Details

Time bar (total: 1.9min)

analyze3.7s (3.2%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04804115
14804115
011
111
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
0%74.9%25.1%2
18.7%56.2%25.1%3
37.5%37.5%25.1%4
42.1%32.8%25.1%5
46.8%28.1%25.1%6
48%26.9%25.1%7
49.2%25.8%25.1%8
49.5%25.5%25.1%9
49.8%25.2%25.1%10
49.8%25.2%25.1%11
49.8%25.1%25.1%12
49.9%25%25.1%13
49.9%25%25.1%14
Compiler

Compiled 126 to 112 computations (11.1% saved)

sample3.1s (2.7%)

Algorithm
intervals
Results
2.9s136×body8192exit
158.0ms256×body128valid
13.0ms392×pre128true
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify95.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
04804115
14804115

prune28.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
1.8b
Counts
2 → 2
Compiler

Compiled 271 to 232 computations (14.4% saved)

localize103.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.6b
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite175.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_1783
18×add-log-exp_binary64_1822
10×add-exp-log_binary64_1821
add-cbrt-cube_binary64_1819 distribute-lft-out_binary64_1734 sum-log_binary64_1874 pow1_binary64_1844
frac-add_binary64_1791
prod-exp_binary64_1832
add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818 flip-+_binary64_1757 flip3-+_binary64_1786
associate-*r*_binary64_1723
cbrt-unprod_binary64_1816
+-commutative_binary64_1713 associate-+l+_binary64_1716 sqrt-pow1_binary64_1801 pow-prod-down_binary64_1854
associate-*r/_binary64_1725 exp-sum_binary64_1829 pow-sub_binary64_1859 pow1/2_binary64_1863 associate-*l*_binary64_1724 associate-*l/_binary64_1726 sqrt-prod_binary64_1799 *-commutative_binary64_1714 pow-to-exp_binary64_1852 pow-exp_binary64_1851
Counts
4 → 70
Calls

4 calls:

65.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
48.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
31.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms
(sqrt.f64 (*.f64 PI.f64 2))

series517.0ms (0.5%)

Counts
4 → 20
Calls

4 calls:

353.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
91.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
72.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 2052 to 1704 computations (17% saved)

simplify124.0ms (0.1%)

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
055632799

prune914.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New83790
Fresh101
Picked101
Done000
Total85792
Error
1.1b
Counts
92 → 7
Compiler

Compiled 7991 to 6169 computations (22.8% saved)

localize121.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
1.0b
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
3.1b
(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))

rewrite316.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
183×times-frac_binary64_1789
162×*-un-lft-identity_binary64_1783
156×add-sqr-sqrt_binary64_1805
111×cancel-sign-sub-inv_binary64_1749
76×add-cube-cbrt_binary64_1818
39×difference-of-squares_binary64_1752
36×distribute-lft-out--_binary64_1735
16×pow1_binary64_1844
12×associate-/r/_binary64_1729 add-exp-log_binary64_1821 flip-+_binary64_1757 flip3-+_binary64_1786
11×add-cbrt-cube_binary64_1819
prod-exp_binary64_1832 frac-sub_binary64_1792 frac-times_binary64_1793 associate-*r*_binary64_1723
flip3--_binary64_1787 flip--_binary64_1758
swap-sqr_binary64_1750 distribute-lft-out_binary64_1734 div-inv_binary64_1780 add-log-exp_binary64_1822
associate-*r/_binary64_1725 associate-*l*_binary64_1724 associate-*l/_binary64_1726
cbrt-unprod_binary64_1816
pow-prod-down_binary64_1854
distribute-lft-in_binary64_1732 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 sqrt-pow1_binary64_1801 associate--l+_binary64_1720
exp-sum_binary64_1829 pow-sub_binary64_1859 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow1/2_binary64_1863 sqrt-prod_binary64_1799 diff-log_binary64_1875 pow-sqr_binary64_1756 unswap-sqr_binary64_1751 pow-to-exp_binary64_1852 sub-neg_binary64_1776 pow-exp_binary64_1851 pow2_binary64_1864
Counts
4 → 207
Calls

4 calls:

117.0ms
(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
47.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
29.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms
(sqrt.f64 (*.f64 PI.f64 2))

series588.0ms (0.5%)

Counts
4 → 24
Calls

4 calls:

351.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
121.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
115.0ms
(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 3068 to 2556 computations (16.7% saved)

simplify233.0ms (0.2%)

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
049407481
149407481

prune4.2s (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2274231
Fresh426
Picked011
Done000
Total2317238
Error
0.3b
Counts
238 → 7
Compiler

