Details

Time bar (total: 2.4s)

analyze5.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 21 to 17 computations (19% saved)

sample18.0ms (0.8%)

Algorithm
1×intervals
Results
13.0ms256×body128valid
Compiler

Compiled 41 to 34 computations (17.1% saved)

simplify286.0ms (12.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (186.0ms)

IterNodesCost
0484328
1484328

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 2
Compiler

Compiled 56 to 44 computations (21.4% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.0b
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.0b
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
0.2b
(*.f64 (*.f64 v v) 6)

rewrite51.0ms (2.1%)

Algorithm
1×rewrite-expression-head
Rules
25×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
22×associate-*r/_binary64_1725
18×flip3--_binary64_1787 sqrt-div_binary64_1800 flip--_binary64_1758
17×add-sqr-sqrt_binary64_1805
16×pow1_binary64_1844
12×*-un-lft-identity_binary64_1783 frac-times_binary64_1793
11×add-cube-cbrt_binary64_1818
10×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*r*_binary64_1723
9×associate-*l*_binary64_1724
8×associate-/r/_binary64_1729
7×pow-prod-down_binary64_1854
6×associate-*l/_binary64_1726
4×sqrt-prod_binary64_1799 add-log-exp_binary64_1822
3×associate-/l*_binary64_1728 times-frac_binary64_1789 cbrt-undiv_binary64_1817 *-commutative_binary64_1714 div-exp_binary64_1834 unswap-sqr_binary64_1751
2×difference-of-squares_binary64_1752
1×div-inv_binary64_1780 associate-/r*_binary64_1727 frac-2neg_binary64_1794 clear-num_binary64_1782
Counts
4 → 108
Calls

4 calls:

12.0ms
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
11.0ms
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
10.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
7.0ms
(*.f64 (*.f64 v v) 6)

series220.0ms (9.3%)

Counts
4 → 12
Calls

4 calls:

94.0ms
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
54.0ms
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
49.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
23.0ms
(*.f64 (*.f64 v v) 6)

simplify64.0ms (2.7%)

Algorithm
1×egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050013300

prune170.0ms (7.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1182120
Fresh101
Picked101
Done000
Total1202122
Error
0b
Counts
122 → 2
Compiler

Compiled 3403 to 2297 computations (32.5% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.0b
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.2b
(*.f64 (*.f64 v v) 6)
1.0b
(/.f64 4/3 PI.f64)

rewrite43.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Rules
40×times-frac_binary64_1789
36×add-sqr-sqrt_binary64_1805
31×*-un-lft-identity_binary64_1783
30×add-cube-cbrt_binary64_1818
25×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
16×associate-/l*_binary64_1728
12×flip3--_binary64_1787 sqrt-div_binary64_1800 flip--_binary64_1758
11×pow1_binary64_1844
9×associate-*r*_binary64_1723
8×associate-/r/_binary64_1729 frac-times_binary64_1793
7×cbrt-undiv_binary64_1817 div-exp_binary64_1834
6×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l*_binary64_1724
4×associate-*r/_binary64_1725 div-inv_binary64_1780 associate-/r*_binary64_1727 associate-*l/_binary64_1726 sqrt-prod_binary64_1799 pow-prod-down_binary64_1854 add-log-exp_binary64_1822
3×unswap-sqr_binary64_1751
2×difference-of-squares_binary64_1752 *-commutative_binary64_1714 frac-2neg_binary64_1794 clear-num_binary64_1782
1×associate-/l/_binary64_1730
Counts
4 → 132
Calls

4 calls:

13.0ms
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
10.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
6.0ms
(*.f64 (*.f64 v v) 6)
3.0ms
(/.f64 4/3 PI.f64)

series164.0ms (7%)

Counts
4 → 10
Calls

4 calls:

98.0ms
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
49.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
17.0ms
(*.f64 (*.f64 v v) 6)
0.0ms
(/.f64 4/3 PI.f64)

simplify86.0ms (3.7%)

Algorithm
1×egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049533504
149533504

prune186.0ms (7.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1420142
Fresh011
Picked011
Done000
Total1422144
Error
0b
Counts
144 → 2
Compiler

Compiled 3735 to 2472 computations (33.8% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 PI.f64 (-.f64 1 (*.f64 v v)))
0.0b
(/.f64 4/3 (*.f64 (*.f64 PI.f64 (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.2b
(*.f64 (*.f64 v v) 6)

rewrite30.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
19×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
12×add-sqr-sqrt_binary64_1805
10×associate-*r/_binary64_1725 pow1_binary64_1844
9×*-un-lft-identity_binary64_1783
8×associate-/r/_binary64_1729 add-cube-cbrt_binary64_1818 associate-*r*_binary64_1723
7×flip3--_binary64_1787 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 flip--_binary64_1758
6×sqrt-div_binary64_1800
4×associate-*l*_binary64_1724 frac-times_binary64_1793 pow-prod-down_binary64_1854
3×associate-/l*_binary64_1728 times-frac_binary64_1789 cbrt-undiv_binary64_1817 div-exp_binary64_1834 add-log-exp_binary64_1822
2×difference-of-squares_binary64_1752 distribute-lft-in_binary64_1732 cancel-sign-sub-inv_binary64_1749 associate-*l/_binary64_1726 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 unswap-sqr_binary64_1751 sub-neg_binary64_1776
1×div-inv_binary64_1780 associate-/r*_binary64_1727 frac-2neg_binary64_1794 clear-num_binary64_1782
Counts
3 → 76
Calls

3 calls:

11.0ms
(/.f64 4/3 (*.f64 (*.f64 PI.f64 (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
6.0ms
(*.f64 PI.f64 (-.f64 1 (*.f64 v v)))
6.0ms
(*.f64 (*.f64 v v) 6)

series142.0ms (6%)

Counts
3 → 9
Calls

3 calls:

87.0ms
(/.f64 4/3 (*.f64 (*.f64 PI.f64 (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
37.0ms
(*.f64 PI.f64 (-.f64 1 (*.f64 v v)))
18.0ms
(*.f64 (*.f64 v v) 6)

simplify67.0ms (2.8%)

Algorithm
1×egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049341779
149341779

prune100.0ms (4.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New85085
Fresh000
Picked011
Done011
Total85287
Error
0b
Counts
87 → 2
Compiler

Compiled 2134 to 1403 computations (34.3% saved)

regimes48.0ms (2%)

Accuracy

Total 0.0b remaining (85.4%)

Threshold costs 0.0b (85.4%)

Compiler

Compiled 460 to 362 computations (21.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05328
15328

end0.0ms (0%)

sample635.0ms (26.9%)

Algorithm
1×intervals
Results
402.0ms8000×body128valid
0.0ms2×body128nan
Compiler

Compiled 133 to 106 computations (20.3% saved)

Profiling

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