Details

Time bar (total: 1.3min)

analyze1.7s (2.2%)

Algorithm
search
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)

sample1.8s (2.3%)

Algorithm
intervals
Results
1.6s152×body8192exit
79.0ms256×body128valid
7.0ms413×pre128true
5.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify147.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04804115
14804115

prune13.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
1.9b
Counts
2 → 2
Compiler

Compiled 271 to 232 computations (14.4% saved)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b
(-.f64 (-.f64 1 z) 1)
5.0b
(-.f64 (-.f64 1 z) 1)
5.0b
(-.f64 (-.f64 1 z) 1)
5.0b
(-.f64 (-.f64 1 z) 1)

rewrite1.1s (1.5%)

Algorithm
rewrite-expression-head
Error
1.9b
Rules
36×*-un-lft-identity_binary64_2806
28×add-sqr-sqrt_binary64_2828
24×add-log-exp_binary64_2845 cancel-sign-sub-inv_binary64_2772
16×associate--l+_binary64_2743
12×diff-log_binary64_2898 add-cube-cbrt_binary64_2841 distribute-lft-out--_binary64_2758
sub-neg_binary64_2799 difference-of-squares_binary64_2775
pow1_binary64_2867 add-exp-log_binary64_2844 add-cbrt-cube_binary64_2842 flip3--_binary64_2810 flip--_binary64_2781 difference-of-sqr-1_binary64_2776 associate--l-_binary64_2744
Counts
4 → 100
Calls

4 calls:

9.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
8.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series213.0ms (0.3%)

Error
1.9b
Counts
4 → 12
Calls

4 calls:

39.0ms
(-.f64 (-.f64 1 z) 1)
39.0ms
(-.f64 (-.f64 1 z) 1)
39.0ms
(-.f64 (-.f64 1 z) 1)
37.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify77.0ms (0.1%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
05392704

prune1.1s (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done000
Total1122114
Error
1.9b
Counts
114 → 2
Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 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)))

rewrite534.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
24×*-un-lft-identity_binary64_2806
23×add-log-exp_binary64_2845
14×frac-add_binary64_2814
13×sum-log_binary64_2897 distribute-lft-out_binary64_2757
10×add-exp-log_binary64_2844
pow1_binary64_2867 add-cbrt-cube_binary64_2842
prod-exp_binary64_2855
flip3-+_binary64_2809 flip-+_binary64_2780
add-cube-cbrt_binary64_2841 add-sqr-sqrt_binary64_2828
associate-*r*_binary64_2746
cbrt-unprod_binary64_2839
associate-+l+_binary64_2739 +-commutative_binary64_2736 pow-prod-down_binary64_2877 sqrt-pow1_binary64_2824
pow1/2_binary64_2886 sqrt-prod_binary64_2822 pow-to-exp_binary64_2875 pow-exp_binary64_2874 pow-sub_binary64_2882 associate-*r/_binary64_2748 associate-*l/_binary64_2749 associate-*l*_binary64_2747 exp-sum_binary64_2852 *-commutative_binary64_2737
Counts
4 → 74
Calls

4 calls:

46.0ms
(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
23.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
22.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 6884 to 5351 computations (22.3% saved)

series439.0ms (0.6%)

Error
1.2b
Counts
4 → 30
Calls

4 calls:

190.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
71.0ms
(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
63.0ms
(+.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 4760 to 3804 computations (20.1% saved)

simplify92.0ms (0.1%)

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049103729
149103729

prune670.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New968104
Fresh000
Picked101
Done101
Total988106
Error
0.3b
Counts
106 → 8
Compiler

Compiled 9420 to 7263 computations (22.9% saved)

localize84.0ms (0.1%)

Local error

Found 4 expressions with local error:

