Details

Time bar (total: 8.3s)

analyze1.2s (13.9%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05278209
055
155
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)

sample32.0ms (0.4%)

Algorithm
intervals
Results
9.0ms212×body128valid
3.0ms25×body512valid
1.0msbody1024valid
1.0ms27×body128invalid
1.0msbody256valid
0.0msbody2048valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify91.0ms (1.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (86.0ms)

IterNodesCost
0493619
1493619

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
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))
1.7b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.1b
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite41.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64_13740 *-un-lft-identity_binary64_13718
13×flip3--_binary64_13722 flip--_binary64_13693
10×add-cbrt-cube_binary64_13754 add-exp-log_binary64_13756
add-cube-cbrt_binary64_13753
frac-times_binary64_13728 associate-/l/_binary64_13665
cancel-sign-sub-inv_binary64_13684
pow1_binary64_13779 associate-/r*_binary64_13662 add-log-exp_binary64_13757 times-frac_binary64_13724 associate-*l*_binary64_13659 associate-*r*_binary64_13658
associate-*r/_binary64_13660 difference-of-squares_binary64_13687 associate-*l/_binary64_13661 distribute-lft-in_binary64_13667 distribute-rgt-in_binary64_13668 distribute-lft-out--_binary64_13670
sub-neg_binary64_13711 prod-exp_binary64_13767 associate-/r/_binary64_13664 div-exp_binary64_13769 cbrt-unprod_binary64_13751 cbrt-undiv_binary64_13752
frac-2neg_binary64_13729 *-commutative_binary64_13649 flip3-+_binary64_13721 distribute-lft-out_binary64_13669 sum-log_binary64_13809 unswap-sqr_binary64_13686 +-commutative_binary64_13648 pow-prod-down_binary64_13789 associate-/l*_binary64_13663 flip-+_binary64_13692 clear-num_binary64_13717 div-inv_binary64_13715
Counts
3 → 85
Calls

3 calls:

14.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
11.0ms
(*.f64 (-.f64 y z) (-.f64 t x))
9.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series436.0ms (5.2%)

Counts
3 → 9
Calls

3 calls:

231.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
167.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
38.0ms
(*.f64 (-.f64 y z) (-.f64 t x))

simplify64.0ms (0.8%)

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050311683

prune101.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New821294
Fresh000
Picked101
Done000
Total831295
Error
3.9b
Counts
95 → 12
Compiler

Compiled 2048 to 542 computations (73.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
2.4b
(*.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))))
7.6b
(+.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)))))

rewrite75.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt_binary64_13740
59×*-un-lft-identity_binary64_13718
52×times-frac_binary64_13724
46×associate-*r*_binary64_13658
37×cbrt-prod_binary64_13749
27×add-cube-cbrt_binary64_13753
25×add-exp-log_binary64_13756
18×add-cbrt-cube_binary64_13754 cbrt-div_binary64_13750
17×associate-*l*_binary64_13659
16×difference-of-squares_binary64_13687 distribute-lft-out--_binary64_13670
10×associate-/r/_binary64_13664
flip3--_binary64_13722 flip--_binary64_13693
prod-exp_binary64_13767 cbrt-unprod_binary64_13751
div-exp_binary64_13769 cbrt-undiv_binary64_13752
pow1_binary64_13779 add-log-exp_binary64_13757 unswap-sqr_binary64_13686
frac-times_binary64_13728
associate-*r/_binary64_13660 associate-*l/_binary64_13661
pow1/3_binary64_13800 div-inv_binary64_13715
*-commutative_binary64_13649 flip3-+_binary64_13721 sum-log_binary64_13809 +-commutative_binary64_13648 pow-prod-down_binary64_13789 flip-+_binary64_13692
Counts
4 → 134
Calls

4 calls:

43.0ms
(*.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))))
4.0ms
(+.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)))))
3.0ms
(cbrt.f64 (-.f64 a z))
3.0ms
(cbrt.f64 (-.f64 a z))

series830.0ms (10%)

Counts
4 → 12
Calls

4 calls:

349.0ms
(*.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))))
253.0ms
(+.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)))))
115.0ms
(cbrt.f64 (-.f64 a z))
114.0ms
(cbrt.f64 (-.f64 a z))

simplify69.0ms (0.8%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
056053915

prune146.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1433146
Fresh2911
Picked011
Done000
Total14513158
Error
3.9b
Counts
158 → 13
Compiler

