Details

Time bar (total: 11.8s)

analyze11.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14
Compiler

Compiled 70 to 33 computations (52.9% saved)

sample66.0ms (0.6%)

Algorithm
intervals
Results
29.0ms256×body128valid
3.0ms256×pre128true
Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify325.0ms (2.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (187.0ms)

IterNodesCost
0505041

prune19.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 2
Compiler

Compiled 119 to 75 computations (37% saved)

localize61.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0b
(+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))
0.0b
(+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))
0.0b
(+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))
0.1b
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.1b
(*.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
1.0b
(sqrt.f64 PI.f64)

rewrite131.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64_1805
39×add-exp-log_binary64_1821
38×add-cbrt-cube_binary64_1819
36×associate-*l*_binary64_1724
35×pow1_binary64_1844
31×times-frac_binary64_1789
29×*-un-lft-identity_binary64_1783
27×add-cube-cbrt_binary64_1818
19×prod-exp_binary64_1832
17×cbrt-unprod_binary64_1816
14×associate-*l/_binary64_1726 sqrt-prod_binary64_1799
12×frac-add_binary64_1791
10×pow-prod-down_binary64_1854
associate-*r*_binary64_1723
associate-*r/_binary64_1725 flip-+_binary64_1757 pow-plus_binary64_1846 pow-prod-up_binary64_1853 frac-times_binary64_1793 flip3-+_binary64_1786 unswap-sqr_binary64_1751
div-exp_binary64_1834
cbrt-undiv_binary64_1817 add-log-exp_binary64_1822
*-commutative_binary64_1714
div-inv_binary64_1780 pow-sqr_binary64_1756 pow2_binary64_1864
pow3_binary64_1866 distribute-lft-in_binary64_1732 1-exp_binary64_1827 pow1/2_binary64_1863 rem-3cbrt-lft_binary64_1808 distribute-rgt-in_binary64_1733 sqrt-pow1_binary64_1801 rem-sqrt-square_binary64_1796 rec-exp_binary64_1833
Counts
4 → 140
Calls

8 calls:

41.0ms
(*.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
3.0ms
(sqrt.f64 PI.f64)
0.0ms
(+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))

series573.0ms (4.8%)

Counts
4 → 9
Calls

4 calls:

449.0ms
(*.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
70.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
53.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 930 to 546 computations (41.3% saved)

simplify128.0ms (1.1%)

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049264689
149264689

prune647.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1454149
Fresh101
Picked011
Done000
Total1465151
Error
0b
Counts
151 → 5
Compiler

Compiled 9575 to 4402 computations (54% saved)

localize31.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.0b
(*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x))))
0.0b
(+.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))
0.0b
(+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
0.1b
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b
(*.f64 (+.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
0.2b
(*.f64 2/3 (*.f64 x x))

rewrite64.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64_1805
31×associate-*r*_binary64_1723
21×add-exp-log_binary64_1821 *-un-lft-identity_binary64_1783
20×add-cube-cbrt_binary64_1818
16×sqrt-prod_binary64_1799
15×add-cbrt-cube_binary64_1819
12×associate-*l*_binary64_1724
11×times-frac_binary64_1789 unswap-sqr_binary64_1751 pow1_binary64_1844
10×prod-exp_binary64_1832
unpow-prod-down_binary64_1862
cbrt-unprod_binary64_1816
sqr-pow_binary64_1755 *-commutative_binary64_1714 pow-prod-down_binary64_1854 add-log-exp_binary64_1822
sqrt-div_binary64_1800
flip-+_binary64_1757 associate-*l/_binary64_1726 frac-times_binary64_1793 flip3-+_binary64_1786 pow-to-exp_binary64_1852 pow-exp_binary64_1851
associate-*r/_binary64_1725 div-inv_binary64_1780
Counts
4 → 108
Calls

8 calls:

28.0ms
(*.f64 (+.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
12.0ms
(*.f64 2/3 (*.f64 x x))
6.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
5.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.0ms
(+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

series744.0ms (6.3%)

Counts
4 → 15
Calls

4 calls:

506.0ms
(*.f64 (+.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
103.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
103.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
31.0ms
(*.f64 2/3 (*.f64 x x))
Compiler

Compiled 880 to 712 computations (19.1% saved)

simplify82.0ms (0.7%)

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049343286
149343286

prune363.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1230123
Fresh033
Picked011
Done011
Total1235128
Error
0b
Counts
128 → 5
Compiler