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
(*.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (*.f64 (-.f64 2 z) (*.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.5b
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite2.6s (3.5%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
36×frac-times_binary64_2816
35×associate-*r/_binary64_2748
31×associate-*l/_binary64_2749
24×flip3-+_binary64_2809 flip3--_binary64_2810 flip-+_binary64_2780 flip--_binary64_2781
19×add-exp-log_binary64_2844
18×pow1_binary64_2867 add-cbrt-cube_binary64_2842
16×frac-add_binary64_2814
13×prod-exp_binary64_2855
cbrt-unprod_binary64_2839
pow-prod-down_binary64_2877
add-log-exp_binary64_2845 add-cube-cbrt_binary64_2841 add-sqr-sqrt_binary64_2828 *-un-lft-identity_binary64_2806
associate-*r*_binary64_2746
associate-*l*_binary64_2747
distribute-rgt-in_binary64_2756 associate-+l+_binary64_2739 distribute-lft-in_binary64_2755 associate-+r+_binary64_2738 sqrt-pow1_binary64_2824 *-commutative_binary64_2737
sum-log_binary64_2897 +-commutative_binary64_2736 pow1/2_binary64_2886 sqrt-prod_binary64_2822 pow-to-exp_binary64_2875 pow-exp_binary64_2874 pow-sub_binary64_2882 exp-sum_binary64_2852
Counts
4 → 110
Calls

4 calls:

35.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
17.0ms
(*.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (*.f64 (-.f64 2 z) (*.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
16.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 22206 to 18069 computations (18.6% saved)

series499.0ms (0.7%)

Error
0.3b
Counts
4 → 18
Calls

4 calls:

214.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
76.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
71.0ms
(*.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (*.f64 (-.f64 2 z) (*.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 6890 to 5668 computations (17.7% saved)

simplify144.0ms (0.2%)

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049337946
149337946

prune2.7s (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1244128
Fresh167
Picked101
Done000
Total12610136
Error
0.3b
Counts
136 → 10
Compiler

Compiled 25137 to 20386 computations (18.9% saved)

localize90.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) 3))
1.0b
(pow.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) 3)
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.5b
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite3.8s (5.1%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
60×associate-*r/_binary64_2748
48×frac-add_binary64_2814
45×flip3-+_binary64_2809 flip-+_binary64_2780
36×cube-div_binary64_2835
24×frac-times_binary64_2816
18×flip3--_binary64_2810 flip--_binary64_2781 cbrt-div_binary64_2838
12×associate-*l/_binary64_2749 cbrt-prod_binary64_2837
10×add-cube-cbrt_binary64_2841 add-sqr-sqrt_binary64_2828 *-un-lft-identity_binary64_2806
pow1_binary64_2867
add-log-exp_binary64_2845 unpow-prod-down_binary64_2885 cube-prod_binary64_2834
add-exp-log_binary64_2844 add-cbrt-cube_binary64_2842
pow-unpow_binary64_2883
distribute-rgt-in_binary64_2756 associate-+l+_binary64_2739 distribute-lft-in_binary64_2755 associate-+r+_binary64_2738 sqrt-pow1_binary64_2824 unpow3_binary64_2872 cube-mult_binary64_2836 sqr-pow_binary64_2778
sum-log_binary64_2897 +-commutative_binary64_2736 pow1/2_binary64_2886 pow-prod-down_binary64_2877 sqrt-prod_binary64_2822 pow-pow_binary64_2878 pow-to-exp_binary64_2875 pow-exp_binary64_2874 rem-cube-cbrt_binary64_2829 pow1/3_binary64_2888 rem-cbrt-cube_binary64_2830
Counts
4 → 122
Calls

4 calls:

38.0ms
(pow.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) 3)
32.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) 3))
29.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 28489 to 23546 computations (17.4% saved)

series345.0ms (0.5%)

Error
0.3b
Counts
4 → 18
Calls

4 calls:

82.0ms
(pow.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) 3)
79.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) 3))
77.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 5938 to 4831 computations (18.6% saved)

simplify175.0ms (0.2%)

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0498412944
1498412944

prune3.1s (4.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1400140
Fresh099
Picked011
Done000
Total14010150
Error
0.3b
Counts
150 → 10
Compiler

Compiled 28449 to 23268 computations (18.2% saved)

regimes1.1s (1.5%)

Accuracy

Total 0.2b remaining (42.6%)

Threshold costs 0.2b (42.6%)

Compiler

Compiled 17222 to 14516 computations (15.7% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0245448
1245448

end0.0ms (0%)

sample52.5s (69.8%)

Algorithm
intervals
Results
43.2s3891×body8192exit
2.4s8000×body128valid
217.0ms11975×pre128true
27.0ms84×body128invalid
Compiler

Compiled 8909 to 7511 computations (15.7% saved)

Profiling

Loading profile data...