Compiled 4666 to 879 computations (81.2% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 t x))
0.6b
(cbrt.f64 (-.f64 t x))
1.5b
(*.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))))))
10.0b
(+.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))))))

rewrite71.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
40×add-exp-log_binary64_13756
36×cbrt-div_binary64_13750
26×add-sqr-sqrt_binary64_13740
22×add-cbrt-cube_binary64_13754
17×associate-*l*_binary64_13659
16×times-frac_binary64_13724 associate-/r/_binary64_13664 associate-*r*_binary64_13658 *-un-lft-identity_binary64_13718
15×prod-exp_binary64_13767 cbrt-unprod_binary64_13751
14×flip3--_binary64_13722 flip--_binary64_13693
13×cbrt-prod_binary64_13749
12×div-exp_binary64_13769 cbrt-undiv_binary64_13752
10×add-cube-cbrt_binary64_13753
frac-times_binary64_13728
pow1_binary64_13779 add-log-exp_binary64_13757 unswap-sqr_binary64_13686
associate-*r/_binary64_13660 associate-*l/_binary64_13661
difference-of-squares_binary64_13687 distribute-lft-out--_binary64_13670
pow1/3_binary64_13800 div-inv_binary64_13715
*-commutative_binary64_13649 flip3-+_binary64_13721 sum-log_binary64_13809 +-commutative_binary64_13648 pow-prod-down_binary64_13789 flip-+_binary64_13692
Counts
4 → 110
Calls

4 calls:

39.0ms
(*.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))))))
3.0ms
(cbrt.f64 (-.f64 t x))
3.0ms
(cbrt.f64 (-.f64 t x))

series1.1s (13.3%)

Counts
4 → 12
Calls

4 calls:

604.0ms
(*.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))))))
273.0ms
(+.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))))))
118.0ms
(cbrt.f64 (-.f64 t x))
112.0ms
(cbrt.f64 (-.f64 t x))

simplify111.0ms (1.3%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049685143
149685143

prune184.0ms (2.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1193122
Fresh01111
Picked011
Done011
Total11916135
Error
3.9b
Counts
135 → 16
Compiler

Compiled 7086 to 1246 computations (82.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
2.4b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
8.1b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite192.0ms (2.3%)

Algorithm
rewrite-expression-head
Rules
384×cbrt-div_binary64_13750
137×frac-times_binary64_13728
111×flip3--_binary64_13722 flip--_binary64_13693
89×associate-*l*_binary64_13659
82×associate-/r/_binary64_13664
67×add-sqr-sqrt_binary64_13740
59×*-un-lft-identity_binary64_13718
51×associate-*r/_binary64_13660
49×add-exp-log_binary64_13756
47×times-frac_binary64_13724
46×associate-*r*_binary64_13658
45×associate-*l/_binary64_13661
36×cbrt-prod_binary64_13749
30×add-cbrt-cube_binary64_13754
27×add-cube-cbrt_binary64_13753
22×prod-exp_binary64_13767 cbrt-unprod_binary64_13751
16×difference-of-squares_binary64_13687 distribute-lft-out--_binary64_13670
13×div-exp_binary64_13769 cbrt-undiv_binary64_13752
pow1_binary64_13779 add-log-exp_binary64_13757
unswap-sqr_binary64_13686
pow1/3_binary64_13800 div-inv_binary64_13715
*-commutative_binary64_13649 flip3-+_binary64_13721 sum-log_binary64_13809 +-commutative_binary64_13648 pow-prod-down_binary64_13789 flip-+_binary64_13692
Counts
4 → 211
Calls

4 calls:

129.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (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)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
4.0ms
(cbrt.f64 (-.f64 a z))
3.0ms
(cbrt.f64 (-.f64 a z))

series814.0ms (9.8%)

Counts
4 → 12
Calls

4 calls:

344.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
251.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
112.0ms
(cbrt.f64 (-.f64 a z))
107.0ms
(cbrt.f64 (-.f64 a z))

simplify127.0ms (1.5%)

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
050196953

prune287.0ms (3.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New2221223
Fresh21113
Picked011
Done022
Total22415239
Error
3.4b
Counts
239 → 15
Compiler

Compiled 9981 to 2035 computations (79.6% saved)

regimes637.0ms (7.6%)

Accuracy

Total 8.2b remaining (70.4%)

Threshold costs 0b (0%)

Compiler

Compiled 7427 to 3983 computations (46.4% saved)

bsearch58.0ms (0.7%)

Steps
ItersRangePoint
8
2.310816315830355e+222
2.507383499261264e+226
3.065242615070413e+225
9
-7.202951108375315e+126
-2.3318518165249053e+121
-3.18081965144141e+126
Compiler

Compiled 1 to 5 computations (-400% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0104102
1104102

end0.0ms (0%)

sample1.6s (19.5%)

Algorithm
intervals
Results
278.0ms6656×body128valid
71.0ms502×body512valid
57.0ms389×body1024valid
53.0ms1203×body128invalid
35.0ms404×body256valid
13.0ms49×body2048valid
Compiler

Compiled 1338 to 715 computations (46.6% saved)

Profiling

Loading profile data...