Details

Time bar (total: 15.0s)

analyze2.0s (13.5%)

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)

sample58.0ms (0.4%)

Algorithm
intervals
Results
17.0ms228×body128valid
4.0ms18×body512valid
3.0ms39×body128invalid
1.0msbody1024valid
1.0msbody256valid
0.0msbody2048valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify301.0ms (2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (131.0ms)

IterNodesCost
0497319
1497319

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.9b

Counts
2 → 1
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 t x) (-.f64 a z))
3.0b
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
6.3b
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite95.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt_binary64_3169
73×*-un-lft-identity_binary64_3147
51×times-frac_binary64_3153
31×associate-*r*_binary64_3087
27×add-cube-cbrt_binary64_3182
23×distribute-lft-out--_binary64_3099 difference-of-squares_binary64_3116
10×add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183
flip--_binary64_3122 flip3--_binary64_3151 associate-/r*_binary64_3091 pow1_binary64_3208 add-log-exp_binary64_3186 associate-/l*_binary64_3092 associate-*l*_binary64_3088
associate-/r/_binary64_3093
frac-times_binary64_3157 unswap-sqr_binary64_3115 associate-*l/_binary64_3090 associate-/l/_binary64_3094 prod-exp_binary64_3196 cbrt-undiv_binary64_3181 cbrt-unprod_binary64_3180 div-exp_binary64_3198 div-inv_binary64_3144
*-commutative_binary64_3078 clear-num_binary64_3146 flip-+_binary64_3121 pow-prod-down_binary64_3218 frac-2neg_binary64_3158 flip3-+_binary64_3150 +-commutative_binary64_3077 div-sub_binary64_3152 associate-*r/_binary64_3089 sum-log_binary64_3238
Counts
3 → 119
Calls

3 calls:

47.0ms
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
18.0ms
(/.f64 (-.f64 t x) (-.f64 a z))
8.0ms
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

series811.0ms (5.4%)

Counts
3 → 9
Calls

3 calls:

415.0ms
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
297.0ms
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
99.0ms
(/.f64 (-.f64 t x) (-.f64 a z))

simplify131.0ms (0.9%)

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
058232420

prune247.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11612128
Fresh000
Picked101
Done000
Total11712129

Merged error: 2.9b

Counts
129 → 12
Compiler

Compiled 2925 to 644 computations (78% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 a z))
0.6b
(cbrt.f64 (-.f64 a z))
0.6b
(cbrt.f64 (-.f64 a z))
6.4b
(+.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)))))

rewrite41.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod_binary64_3178
13×*-un-lft-identity_binary64_3147 add-sqr-sqrt_binary64_3169
add-cube-cbrt_binary64_3182
cbrt-div_binary64_3179 add-log-exp_binary64_3186
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 pow1_binary64_3208
flip--_binary64_3122 pow1/3_binary64_3229 flip3--_binary64_3151 distribute-lft-out--_binary64_3099 difference-of-squares_binary64_3116
flip-+_binary64_3121 flip3-+_binary64_3150 +-commutative_binary64_3077 sum-log_binary64_3238
Counts
4 → 56
Calls

4 calls:

9.0ms
(+.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)))))
6.0ms
(cbrt.f64 (-.f64 a z))
6.0ms
(cbrt.f64 (-.f64 a z))
6.0ms
(cbrt.f64 (-.f64 a z))

series1.1s (7.2%)

Counts
4 → 12
Calls

4 calls:

458.0ms
(+.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)))))
208.0ms
(cbrt.f64 (-.f64 a z))
206.0ms
(cbrt.f64 (-.f64 a z))
200.0ms
(cbrt.f64 (-.f64 a z))

simplify117.0ms (0.8%)

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
056811067

prune155.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh01111
Picked011
Done000
Total681280