Compiled 4819 to 3269 computations (32.2% saved)

localize43.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64)))
0.0b
(*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x))))
0.0b
(+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
0.0b
(+.f64 (/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64)) (*.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64))))
0.3b
(/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
1.0b
(/.f64 1/21 (sqrt.f64 PI.f64))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)

rewrite54.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64_1805
36×add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783 times-frac_binary64_1789
30×sqrt-prod_binary64_1799
12×associate-/r*_binary64_1727
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
associate-/l*_binary64_1728 pow1_binary64_1844
add-log-exp_binary64_1822
associate-/l/_binary64_1730 div-inv_binary64_1780 pow1/2_binary64_1863 cbrt-undiv_binary64_1817 frac-2neg_binary64_1794 div-exp_binary64_1834 sqrt-pow1_binary64_1801 clear-num_binary64_1782 rem-sqrt-square_binary64_1796
flip-+_binary64_1757 flip3-+_binary64_1786
Counts
4 → 106
Calls

8 calls:

18.0ms
(/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
7.0ms
(/.f64 1/21 (sqrt.f64 PI.f64))
2.0ms
(sqrt.f64 PI.f64)
2.0ms
(sqrt.f64 PI.f64)
0.0ms
(+.f64 (/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64)) (*.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64))))

series321.0ms (2.7%)

Counts
4 → 6
Calls

4 calls:

321.0ms
(/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 351 to 278 computations (20.8% saved)

simplify99.0ms (0.8%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
050372946

prune358.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1102112
Fresh202
Picked101
Done022
Total1134117
Error
0b
Counts
117 → 4
Compiler

Compiled 4516 to 2660 computations (41.1% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (pow.f64 (fabs.f64 x) 7) (*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64))))
0.0b
(*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x))))
0.0b
(+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
0.0b
(+.f64 (/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64)) (*.f64 (pow.f64 (fabs.f64 x) 7) (*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))))
0.3b
(/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
1.0b
(*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))

rewrite56.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt_binary64_1805
40×times-frac_binary64_1789
37×*-un-lft-identity_binary64_1783
35×add-cube-cbrt_binary64_1818
29×sqrt-prod_binary64_1799
22×associate-*r*_binary64_1723
15×add-exp-log_binary64_1821
11×add-cbrt-cube_binary64_1819
pow1_binary64_1844
associate-/r*_binary64_1727
unswap-sqr_binary64_1751
prod-exp_binary64_1832 add-log-exp_binary64_1822
associate-/l*_binary64_1728 associate-*l*_binary64_1724 div-exp_binary64_1834
associate-/l/_binary64_1730 cbrt-unprod_binary64_1816 div-inv_binary64_1780 pow1/2_binary64_1863 cbrt-undiv_binary64_1817 sqrt-pow1_binary64_1801 rem-sqrt-square_binary64_1796
associate-*r/_binary64_1725 un-div-inv_binary64_1781 1-exp_binary64_1827 flip-+_binary64_1757 *-commutative_binary64_1714 frac-2neg_binary64_1794 flip3-+_binary64_1786 clear-num_binary64_1782 pow-prod-down_binary64_1854 rec-exp_binary64_1833
Counts
4 → 114
Calls

8 calls:

16.0ms
(/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
11.0ms
(*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
0.0ms
(+.f64 (/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64)) (*.f64 (pow.f64 (fabs.f64 x) 7) (*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))))

series320.0ms (2.7%)

Counts
4 → 6
Calls

4 calls:

319.0ms
(/.f64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 2/3 (*.f64 x x)))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
0.0ms
(*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 369 to 296 computations (19.8% saved)

simplify149.0ms (1.3%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
049732909
149732909

prune346.0ms (2.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1200120
Fresh011
Picked011
Done022
Total1204124
Error
0b
Counts
124 → 4
Compiler

Compiled 4915 to 2968 computations (39.6% saved)

simplify41.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (8.0ms)

IterNodesCost
04512230
14512230

regimes332.0ms (2.8%)

Accuracy

Total 0.2b remaining (99.7%)

Threshold costs 0.2b (99.7%)

Compiler

Compiled 2742 to 1958 computations (28.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04289
14289

end0.0ms (0%)

sample6.4s (54.4%)

Algorithm
intervals
Results
1.1s8000×body128valid
130.0ms8003×pre128true
1.0msbody128invalid
Compiler

Compiled 4125 to 2879 computations (30.2% saved)

Pareto

0.37528579296835046

Profiling

Loading profile data...