Details

Time bar (total: 10.0s)

analyze1.1s (10.9%)

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
0%99.8%0.2%9
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.4%0.2%12
12.2%87.6%0.2%13
21.8%77.8%0.4%14
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample29.0ms (0.3%)

Algorithm
intervals
Results
9.0ms223×body128valid
2.0ms18×body512valid
2.0ms47×body128invalid
1.0msbody1024valid
1.0msbody256valid
0.0msbody2048valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify262.0ms (2.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
0488719
1488719

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.7b

Counts
2 → 1
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (-.f64 y z) (-.f64 t x))
1.8b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.5b
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite48.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64_18677 *-un-lft-identity_binary64_18655
13×flip--_binary64_18630 flip3--_binary64_18659
10×add-cbrt-cube_binary64_18691 add-exp-log_binary64_18693
add-cube-cbrt_binary64_18690
associate-/l/_binary64_18602 frac-times_binary64_18665
cancel-sign-sub-inv_binary64_18621
associate-*l*_binary64_18596 times-frac_binary64_18661 associate-*r*_binary64_18595 associate-/r*_binary64_18599 pow1_binary64_18716 add-log-exp_binary64_18694
distribute-rgt-in_binary64_18605 difference-of-squares_binary64_18624 associate-*r/_binary64_18597 distribute-lft-in_binary64_18604 distribute-lft-out--_binary64_18607 associate-*l/_binary64_18598
associate-/r/_binary64_18601 div-exp_binary64_18706 cbrt-unprod_binary64_18688 prod-exp_binary64_18704 cbrt-undiv_binary64_18689 sub-neg_binary64_18648
sum-log_binary64_18746 distribute-lft-out_binary64_18606 frac-2neg_binary64_18666 flip-+_binary64_18629 unswap-sqr_binary64_18623 div-inv_binary64_18652 clear-num_binary64_18654 flip3-+_binary64_18658 associate-/l*_binary64_18600 *-commutative_binary64_18586 +-commutative_binary64_18585 pow-prod-down_binary64_18726
Counts
3 → 85
Calls

3 calls:

16.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
12.0ms
(*.f64 (-.f64 y z) (-.f64 t x))
10.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series960.0ms (9.6%)

Counts
3 → 9
Calls

3 calls:

515.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
369.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
76.0ms
(*.f64 (-.f64 y z) (-.f64 t x))

simplify67.0ms (0.7%)

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
070211683

prune525.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New85994
Fresh000
Picked101
Done000
Total86995

Merged error: 2.7b

Counts
95 → 9
Compiler

Compiled 9877 to 5597 computations (43.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.6b
(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
2.3b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
6.3b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite97.0ms (1%)

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt_binary64_18677
78×*-un-lft-identity_binary64_18655
60×cbrt-prod_binary64_18686
54×associate-*r*_binary64_18595
52×times-frac_binary64_18661
34×add-cube-cbrt_binary64_18690
28×cbrt-div_binary64_18687
27×add-exp-log_binary64_18693
25×associate-*l*_binary64_18596
21×distribute-lft-out--_binary64_18607
19×difference-of-squares_binary64_18624
18×add-cbrt-cube_binary64_18691
14×flip--_binary64_18630 flip3--_binary64_18659
13×pow1_binary64_18716
10×associate-/r/_binary64_18601 unswap-sqr_binary64_18623 swap-sqr_binary64_18622
cbrt-unprod_binary64_18688 prod-exp_binary64_18704 frac-times_binary64_18665
div-exp_binary64_18706 pow1/3_binary64_18737 cbrt-undiv_binary64_18689
add-log-exp_binary64_18694
associate-*r/_binary64_18597 associate-*l/_binary64_18598
pow-prod-down_binary64_18726
div-inv_binary64_18652 pow-prod-up_binary64_18725 *-commutative_binary64_18586 pow-sqr_binary64_18628
sum-log_binary64_18746 flip-+_binary64_18629 pow2_binary64_18736 flip3-+_binary64_18658 pow-plus_binary64_18718 +-commutative_binary64_18585
Counts
4 → 175
Calls

4 calls:

45.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
14.0ms
(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
7.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
4.0ms
(cbrt.f64 (-.f64 a z))

series1.8s (17.7%)

Counts
4 → 12
Calls

4 calls:

773.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
525.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
254.0ms
(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
219.0ms
(cbrt.f64 (-.f64 a z))

simplify90.0ms (0.9%)

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
057124478

prune335.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1843187
Fresh268
Picked011
Done000
Total18610196

