Details

Time bar (total: 10.2s)

analyze962.0ms (9.4%)

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
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
15.6%84.2%0.2%8
15.6%84.2%0.2%9
20.3%79.5%0.2%10
25.3%74.5%0.2%11
34.2%65.6%0.2%12
37.4%62%0.6%13
41.7%57.7%0.6%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample105.0ms (1%)

Algorithm
intervals
Results
13.0ms256×body128valid
11.0ms112×body128invalid
Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify94.0ms (0.9%)

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

prune4.0ms (0%)

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
4.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.7b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
Compiler

Compiled 95 to 62 computations (34.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 y (/.f64 t y))
0.3b
(/.f64 -1/3 z)
3.5b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

series40.0ms (0.4%)

Counts
3 → 54
Calls

3 calls:

34.0ms
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
5.0ms
(-.f64 y (/.f64 t y))
1.0ms
(/.f64 -1/3 z)

rewrite21.0ms (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)

simplify120.0ms (1.2%)

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

prune168.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1316137
Fresh011
Picked101
Done000
Total1327139
Error
0.0b
Counts
139 → 7
Alt Table
StatusErrorProgram
34.9b
(*.f64 (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
3.8b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
4.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
37.0b
(fma.f64 (/.f64 -1/3 z) (/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (/.f64 t y) 3)) (+.f64 (*.f64 y y) (+.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (*.f64 y (/.f64 t y))))) x)
4.0b
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)
4.0b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (/.f64 1 y) t))) (fma.f64 (neg.f64 (/.f64 1 y)) t (*.f64 (/.f64 1 y) t))) x)
Compiler

Compiled 3603 to 1287 computations (64.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 t y) y)
0.4b
(/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y)))
3.5b
(/.f64 z (-.f64 (/.f64 t y) y))

series53.0ms (0.5%)

Counts
3 → 66
Calls

3 calls:

29.0ms
(/.f64 z (-.f64 (/.f64 t y) y))
19.0ms
(/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y)))
5.0ms
(-.f64 (/.f64 t y) y)

rewrite48.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
215×times-frac_binary64
206×add-sqr-sqrt_binary64
155×*-un-lft-identity_binary64
121×add-cube-cbrt_binary64
39×prod-diff_binary64
Counts
3 → 230
Calls

3 calls:

9.0ms
(/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y)))
8.0ms
(-.f64 (/.f64 t y) y)
7.0ms
(/.f64 z (-.f64 (/.f64 t y) y))

simplify196.0ms (1.9%)

Algorithm
egg-herbie
Rules
758×fma-def_binary64
336×distribute-rgt-in_binary64
234×associate-/r/_binary64
213×fma-neg_binary64
168×associate-*l/_binary64
Counts
296 → 328
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03886880
17956125
229055851
346055844
449085844

prune301.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3253328
Fresh246
Picked011
Done000
Total3278335
Error
0.0b
Counts
335 → 8
Alt Table
StatusErrorProgram
33.8b
(+.f64 (/.f64 1/3 (/.f64 (/.f64 z (sqrt.f64 (-.f64 (/.f64 t y) y))) (sqrt.f64 (-.f64 (/.f64 t y) y)))) x)
4.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.8b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
37.0b
(fma.f64 (/.f64 -1/3 z) (/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (/.f64 t y) 3)) (+.f64 (*.f64 y y) (+.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (*.f64 y (/.f64 t y))))) x)
3.8b
(+.f64 (/.f64 1/3 (/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z))) x)
4.0b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (/.f64 1 y) t))) (fma.f64 (neg.f64 (/.f64 1 y)) t (*.f64 (/.f64 1 y) t))) x)
33.8b
(+.f64 (/.f64 (/.f64 1/3 (sqrt.f64 (/.f64 z (-.f64 (/.f64 t y) y)))) (sqrt.f64 (/.f64 z (-.f64 (/.f64 t y) y)))) x)
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
Compiler

Compiled 8297 to 2773 computations (66.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 t y) y)
0.3b
(/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z))
0.4b
(/.f64 1/3 (/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z)))
3.4b
(/.f64 (-.f64 (/.f64 t y) y) z)

series63.0ms (0.6%)

Counts
3 → 100
Calls

3 calls:

27.0ms
(/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z))
19.0ms
(/.f64 1/3 (/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z)))
16.0ms
(/.f64 (-.f64 (/.f64 t y) y) z)

rewrite114.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
901×times-frac_binary64
621×add-sqr-sqrt_binary64
465×*-un-lft-identity_binary64
361×add-cube-cbrt_binary64
104×difference-of-squares_binary64
Counts
3 → 468
Calls

3 calls:

17.0ms
(/.f64 1/3 (/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z)))
11.0ms
(/.f64 1 (/.f64 (-.f64 (/.f64 t y) y) z))
8.0ms
(/.f64 (-.f64 (/.f64 t y) y) z)

simplify390.0ms (3.8%)

Algorithm
egg-herbie
Rules
361×fma-neg_binary64
331×fma-def_binary64
323×distribute-rgt-in_binary64
310×associate-/r/_binary64
289×distribute-lft-in_binary64
Counts
568 → 618
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037214308
182413614
2277513476
3462013476
4493713476

prune629.0ms (6.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New6974701
Fresh336
Picked101
Done011
Total7018709
Error
0.0b
Counts
709 → 8
Alt Table
StatusErrorProgram
46.6b
(+.f64 (/.f64 1/3 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 t) (sqrt.f64 y))) (/.f64 (-.f64 (/.f64 (sqrt.f64 t) (sqrt.f64 y)) (sqrt.f64 y)) z)))) x)
4.0b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (/.f64 1 y) t))) (fma.f64 (neg.f64 (/.f64 1 y)) t (*.f64 (/.f64 1 y) t))) x)
3.8b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
4.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.8b
(+.f64 (*.f64 (/.f64 1/3 1) (/.f64 (-.f64 (/.f64 t y) y) z)) x)
3.7b
(+.f64 (/.f64 1 (*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y)))) x)
3.8b
(+.f64 (/.f64 1/3 (/.f64 1 (*.f64 (-.f64 (/.f64 t y) y) (/.f64 1 z)))) x)
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
Compiler

Compiled 19653 to 7565 computations (61.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 t y) y)
0.3b
(/.f64 1 (*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y))))
0.3b
(*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y)))
3.5b
(/.f64 z (-.f64 (/.f64 t y) y))

series48.0ms (0.5%)

Counts
2 → 60
Calls

2 calls:

30.0ms
(*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y)))
18.0ms
(/.f64 1 (*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y))))

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt_binary64
28×add-exp-log_binary64
25×times-frac_binary64
24×associate-*r*_binary64
21×*-un-lft-identity_binary64
Counts
2 → 80
Calls

2 calls:

11.0ms
(*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y)))
8.0ms
(/.f64 1 (*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y))))

simplify123.0ms (1.2%)

Algorithm
egg-herbie
Rules
495×times-frac_binary64
489×associate-/l*_binary64
334×fma-def_binary64
309×associate-*l/_binary64
303×associate-/r*_binary64
Counts
140 → 123
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992574
15132365
215022268
347642268
450002268
549982268
649342268

prune241.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2681269
Fresh066
Picked011
Done011
Total2689277
Error
0b
Counts
277 → 9
Alt Table
StatusErrorProgram
22.0b
(+.f64 (/.f64 1 (*.f64 3 (/.f64 (*.f64 y z) t))) x)
4.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
46.6b
(+.f64 (/.f64 1/3 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 t) (sqrt.f64 y))) (/.f64 (-.f64 (/.f64 (sqrt.f64 t) (sqrt.f64 y)) (sqrt.f64 y)) z)))) x)
4.0b
(fma.f64 (/.f64 -1/3 z) (+.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 (/.f64 1 y) t))) (fma.f64 (neg.f64 (/.f64 1 y)) t (*.f64 (/.f64 1 y) t))) x)
3.8b
(+.f64 (/.f64 1/3 (/.f64 z (-.f64 (/.f64 t y) y))) x)
3.8b
(+.f64 (*.f64 (/.f64 1/3 1) (/.f64 (-.f64 (/.f64 t y) y) z)) x)
3.7b
(+.f64 (/.f64 1 (*.f64 3 (/.f64 z (-.f64 (/.f64 t y) y)))) x)
3.8b
(+.f64 (/.f64 1/3 (/.f64 1 (*.f64 (-.f64 (/.f64 t y) y) (/.f64 1 z)))) x)
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
Compiler

Compiled 6554 to 2634 computations (59.8% saved)

regimes5.2s (50.9%)

Accuracy

Total 1.1b remaining (98.1%)

Threshold costs 0b (0%)

Counts
377 → 3
Compiler

Compiled 56499 to 35469 computations (37.2% saved)

bsearch55.0ms (0.5%)

Steps
ItersRangePoint
4
1.7254034813855388e-28
7.737074436954655e-25
5.53228479313245e-26
8
-9.527017073002953e+179
-6.122118871240926e+176
-6.22726511139875e+176
Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03375
15375
26775
37675
48175
58275
68075

end1.0ms (0%)

Compiler

Compiled 55 to 36 computations (34.5% saved)

sample1.2s (11.5%)

Algorithm
intervals
Results
466.0ms8000×body128valid
175.0ms3101×body128invalid
Compiler

Compiled 264 to 177 computations (33% saved)

Profiling

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