Details

Time bar (total: 10.8s)

analyze1.0s (9.5%)

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%89.3%0.2%12
12.2%87.5%0.2%13
21.9%77.7%0.4%14
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample28.0ms (0.3%)

Algorithm
intervals
Results
9.0ms215×body128valid
2.0ms16×body1024valid
2.0ms46×body128invalid
1.0ms11×body512valid
1.0ms13×body256valid
0.0msbody2048valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify103.0ms (1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
0508419

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.5b

Counts
2 → 1
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 t x) (-.f64 a z))
4.4b
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
5.1b
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite53.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt_binary64
73×*-un-lft-identity_binary64
51×times-frac_binary64
31×associate-*r*_binary64
27×add-cube-cbrt_binary64
23×difference-of-squares_binary64 distribute-lft-out--_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
associate-/r*_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 associate-*l*_binary64 associate-/l*_binary64 flip--_binary64
associate-/r/_binary64
associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64 frac-times_binary64 associate-*l/_binary64
pow-prod-down_binary64 flip3-+_binary64 associate-*r/_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
3 → 119
Calls

3 calls:

26.0ms
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
9.0ms
(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

series990.0ms (9.2%)

Counts
3 → 9
Calls

3 calls:

493.0ms
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
361.0ms
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
136.0ms
(/.f64 (-.f64 t x) (-.f64 a z))

simplify68.0ms (0.6%)

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
055602420

prune899.0ms (8.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New11612128
Fresh000
Picked011
Done000
Total11613129

Merged error: 3.6b

Counts
129 → 13
Compiler

Compiled 20342 to 10721 computations (47.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 t x))
0.6b
(cbrt.f64 (-.f64 t x))
0.6b
(cbrt.f64 (-.f64 t x))
8.3b
(+.f64 x (*.f64 (*.f64 (-.f64 y z) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod_binary64
13×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
add-cube-cbrt_binary64
cbrt-div_binary64 add-log-exp_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
flip3--_binary64 pow1/3_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 flip--_binary64
flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 56
Calls

4 calls:

5.0ms
(+.f64 x (*.f64 (*.f64 (-.f64 y z) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
4.0ms
(cbrt.f64 (-.f64 t x))
4.0ms
(cbrt.f64 (-.f64 t x))
4.0ms
(cbrt.f64 (-.f64 t x))

series1.2s (10.9%)

Counts
4 → 12
Calls

4 calls:

535.0ms
(+.f64 x (*.f64 (*.f64 (-.f64 y z) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
219.0ms
(cbrt.f64 (-.f64 t x))
217.0ms
(cbrt.f64 (-.f64 t x))
208.0ms
(cbrt.f64 (-.f64 t x))

simplify58.0ms (0.5%)

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
056061073

prune88.0ms (0.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh01111
Picked011
Done011
Total681381

Merged error: 3.6b

Counts
81 → 13
Compiler

Compiled 2835 to 599 computations (78.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
2.1b
(*.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))))
8.3b
(+.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)))))

rewrite80.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt_binary64
59×*-un-lft-identity_binary64
52×times-frac_binary64
46×associate-*r*_binary64
37×cbrt-prod_binary64
27×add-cube-cbrt_binary64
25×add-exp-log_binary64
18×cbrt-div_binary64 add-cbrt-cube_binary64
17×associate-*l*_binary64
16×difference-of-squares_binary64 distribute-lft-out--_binary64
10×associate-/r/_binary64
flip3--_binary64 flip--_binary64
cbrt-unprod_binary64 prod-exp_binary64
cbrt-undiv_binary64 div-exp_binary64
add-log-exp_binary64 pow1_binary64 unswap-sqr_binary64
frac-times_binary64
associate-*r/_binary64 associate-*l/_binary64
pow1/3_binary64 div-inv_binary64
pow-prod-down_binary64 flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 134
Calls

4 calls:

47.0ms
(*.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))))
5.0ms
(+.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))
4.0ms
(cbrt.f64 (-.f64 a z))

series1.6s (15%)

Counts
4 → 12
Calls

4 calls:

703.0ms
(*.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))))
502.0ms
(+.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)))))
210.0ms
(cbrt.f64 (-.f64 a z))
205.0ms
(cbrt.f64 (-.f64 a z))

simplify66.0ms (0.6%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
055843915

prune412.0ms (3.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New1406146
Fresh5510
Picked011
Done022
Total14514159

Merged error: 3.6b

Counts
159 → 14
Compiler

Compiled 10947 to 4367 computations (60.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 t x))
0.6b
(cbrt.f64 (cbrt.f64 (-.f64 a z)))
1.4b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))
8.8b
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite74.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
40×add-exp-log_binary64
38×cbrt-div_binary64
27×add-sqr-sqrt_binary64
22×add-cbrt-cube_binary64
21×cbrt-prod_binary64
17×*-un-lft-identity_binary64 associate-*l*_binary64
16×associate-*r*_binary64 associate-/r/_binary64 times-frac_binary64
15×cbrt-unprod_binary64 prod-exp_binary64
14×flip3--_binary64 flip--_binary64
12×cbrt-undiv_binary64 div-exp_binary64
11×add-cube-cbrt_binary64
frac-times_binary64
add-log-exp_binary64 pow1_binary64 unswap-sqr_binary64
associate-*r/_binary64 associate-*l/_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64
pow1/3_binary64 div-inv_binary64
pow-prod-down_binary64 flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 113
Calls

4 calls:

37.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))
6.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
5.0ms
(cbrt.f64 (cbrt.f64 (-.f64 a z)))
3.0ms
(cbrt.f64 (-.f64 t x))

series2.1s (19.8%)

Counts
4 → 12
Calls

4 calls:

1.2s
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))
545.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
220.0ms
(cbrt.f64 (-.f64 t x))
218.0ms
(cbrt.f64 (cbrt.f64 (-.f64 a z)))

simplify82.0ms (0.8%)

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050655219

prune238.0ms (2.2%)

Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New1232125
Fresh01010
Picked011
Done033
Total12316139

Merged error: 3.6b

Counts
139 → 16
Compiler

Compiled 7865 to 1985 computations (74.8% saved)

regimes317.0ms (2.9%)

Compiler

Compiled 3570 to 1788 computations (49.9% saved)

bsearch3.0ms (0%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
075174
175174

end0.0ms (0%)

sample1.2s (10.9%)

Algorithm
intervals
Results
271.0ms6652×body128valid
74.0ms409×body1024valid
58.0ms1151×body128invalid
55.0ms500×body512valid
28.0ms373×body256valid
12.0ms66×body2048valid
Compiler

Compiled 716 to 334 computations (53.4% saved)

Profiling

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