 | 52 |
| 7 | 98 | 52 |
| 8 | 121 | 52 |
| 9 | 188 | 52 |
| 0 | 188 | 52 |
| 0 | 4 | 3 |
| 1 | 11 | 3 |
| 2 | 14 | 3 |
| 3 | 17 | 3 |
| 0 | 17 | 3 |
| 0 | 3 | 1 |
| 1 | 6 | 1 |
| 2 | 7 | 1 |
| 0 | 7 | 1 |
| 0 | 4 | 6 |
| 1 | 7 | 6 |
| 2 | 14 | 6 |
| 3 | 34 | 6 |
| 4 | 84 | 6 |
| 5 | 220 | 6 |
| 0 | 1024 | 6 |
| 1× | fuel |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
Compiled 28 to 17 computations (39.3% saved)
(abs x)
Compiled 44 to 20 computations (54.5% saved)
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