Merged error: 2.7b

Counts
196 → 10
Compiler

Compiled 8376 to 2934 computations (65% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 y z) (-.f64 a z))
1.8b
(+.f64 x (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 1))
2.3b
(*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))

rewrite53.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt_binary64_18677
75×*-un-lft-identity_binary64_18655
51×times-frac_binary64_18661
31×associate-*r*_binary64_18595
27×add-cube-cbrt_binary64_18690
23×difference-of-squares_binary64_18624 distribute-lft-out--_binary64_18607
10×add-cbrt-cube_binary64_18691 add-exp-log_binary64_18693
associate-*l*_binary64_18596 flip--_binary64_18630 flip3--_binary64_18659 associate-/l*_binary64_18600 associate-/r*_binary64_18599 pow1_binary64_18716 add-log-exp_binary64_18694
associate-/r/_binary64_18601
div-exp_binary64_18706 cbrt-unprod_binary64_18688 unswap-sqr_binary64_18623 div-inv_binary64_18652 prod-exp_binary64_18704 associate-/l/_binary64_18602 associate-*l/_binary64_18598 frac-times_binary64_18665 cbrt-undiv_binary64_18689
div-sub_binary64_18660 sum-log_binary64_18746 distribute-lft-out_binary64_18606 frac-2neg_binary64_18666 flip-+_binary64_18629 clear-num_binary64_18654 flip3-+_binary64_18658 associate-*r/_binary64_18597 *-commutative_binary64_18586 +-commutative_binary64_18585 pow-prod-down_binary64_18726
Counts
3 → 120
Calls

3 calls:

23.0ms
(*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))
10.0ms
(/.f64 (-.f64 y z) (-.f64 a z))
6.0ms
(+.f64 x (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 1))

series1.1s (10.5%)

Counts
3 → 9
Calls

3 calls:

549.0ms
(+.f64 x (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 1))
407.0ms
(*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))
97.0ms
(/.f64 (-.f64 y z) (-.f64 a z))

simplify71.0ms (0.7%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049742424
149742424

prune162.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1281129
Fresh268
Picked011
Done011
Total1309139

Merged error: 2.7b

Counts
139 → 9
Compiler

Compiled 3776 to 1280 computations (66.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 y z))
0.6b
(cbrt.f64 (-.f64 y z))
1.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))
2.6b
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))))

rewrite81.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
73×add-exp-log_binary64_18693
35×add-cbrt-cube_binary64_18691
32×cbrt-unprod_binary64_18688 prod-exp_binary64_18704
22×div-exp_binary64_18706 cbrt-undiv_binary64_18689
15×cbrt-prod_binary64_18686 add-sqr-sqrt_binary64_18677 *-un-lft-identity_binary64_18655
14×associate-*l*_binary64_18596
pow1_binary64_18716 add-cube-cbrt_binary64_18690
times-frac_binary64_18661
cbrt-div_binary64_18687 add-log-exp_binary64_18694
associate-*r/_binary64_18597 frac-times_binary64_18665
flip--_binary64_18630 flip3--_binary64_18659 difference-of-squares_binary64_18624 distribute-lft-out--_binary64_18607 associate-*l/_binary64_18598 pow-prod-down_binary64_18726
associate-/r/_binary64_18601 pow1/3_binary64_18737
sum-log_binary64_18746 flip-+_binary64_18629 div-inv_binary64_18652 associate-*r*_binary64_18595 flip3-+_binary64_18658 *-commutative_binary64_18586 +-commutative_binary64_18585
Counts
4 → 103
Calls

4 calls:

47.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))
7.0ms
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))))
4.0ms
(cbrt.f64 (-.f64 y z))
4.0ms
(cbrt.f64 (-.f64 y z))

series1.7s (17.4%)

Counts
4 → 12
Calls

4 calls:

769.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))
539.0ms
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))))
221.0ms
(cbrt.f64 (-.f64 y z))
216.0ms
(cbrt.f64 (-.f64 y z))

simplify103.0ms (1%)

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049443350
149443350

prune114.0ms (1.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1150115
Fresh066
Picked011
Done022
Total1159124

Merged error: 2.7b

Counts
124 → 9
Compiler

Compiled 3952 to 558 computations (85.9% saved)

regimes158.0ms (1.6%)

Compiler

Compiled 1065 to 680 computations (36.2% saved)

bsearch64.0ms (0.6%)

Steps
ItersRangePoint
10
3.661447482884462e-189
1.8835578794892312e-172
1.2510594565503939e-175
9
-5.873724201705015e-97
-7.764343139022992e-102
-7.87713316621998e-102
Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06849
16849

end0.0ms (0%)

sample1.1s (11%)

Algorithm
intervals
Results
312.0ms6720×body128valid
56.0ms499×body512valid
56.0ms378×body1024valid
51.0ms1204×body128invalid
27.0ms341×body256valid
15.0ms62×body2048valid
Compiler

Compiled 297 to 186 computations (37.4% saved)

Profiling

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