Details

Time bar (total: 7.8s)

analyze2.3s (29.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
3.1%96.5%0.3%9
4.7%95%0.3%10
4.7%95%0.3%11
5.1%82.1%12.8%12
6.2%74.7%19%13
6.4%74.5%19%14
Compiler

Compiled 41 to 30 computations (26.8% saved)

sample136.0ms (1.7%)

Algorithm
intervals
Results
33.0ms256×body128valid
21.0ms165×body128nan
Compiler

Compiled 88 to 66 computations (25% saved)

simplify48.0ms (0.6%)

Algorithm
egg-herbie
Rules
829×fma-neg_binary64
433×exp-sum_binary64
321×distribute-rgt-in_binary64
303×distribute-lft-in_binary64
279×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03047
15542
213640
351240
4210640
5452040
6499240

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
1.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
1.9b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
Compiler

Compiled 135 to 87 computations (35.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b
(/.f64 2/3 t)
0.8b
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
4.2b
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series148.0ms (1.9%)

Counts
4 → 88
Calls

4 calls:

70.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
40.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
32.0ms
(*.f64 z (sqrt.f64 (+.f64 t a)))
5.0ms
(/.f64 2/3 t)

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
Counts
4 → 91
Calls

4 calls:

6.0ms
(*.f64 z (sqrt.f64 (+.f64 t a)))
6.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
2.0ms
(/.f64 2/3 t)
0.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify120.0ms (1.5%)

Algorithm
egg-herbie
Rules
801×times-frac_binary64
430×cancel-sign-sub-inv_binary64
324×fma-neg_binary64
272×sub-neg_binary64
270×fma-def_binary64
Counts
179 → 189
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03214150
18643932
229923925
348653924
449563924

prune204.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1863189
Fresh000
Picked101
Done000
Total1873190
Error
0.0b
Counts
190 → 3
Alt Table
StatusErrorProgram
1.2b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
19.4b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
15.0b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
Compiler

Compiled 6995 to 3540 computations (49.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 a t))
0.4b
(/.f64 2/3 t)
0.8b
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
6.5b
(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))

series136.0ms (1.7%)

Counts
3 → 64
Calls

3 calls:

71.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
41.0ms
(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))
23.0ms
(sqrt.f64 (+.f64 a t))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64
13×associate-*l*_binary64
13×add-cube-cbrt_binary64
11×times-frac_binary64
Counts
3 → 73
Calls

3 calls:

9.0ms
(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))
2.0ms
(sqrt.f64 (+.f64 a t))
0.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))

simplify132.0ms (1.7%)

Algorithm
egg-herbie
Rules
397×cancel-sign-sub-inv_binary64
304×fma-neg_binary64
266×sub-neg_binary64
252×fma-def_binary64
249×distribute-rgt-in_binary64
Counts
137 → 160
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02803737
18013571
225373549
346013544
449873544
549633544

prune202.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1930193
Fresh022
Picked011
Done000
Total1933196
Error
0.0b
Counts
196 → 3
Alt Table
StatusErrorProgram
1.2b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
19.4b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
15.0b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
Compiler

Compiled 7162 to 3568 computations (50.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 t))
0.2b
(*.f64 (sqrt.f64 (/.f64 1 t)) z)
0.3b
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))
0.4b
(/.f64 2/3 t)

series67.0ms (0.9%)

Counts
3 → 51
Calls

3 calls:

49.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))
13.0ms
(*.f64 (sqrt.f64 (/.f64 1 t)) z)
5.0ms
(sqrt.f64 (/.f64 1 t))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64
29×sqrt-prod_binary64
22×times-frac_binary64
21×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
Counts
3 → 77
Calls

3 calls:

11.0ms
(*.f64 (sqrt.f64 (/.f64 1 t)) z)
2.0ms
(sqrt.f64 (/.f64 1 t))
0.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

simplify149.0ms (1.9%)

Algorithm
egg-herbie
Rules
659×distribute-rgt-in_binary64
617×distribute-lft-in_binary64
462×fma-neg_binary64
279×sub-neg_binary64
268×fma-def_binary64
Counts
128 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01322796
12922685
28622514
322302438
452672438

prune160.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1511152
Fresh101
Picked101
Done011
Total1532155
Error
0.0b
Counts
155 → 2
Alt Table
StatusErrorProgram
1.2b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
8.3b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))) x))
Compiler

Compiled 4735 to 2962 computations (37.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 b (-.f64 -5/6 a))
0.4b
(/.f64 2/3 t)
0.5b
(fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))
1.6b
(fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a)))

series67.0ms (0.9%)

Counts
3 → 120
Calls

3 calls:

34.0ms
(fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a)))
28.0ms
(fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))
5.0ms
(*.f64 b (-.f64 -5/6 a))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
18×prod-diff_binary64
13×distribute-lft-in_binary64
Counts
3 → 70
Calls

3 calls:

6.0ms
(*.f64 b (-.f64 -5/6 a))
0.0ms
(fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a)))
0.0ms
(fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))

simplify125.0ms (1.6%)

Algorithm
egg-herbie
Rules
787×fma-neg_binary64
636×fma-def_binary64
294×distribute-rgt-in_binary64
288×exp-prod_binary64
273×distribute-lft-in_binary64
Counts
190 → 126
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01913719
13653319
211682773
332402773
448822773
549112773

prune299.0ms (3.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1590159
Fresh000
Picked011
Done011
Total1592161
Error
0.0b
Counts
161 → 2
Alt Table
StatusErrorProgram
1.2b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
8.3b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))) x))
Compiler

Compiled 5094 to 2834 computations (44.4% saved)

regimes1.0s (13.3%)

Accuracy

Total 1.7b remaining (93.2%)

Threshold costs 0b (0%)

Counts
71 → 1
Compiler

Compiled 27429 to 19725 computations (28.1% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02440
13140
24240
34640
44840
54740

end1.0ms (0%)

Compiler

Compiled 34 to 23 computations (32.4% saved)

sample2.3s (29.5%)

Algorithm
intervals
Results
1.0s8000×body128valid
580.0ms4842×body128nan
Compiler

Compiled 148 to 105 computations (29.1% saved)

Profiling

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