Details

Time bar (total: 9.7s)

analyze1.0s (10.6%)

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)

sample33.0ms (0.3%)

Algorithm
intervals
Results
8.0ms216×body80valid
6.0ms36×body80invalid
2.0ms12×body640valid
1.0msbody1280valid
1.0ms12×body320valid
1.0msbody160valid
0.0msbody2560valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify169.0ms (1.8%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (154.0ms)

IterNodesCost
0485219
1485219

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 20.0b

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))
2.0b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
14.3b
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite42.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
13×flip3--_binary64 flip--_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
associate-/l/_binary64 frac-times_binary64
add-cube-cbrt_binary64
associate-/r*_binary64 add-log-exp_binary64 pow1_binary64 associate-*r*_binary64 associate-*l*_binary64 times-frac_binary64
associate-*r/_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 associate-*l/_binary64
insert-posit16
sub-neg_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-/r/_binary64 prod-exp_binary64 div-exp_binary64
pow-prod-down_binary64 flip3-+_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
3 → 82
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)))

series852.0ms (8.8%)

Counts
3 → 9
Calls

3 calls:

445.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
332.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
74.0ms
(*.f64 (-.f64 y z) (-.f64 t x))

simplify115.0ms (1.2%)

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
067471650

prune109.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New791291
Fresh000
Picked011
Done000
Total791392

Merged error: 3.0b

Counts
92 → 13
Compiler

Compiled 2087 to 570 computations (72.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
1.6b
(*.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))))
6.9b
(+.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)))))

rewrite69.0ms (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
insert-posit16
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 → 138
Calls

4 calls:

44.0ms
(*.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 (16.2%)

Counts
4 → 12
Calls

4 calls:

641.0ms
(*.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))))
480.0ms
(+.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)))))
223.0ms
(cbrt.f64 (-.f64 a z))
222.0ms
(cbrt.f64 (-.f64 a z))

simplify100.0ms (1%)

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
053143985

prune158.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1464150
Fresh3811
Picked101
Done011
Total15013163

Merged error: 3.0b

Counts
163 → 13
Compiler

Compiled 4863 to 904 computations (81.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 y z))
0.5b
(cbrt.f64 (-.f64 y z))
0.7b
(*.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)))))
3.7b
(+.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))))))

rewrite65.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
73×add-exp-log_binary64
35×add-cbrt-cube_binary64
32×cbrt-unprod_binary64 prod-exp_binary64
22×cbrt-undiv_binary64 div-exp_binary64
15×*-un-lft-identity_binary64 add-sqr-sqrt_binary64 cbrt-prod_binary64
14×associate-*l*_binary64
pow1_binary64 add-cube-cbrt_binary64
times-frac_binary64
cbrt-div_binary64 add-log-exp_binary64
associate-*r/_binary64 frac-times_binary64
insert-posit16
pow-prod-down_binary64 flip3--_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 flip--_binary64 associate-*l/_binary64
pow1/3_binary64 associate-/r/_binary64
flip3-+_binary64 associate-*r*_binary64 div-inv_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 107
Calls

4 calls:

45.0ms
(*.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))

series1.6s (16.2%)

Counts
4 → 12
Calls

4 calls:

654.0ms
(*.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)))))
486.0ms
(+.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))))))
210.0ms
(cbrt.f64 (-.f64 y z))
209.0ms
(cbrt.f64 (-.f64 y z))

simplify138.0ms (1.4%)

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049743381
149743381

prune137.0ms (1.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1172119
Fresh11011
Picked011
Done011
Total11814132

Merged error: 3.0b

Counts
132 → 14
Compiler

Compiled 4422 to 747 computations (83.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.6b
(cbrt.f64 (cbrt.f64 (-.f64 a z)))
1.6b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
7.1b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))))

rewrite76.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
114×cbrt-div_binary64
40×add-exp-log_binary64
35×flip3--_binary64 associate-*r*_binary64 flip--_binary64
34×associate-/r/_binary64
33×frac-times_binary64
28×add-cbrt-cube_binary64
23×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
18×cbrt-prod_binary64
17×associate-*l*_binary64 associate-*l/_binary64
15×cbrt-unprod_binary64 prod-exp_binary64
12×cbrt-undiv_binary64 div-exp_binary64
11×associate-*r/_binary64 add-cube-cbrt_binary64 times-frac_binary64
add-log-exp_binary64 pow1_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64 insert-posit16
pow1/3_binary64 unswap-sqr_binary64 div-inv_binary64
pow-prod-down_binary64 flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 132
Calls

4 calls:

51.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
6.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))))
5.0ms
(cbrt.f64 (cbrt.f64 (-.f64 a z)))
4.0ms
(cbrt.f64 (-.f64 a z))

series1.5s (15.7%)

Counts
4 → 12
Calls

4 calls:

631.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
464.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))))
218.0ms
(cbrt.f64 (cbrt.f64 (-.f64 a z)))
205.0ms
(cbrt.f64 (-.f64 a z))

simplify169.0ms (1.7%)

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (104.0ms)

IterNodesCost
049666199
149666199

prune193.0ms (2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1422144
Fresh11011
Picked101
Done022
Total14414158

Merged error: 3.0b

Counts
158 → 14
Compiler

Compiled 6665 to 1267 computations (81% saved)

regimes256.0ms (2.6%)

Compiler

Compiled 2550 to 1386 computations (45.6% saved)

bsearch64.0ms (0.7%)

Steps
ItersRangePoint
9
6.6084722510070706e+181
5.1747654501196066e+187
3.336535496648698e+182
9
-2.1984649121398943e+196
-1.558069888018195e+189
-2.2761584503191938e+195
Compiler

Compiled 1 to 5 computations (-400% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
07385
17385

end0.0ms (0%)

sample1.2s (12.2%)

Algorithm
intervals
Results
279.0ms6577×body80valid
73.0ms489×body640valid
52.0ms418×body320valid
46.0ms1164×body80invalid
43.0ms240×body1280valid
23.0ms257×body160valid
4.0ms19×body2560valid
Compiler

Compiled 527 to 285 computations (45.9% saved)

Profiling

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