Details

Time bar (total: 8.7s)

analyze1.2s (14%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
9.4%90.4%0.2%10
14%83.4%2.5%11
18.7%78.2%3.1%12
28.1%65.5%6.4%13
30.7%59.4%9.9%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample2.0s (22.7%)

Results
1.1s8256×body128valid
863.0ms6251×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
associate-/l*_binary64
associate-*r/_binary64
associate-/r/_binary64
fma-def_binary64
associate-/r*_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01222
12520
24520
35520
45520
55520

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
28.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
28.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
31.8b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 107 to 55 computations (48.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
3.1b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
10.2b
(/.f64 x (*.f64 y y))
21.1b
(/.f64 (*.f64 z z) (*.f64 t t))

series166.0ms (1.9%)

Counts
3 → 96
Calls

3 calls:

105.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
32.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
29.0ms
(/.f64 x (*.f64 y y))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
cbrt-undiv_binary64
div-exp_binary64
*-un-lft-identity_binary64
Counts
3 → 56
Calls

3 calls:

5.0ms
(/.f64 x (*.f64 y y))
4.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
0.0ms
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))

simplify106.0ms (1.2%)

Algorithm
egg-herbie
Rules
652×times-frac_binary64
469×unswap-sqr_binary64
438×associate-/l*_binary64
258×associate-*l/_binary64
229×associate-/r*_binary64
Counts
152 → 75
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01062182
12241962
26561913
325971888
443921885
549441885
649651885

prune81.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New68775
Fresh101
Picked101
Done000
Total70777
Error
0.1b
Counts
77 → 7
Alt Table
StatusErrorProgram
14.6b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
24.2b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (/.f64 (*.f64 z z) t) t))
16.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
22.3b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
22.3b
(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (*.f64 z z) (*.f64 t t)))
22.6b
(fma.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 1692 to 419 computations (75.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (/.f64 z t) (/.f64 x y))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))

series328.0ms (3.8%)

Counts
2 → 96
Calls

2 calls:

275.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
53.0ms
(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
pow1_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
hypot-udef_binary64
Counts
2 → 39
Calls

2 calls:

3.0ms
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
0.0ms
(hypot.f64 (/.f64 z t) (/.f64 x y))

simplify72.0ms (0.8%)

Algorithm
egg-herbie
Rules
928×associate-/l*_binary64
772×associate-/r*_binary64
212×fma-def_binary64
151×unswap-sqr_binary64
148×associate-/r/_binary64
Counts
135 → 87
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01173714
13423389
213143211
352683211

prune120.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1236129
Fresh336
Picked011
Done000
Total12610136
Error
0.0b
Counts
136 → 10
Alt Table
StatusErrorProgram
0.6b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
14.6b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
1.1b
(*.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
16.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
22.3b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
0.6b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
3.2b
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)))
1.1b
(*.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
Compiler

Compiled 4190 to 1429 computations (65.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (/.f64 z t) (/.f64 x y))
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
1.8b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series454.0ms (5.3%)

Counts
3 → 96
Calls

3 calls:

273.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
106.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
75.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
28×pow1_binary64
16×add-sqr-sqrt_binary64
15×pow-prod-up_binary64
12×associate-*l*_binary64
11×sqrt-pow1_binary64
Counts
3 → 78
Calls

3 calls:

7.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
4.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
1.0ms
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

simplify121.0ms (1.4%)

Algorithm
egg-herbie
Rules
777×fma-def_binary64
751×times-frac_binary64
417×associate-/r*_binary64
388×associate-/l*_binary64
288×associate-*l/_binary64
Counts
174 → 133
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01985187
14764629
213844233
348484233
453224233

prune293.0ms (3.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2845289
Fresh268
Picked101
Done011
Total28712299
Error
0.0b
Counts
299 → 12
Alt Table
StatusErrorProgram
1.1b
(*.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
16.0b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (fabs.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
22.3b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
0.7b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.8b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
14.6b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
1.2b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
3.2b
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)))
Compiler

Compiled 11757 to 3461 computations (70.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (/.f64 z t) (/.f64 x y))
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
0.3b
(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)
1.8b
(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series427.0ms (4.9%)

Counts
2 → 96
Calls

2 calls:

279.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
147.0ms
(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
unpow-prod-down_binary64
add-cube-cbrt_binary64
Counts
2 → 55
Calls

2 calls:

5.0ms
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
1.0ms
(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)

simplify329.0ms (3.8%)

Algorithm
egg-herbie
Rules
727×fma-def_binary64
307×times-frac_binary64
246×associate-*r*_binary64
238×cancel-sign-sub-inv_binary64
228×unswap-sqr_binary64
Counts
151 → 135
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02795734
18215456
229135228
349105228
450675228

prune290.0ms (3.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New2445249
Fresh4610
Picked011
Done011
Total24813261
Error
0.0b
Counts
261 → 13
Alt Table
StatusErrorProgram
0.8b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (fabs.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.4b
(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
22.3b
(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (*.f64 z z) (*.f64 t t)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
0.7b
(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))
0.8b
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 5/2) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3/2))
3.2b
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)))
1.2b
(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2))))
1.1b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)))
14.6b
(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
1.1b
(*.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
0.6b
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)))
Compiler

Compiled 9636 to 4195 computations (56.5% saved)

regimes2.4s (28%)

Accuracy

Total 0.4b remaining (92%)

Threshold costs 0.4b (92%)

Counts
191 → 1
Compiler

Compiled 59822 to 27330 computations (54.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0922
1922

end174.0ms (2%)

Compiler

Compiled 434 to 177 computations (59.2% saved)

Profiling

Loading profile data...