Details

Time bar (total: 8.6s)

analyze632.0ms (7.4%)

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
25%74.9%0.2%4
25%74.9%0.2%5
25%74.9%0.2%6
37.4%62.4%0.2%7
56.1%43.7%0.2%8
56.1%43.7%0.2%9
56.1%43.7%0.2%10
65.5%34.3%0.2%11
76.4%23.4%0.2%12
76.4%23.4%0.2%13
76.4%23.4%0.2%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample1.2s (14%)

Results
1.1s8256×body128valid
Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify112.0ms (1.3%)

Algorithm
egg-herbie
Rules
871×distribute-rgt-in_binary64
685×div-sub_binary64
652×distribute-lft-in_binary64
409×distribute-neg-frac_binary64
395×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01222
12522
25822
310922
422320
543716
687614
7209814
8232014
9245114
10304214
11322614
12332714
13491314

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
3.2b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
3.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
Compiler

Compiled 95 to 62 computations (34.7% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 y (/.f64 t y))
0.4b
(/.f64 -1/3 z)
3.2b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

series61.0ms (0.7%)

Counts
3 → 54
Calls

3 calls:

50.0ms
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
7.0ms
(-.f64 y (/.f64 t y))
3.0ms
(/.f64 -1/3 z)

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt_binary64
55×*-un-lft-identity_binary64
53×add-cube-cbrt_binary64
46×times-frac_binary64
39×prod-diff_binary64
Counts
3 → 110
Calls

3 calls:

6.0ms
(-.f64 y (/.f64 t y))
2.0ms
(/.f64 -1/3 z)
0.0ms
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

simplify97.0ms (1.1%)

Algorithm
egg-herbie
Rules
421×associate-/l*_binary64
411×associate-*l/_binary64
388×associate-*r/_binary64
368×times-frac_binary64
350×fma-def_binary64
Counts
164 → 137
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02442830
15661960
212561654
344141654
448411654

prune136.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1334137
Fresh011
Picked011
Done000
Total1336139
Error
0b
Counts
139 → 6
Alt Table
StatusErrorProgram
18.4b
(fma.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 -1/3 -1/3) -1/3) (*.f64 (*.f64 z z) z))) (-.f64 y (/.f64 t y)) x)
3.2b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
32.4b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y)) (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) x)
3.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.5b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
3.2b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
Compiler

Compiled 3513 to 1220 computations (65.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 t y) y)
0.0b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
0.4b
(/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y)))
3.2b
(/.f64 z (-.f64 (/.f64 t y) y))

series157.0ms (1.8%)

Counts
4 → 114
Calls

4 calls:

56.0ms
(/.f64 z (-.f64 (/.f64 t y) y))
52.0ms
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
39.0ms
(/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y)))
9.0ms
(-.f64 (/.f64 t y) y)

rewrite185.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
350×times-frac_binary64
307×add-sqr-sqrt_binary64
231×*-un-lft-identity_binary64
177×add-cube-cbrt_binary64
77×fma-def_binary64
Counts
4 → 321
Calls

4 calls:

52.0ms
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
19.0ms
(/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y)))
14.0ms
(/.f64 z (-.f64 (/.f64 t y) y))
12.0ms
(-.f64 (/.f64 t y) y)

simplify358.0ms (4.2%)

Algorithm
egg-herbie
Rules
876×fma-def_binary64
235×associate-/r/_binary64
207×fma-neg_binary64
174×*-commutative_binary64
171×associate-*l/_binary64
Counts
435 → 425
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04137929
18756936
230926719
345476718
449206718
549106718

prune468.0ms (5.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New4250425
Fresh044
Picked011
Done011
Total4256431
Error
0b
Counts
431 → 6
Alt Table
StatusErrorProgram
18.4b
(fma.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 -1/3 -1/3) -1/3) (*.f64 (*.f64 z z) z))) (-.f64 y (/.f64 t y)) x)
3.2b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
32.4b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y)) (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) x)
3.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.5b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
3.2b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
Compiler