Compiled 25965 to 20406 computations (21.4% saved)

localize125.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
1.0b
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(sqrt.f64 PI.f64)
3.1b
(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))

rewrite346.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
183×times-frac_binary64_1789
163×*-un-lft-identity_binary64_1783
158×add-sqr-sqrt_binary64_1805
111×cancel-sign-sub-inv_binary64_1749
77×add-cube-cbrt_binary64_1818
39×difference-of-squares_binary64_1752
36×distribute-lft-out--_binary64_1735
20×add-exp-log_binary64_1821
17×prod-exp_binary64_1832
15×add-cbrt-cube_binary64_1819
14×pow1_binary64_1844
12×associate-/r/_binary64_1729 flip-+_binary64_1757 flip3-+_binary64_1786
frac-sub_binary64_1792 frac-times_binary64_1793 associate-*r*_binary64_1723
flip3--_binary64_1787 cbrt-unprod_binary64_1816 flip--_binary64_1758
swap-sqr_binary64_1750 distribute-lft-out_binary64_1734 div-inv_binary64_1780 add-log-exp_binary64_1822
associate-*r/_binary64_1725 associate-*l*_binary64_1724 associate-*l/_binary64_1726
sqrt-prod_binary64_1799
distribute-lft-in_binary64_1732 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 pow-prod-down_binary64_1854 associate--l+_binary64_1720 pow-to-exp_binary64_1852 pow-exp_binary64_1851
exp-sum_binary64_1829 pow-sub_binary64_1859 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow1/2_binary64_1863 diff-log_binary64_1875 pow-sqr_binary64_1756 sqrt-pow1_binary64_1801 unswap-sqr_binary64_1751 rem-sqrt-square_binary64_1796 sub-neg_binary64_1776 pow2_binary64_1864
Counts
4 → 213
Calls

4 calls:

125.0ms
(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
50.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
37.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms
(sqrt.f64 PI.f64)

series612.0ms (0.5%)

Counts
4 → 24
Calls

4 calls:

360.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
131.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
120.0ms
(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 3090 to 2578 computations (16.6% saved)

simplify252.0ms (0.2%)

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
049327646
149327646

prune5.2s (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2352237
Fresh325
Picked101
Done011
Total2395244
Error
0.3b
Counts
244 → 5
Compiler

Compiled 26626 to 20724 computations (22.2% saved)

localize129.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
1.0b
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(sqrt.f64 PI.f64)
3.1b
(+.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (*.f64 (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 4 (*.f64 z z))) (/.f64 (+.f64 z 2) (-.f64 2 z))))

rewrite189.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
25×flip-+_binary64_1757 flip3-+_binary64_1786
24×frac-add_binary64_1791 *-un-lft-identity_binary64_1783 frac-times_binary64_1793
20×add-exp-log_binary64_1821
17×associate-*r/_binary64_1725 prod-exp_binary64_1832 associate-*l/_binary64_1726
15×add-cbrt-cube_binary64_1819
14×pow1_binary64_1844
13×add-sqr-sqrt_binary64_1805
10×add-cube-cbrt_binary64_1818
associate-*r*_binary64_1723
cbrt-unprod_binary64_1816
swap-sqr_binary64_1750 distribute-lft-out_binary64_1734 add-log-exp_binary64_1822
associate-*l*_binary64_1724
sqrt-prod_binary64_1799
distribute-lft-in_binary64_1732 associate-+l+_binary64_1716 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 pow-prod-down_binary64_1854 pow-to-exp_binary64_1852 pow-exp_binary64_1851
+-commutative_binary64_1713 exp-sum_binary64_1829 pow-sub_binary64_1859 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow1/2_binary64_1863 pow-sqr_binary64_1756 sum-log_binary64_1874 sqrt-pow1_binary64_1801 unswap-sqr_binary64_1751 rem-sqrt-square_binary64_1796 pow2_binary64_1864
Counts
4 → 115
Calls

4 calls:

51.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
49.0ms
(+.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (*.f64 (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 4 (*.f64 z z))) (/.f64 (+.f64 z 2) (-.f64 2 z))))
30.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms
(sqrt.f64 PI.f64)

series608.0ms (0.5%)

Counts
4 → 24
Calls

4 calls:

347.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
135.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
124.0ms
(+.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (*.f64 (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 4 (*.f64 z z))) (/.f64 (+.f64 z 2) (-.f64 2 z))))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 3210 to 2658 computations (17.2% saved)

simplify262.0ms (0.2%)

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 0 (146.0ms)

IterNodesCost
049405856
149405856

prune2.7s (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1390139
Fresh033
Picked011
Done011
Total1395144
Error
0.3b
Counts
144 → 5
Compiler

Compiled 16506 to 12640 computations (23.4% saved)

regimes905.0ms (0.8%)

Accuracy

Total 0.1b remaining (37.8%)

Threshold costs 0.1b (37.8%)

Compiler

Compiled 6632 to 5550 computations (16.3% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0142165
1142165

end0.0ms (0%)

sample1.5min (77.5%)

Algorithm
intervals
Results
1.3min3726×body8192exit
4.6s8000×body128valid
375.0ms11812×pre128true
57.0ms86×body128invalid
Compiler

Compiled 3425 to 2865 computations (16.4% saved)

Profiling

Loading profile data...