Details

Time bar (total: 4.0s)

analyze235.0ms (5.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
50%50%0.1%6
68.7%31.2%0.1%7
81.2%18.7%0.1%8
89%10.9%0.1%9
92.1%7.8%0.1%10
95.6%4.3%0.1%11
96.4%3.5%0.1%12
98%1.9%0.1%13
98.2%1.7%0.1%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample31.0ms (0.8%)

Algorithm
intervals
Results
17.0ms256×body128valid
Compiler

Compiled 25 to 17 computations (32% saved)

simplify152.0ms (3.8%)

Algorithm
egg-herbie
Rules
878×div-sub_binary64
546×times-frac_binary64
500×sub-neg_binary64
408×fma-def_binary64
395×neg-sub0_binary64
Counts
1 → 2
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0813
11613
24013
38113
415313
524813
643511
7107711
8302911
9355811
10395911
11415811
12437711
13455211
14508311

prune7.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
9.2b
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
13.6b
(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))
Compiler

Compiled 61 to 40 computations (34.4% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 1/2 (/.f64 x y) -1/2)
9.2b
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series32.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

21.0ms
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
11.0ms
(fma.f64 1/2 (/.f64 x y) -1/2)

rewrite7.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 39
Calls

2 calls:

4.0ms
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
1.0ms
(fma.f64 1/2 (/.f64 x y) -1/2)

simplify159.0ms (4%)

Algorithm
egg-herbie
Rules
427×fma-neg_binary64
381×cancel-sign-sub-inv_binary64
231×fma-def_binary64
198×associate-/l*_binary64
198×times-frac_binary64
Counts
87 → 62
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0981389
12261308
26791260
324111246
445771246
549931246
649411246

prune69.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New59362
Fresh101
Picked011
Done000
Total60464
Error
0b
Counts
64 → 4
Alt Table
StatusErrorProgram
9.2b
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
20.5b
(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
10.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
32.9b
(*.f64 2 y)
Compiler

Compiled 1046 to 614 computations (41.3% saved)

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 x)
0.7b
(*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))
3.2b
(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
9.5b
(cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))

series242.0ms (6%)

Counts
4 → 84
Calls

4 calls:

84.0ms
(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
65.0ms
(cbrt.f64 x)
47.0ms
(*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))
45.0ms
(cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))

rewrite34.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
22×cbrt-prod_binary64
18×add-exp-log_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
Counts
4 → 91
Calls

4 calls:

13.0ms
(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
9.0ms
(*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))
1.0ms
(cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))
1.0ms
(cbrt.f64 x)

simplify365.0ms (9%)

Algorithm
egg-herbie
Rules
353×times-frac_binary64
263×fma-neg_binary64
256×associate-/r*_binary64
248×associate-*r*_binary64
240×associate-/l*_binary64
Counts
175 → 230
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03915998
110845235
242934812
349784810
450904810

prune644.0ms (16%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New3660366
Fresh022
Picked011
Done011
Total3664370
Error
0b
Counts
370 → 4
Alt Table
StatusErrorProgram
9.2b
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
20.5b
(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
10.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
32.9b
(*.f64 2 y)
Compiler

Compiled 17118 to 10312 computations (39.8% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 1/2 (/.f64 x y) -1/2)
1.0b
(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))
4.7b
(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
4.9b
(log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))

series55.0ms (1.4%)

Counts
3 → 72
Calls

3 calls:

20.0ms
(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
19.0ms
(log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))
15.0ms
(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))

rewrite9.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
3 → 51
Calls

3 calls:

4.0ms
(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
1.0ms
(log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))
1.0ms
(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))

simplify171.0ms (4.2%)

Algorithm
egg-herbie
Rules
383×fma-def_binary64
314×times-frac_binary64
278×associate-/l*_binary64
235×associate-+l+_binary64
216×associate-/r*_binary64
Counts
123 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01632115
13941984
212521905
347931905
449881905
549391905

prune140.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1431144
Fresh101
Picked101
Done022
Total1453148
Error
0b
Counts
148 → 3
Alt Table
StatusErrorProgram
33.5b
(*.f64 2 (+.f64 y (*.f64 (/.f64 y x) y)))
9.2b
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
10.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
Compiler

Compiled 2508 to 1554 computations (38% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 y (*.f64 (/.f64 y x) y))
0.1b
(*.f64 (/.f64 y x) y)

series37.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

22.0ms
(*.f64 (/.f64 y x) y)
13.0ms
(+.f64 y (*.f64 (/.f64 y x) y))

rewrite16.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
13×associate-*l*_binary64
12×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
10×times-frac_binary64
Counts
2 → 52
Calls

2 calls:

8.0ms
(*.f64 (/.f64 y x) y)
4.0ms
(+.f64 y (*.f64 (/.f64 y x) y))

simplify173.0ms (4.3%)

Algorithm
egg-herbie
Rules
509×fma-neg_binary64
366×associate-*l*_binary64
317×associate-*r*_binary64
296×associate-/r/_binary64
282×distribute-rgt-in_binary64
Counts
100 → 87
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
089952
1216847
2587844
32238836
44495836
54989836
64994836
74950836

prune65.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New87087
Fresh000
Picked011
Done022
Total87390
Error
0b
Counts
90 → 3
Alt Table
StatusErrorProgram
33.5b
(*.f64 2 (+.f64 y (*.f64 (/.f64 y x) y)))
9.2b
(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
10.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
Compiler

Compiled 1359 to 532 computations (60.9% saved)

regimes236.0ms (5.9%)

Accuracy

Total 0.9b remaining (99%)

Threshold costs 0.9b (99%)

Counts
18 → 5
Compiler

Compiled 847 to 568 computations (32.9% saved)

bsearch1.0ms (0%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.3%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
if-not_binary64
if-if-or-not_binary64
not-not_bool
not-or_bool
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
026122
133111
240102
348100
452100
555100
655100
756100
856100

end2.0ms (0.1%)

Compiler

Compiled 69 to 42 computations (39.1% saved)

sample1.1s (26.6%)

Algorithm
intervals
Results
559.0ms8000×body128valid
Compiler

Compiled 138 to 87 computations (37% saved)

Profiling

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