Compiled 10532 to 3430 computations (67.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 z 3) y)
0.2b
(/.f64 y (*.f64 z 3))
0.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.7b
(/.f64 t (*.f64 (*.f64 z 3) y))

series64.0ms (0.7%)

Counts
4 → 132
Calls

4 calls:

30.0ms
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
21.0ms
(/.f64 t (*.f64 (*.f64 z 3) y))
7.0ms
(/.f64 y (*.f64 z 3))
6.0ms
(*.f64 (*.f64 z 3) y)

rewrite37.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity_binary64
29×associate-+l+_binary64
27×add-sqr-sqrt_binary64
25×add-cube-cbrt_binary64
23×add-cbrt-cube_binary64
Counts
4 → 121
Calls

4 calls:

13.0ms
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
5.0ms
(/.f64 t (*.f64 (*.f64 z 3) y))
4.0ms
(*.f64 (*.f64 z 3) y)
3.0ms
(/.f64 y (*.f64 z 3))

simplify186.0ms (2.2%)

Algorithm
egg-herbie
Rules
588×fma-def_binary64
317×associate-/l/_binary64
254×distribute-rgt-in_binary64
243×fma-neg_binary64
235×distribute-lft-in_binary64
Counts
253 → 200
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02144171
16013297
220652964
344982964
448762964

prune356.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1991200
Fresh123
Picked011
Done112
Total2015206
Error
0b
Counts
206 → 5
Alt Table
StatusErrorProgram
3.2b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
4.0b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 (/.f64 1 (*.f64 z 3)) (/.f64 t y)))
32.4b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y)) (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) x)
3.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.5b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
Compiler

Compiled 5082 to 2907 computations (42.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 1/3 (/.f64 t (*.f64 y z)))
0.5b
(*.f64 1/3 (/.f64 y z))
0.7b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
4.7b
(/.f64 t (*.f64 y z))

series181.0ms (2.1%)

Counts
4 → 15
Calls

4 calls:

78.0ms
(*.f64 1/3 (/.f64 t (*.f64 y z)))
54.0ms
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
35.0ms
(/.f64 t (*.f64 y z))
13.0ms
(*.f64 1/3 (/.f64 y z))

rewrite59.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
20×associate-*r*_binary64
19×*-un-lft-identity_binary64
Counts
4 → 110
Calls

4 calls:

16.0ms
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
12.0ms
(*.f64 1/3 (/.f64 y z))
12.0ms
(*.f64 1/3 (/.f64 t (*.f64 y z)))
7.0ms
(/.f64 t (*.f64 y z))

simplify169.0ms (2%)

Algorithm
egg-herbie
Rules
570×times-frac_binary64
427×associate-/l*_binary64
387×fma-def_binary64
356×associate-/r*_binary64
228×distribute-rgt-in_binary64
Counts
125 → 152
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02001927
15101647
215641586
348111584
449821584
549991584
649431584

prune155.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1520152
Fresh022
Picked011
Done022
Total1525157
Error
0b
Counts
157 → 5
Alt Table
StatusErrorProgram
3.2b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
4.0b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 (/.f64 1 (*.f64 z 3)) (/.f64 t y)))
32.4b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y)) (*.f64 (sqrt.f64 (/.f64 t y)) (sqrt.f64 (/.f64 t y))))) x)
3.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.5b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
Compiler

Compiled 3487 to 1551 computations (55.5% saved)

regimes3.8s (43.9%)

Accuracy

Total 0.5b remaining (94.2%)

Threshold costs 0.5b (94.2%)

Counts
301 → 3
Compiler

Compiled 48869 to 28866 computations (40.9% saved)

bsearch16.0ms (0.2%)

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02979
13979
24779
35179
45379
55279

end93.0ms (1.1%)

Compiler

Compiled 237 to 146 computations (38.4% saved)

Profiling

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