Merged error: 2.9b

Counts
80 → 12
Compiler

Compiled 2838 to 596 computations (79% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 a z))
0.6b
(cbrt.f64 (-.f64 a z))
2.2b
(*.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))))
6.1b
(+.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)))))

rewrite135.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt_binary64_3169
59×*-un-lft-identity_binary64_3147
52×times-frac_binary64_3153
46×associate-*r*_binary64_3087
37×cbrt-prod_binary64_3178
27×add-cube-cbrt_binary64_3182
25×add-exp-log_binary64_3185
18×cbrt-div_binary64_3179 add-cbrt-cube_binary64_3183
17×associate-*l*_binary64_3088
16×distribute-lft-out--_binary64_3099 difference-of-squares_binary64_3116
10×associate-/r/_binary64_3093
flip--_binary64_3122 flip3--_binary64_3151
prod-exp_binary64_3196 cbrt-unprod_binary64_3180
cbrt-undiv_binary64_3181 div-exp_binary64_3198
unswap-sqr_binary64_3115 pow1_binary64_3208 add-log-exp_binary64_3186
frac-times_binary64_3157
associate-*l/_binary64_3090 associate-*r/_binary64_3089
pow1/3_binary64_3229 div-inv_binary64_3144
*-commutative_binary64_3078 flip-+_binary64_3121 pow-prod-down_binary64_3218 flip3-+_binary64_3150 +-commutative_binary64_3077 sum-log_binary64_3238
Counts
4 → 134
Calls

4 calls:

81.0ms
(*.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))))
8.0ms
(+.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)))))
6.0ms
(cbrt.f64 (-.f64 a z))
6.0ms
(cbrt.f64 (-.f64 a z))

series1.5s (9.7%)

Counts
4 → 12
Calls

4 calls:

608.0ms
(*.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))))
442.0ms
(+.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)))))
205.0ms
(cbrt.f64 (-.f64 a z))
202.0ms
(cbrt.f64 (-.f64 a z))

simplify124.0ms (0.8%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
056053915

prune271.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1433146
Fresh2810
Picked101
Done011
Total14612158

Merged error: 2.9b

Counts
158 → 12
Compiler

Compiled 4729 to 880 computations (81.4% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.1b
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
2.1b
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
2.1b
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
6.1b
(+.f64 x (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

rewrite129.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
51×cbrt-prod_binary64_3178
39×cbrt-div_binary64_3179
24×associate-/r/_binary64_3093
18×flip--_binary64_3122 flip3--_binary64_3151
16×*-un-lft-identity_binary64_3147 add-sqr-sqrt_binary64_3169
15×times-frac_binary64_3153
12×frac-times_binary64_3157
10×add-cube-cbrt_binary64_3182
associate-*l/_binary64_3090 add-log-exp_binary64_3186 associate-*r/_binary64_3089
add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 pow1_binary64_3208
pow1/3_binary64_3229 distribute-lft-out--_binary64_3099 difference-of-squares_binary64_3116 div-inv_binary64_3144
flip-+_binary64_3121 flip3-+_binary64_3150 +-commutative_binary64_3077 sum-log_binary64_3238
Counts
4 → 89
Calls

4 calls:

29.0ms
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
29.0ms
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
28.0ms
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
8.0ms
(+.f64 x (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

series2.9s (19.3%)

Counts
4 → 12
Calls

4 calls:

799.0ms
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
793.0ms
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
789.0ms
(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
505.0ms
(+.f64 x (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

simplify171.0ms (1.1%)

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
049723603
149723603

prune244.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1010101
Fresh01010
Picked011
Done011
Total10112113

Merged error: 2.9b

Counts
113 → 12
Compiler

Compiled 6252 to 710 computations (88.6% saved)

regimes1.3s (8.6%)

Compiler

Compiled 7578 to 4646 computations (38.7% saved)

bsearch7.0ms (0%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
077121
177121

end0.0ms (0%)

sample3.1s (20.5%)

Algorithm
intervals
Results
518.0ms6767×body128valid
113.0ms369×body1024valid
94.0ms457×body512valid
91.0ms1173×body128invalid
55.0ms350×body256valid
20.0ms57×body2048valid
Compiler

Compiled 1331 to 799 computations (40% saved)

Profiling

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