Details

Time bar (total: 1.1min)

analyze1.8s (2.7%)

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)

sample1.4s (2.1%)

Algorithm
intervals
Results
1.3s114×body8192exit
80.0ms256×body128valid
10.0ms372×pre128true
1.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify141.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04804115
14804115

prune12.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.8b

Counts
2 → 2
Compiler

Compiled 271 to 232 computations (14.4% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.3b
(-.f64 (-.f64 1 z) 1)
5.3b
(-.f64 (-.f64 1 z) 1)
5.3b
(-.f64 (-.f64 1 z) 1)
5.3b
(-.f64 (-.f64 1 z) 1)

rewrite67.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity_binary64_3147
28×add-sqr-sqrt_binary64_3169
24×cancel-sign-sub-inv_binary64_3113 add-log-exp_binary64_3186
16×associate--l+_binary64_3084
12×distribute-lft-out--_binary64_3099 diff-log_binary64_3239 add-cube-cbrt_binary64_3182
sub-neg_binary64_3140 difference-of-squares_binary64_3116
flip--_binary64_3122 add-exp-log_binary64_3185 difference-of-sqr-1_binary64_3117 add-cbrt-cube_binary64_3183 flip3--_binary64_3151 pow1_binary64_3208 associate--l-_binary64_3085
Counts
4 → 100
Calls

4 calls:

15.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)

series35.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

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

simplify76.0ms (0.1%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
05392704

prune1.2s (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done000
Total1122114

Merged error: 1.8b

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)))

rewrite107.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_3147
23×add-log-exp_binary64_3186
14×frac-add_binary64_3155
13×distribute-lft-out_binary64_3098 sum-log_binary64_3238
10×add-exp-log_binary64_3185
add-cbrt-cube_binary64_3183 pow1_binary64_3208
prod-exp_binary64_3196
flip-+_binary64_3121 flip3-+_binary64_3150
add-sqr-sqrt_binary64_3169 add-cube-cbrt_binary64_3182
associate-*r*_binary64_3087
cbrt-unprod_binary64_3180
pow-prod-down_binary64_3218 associate-+l+_binary64_3080 +-commutative_binary64_3077 sqrt-pow1_binary64_3165
*-commutative_binary64_3078 pow-exp_binary64_3215 pow-sub_binary64_3223 exp-sum_binary64_3193 associate-*l/_binary64_3090 pow-to-exp_binary64_3216 pow1/2_binary64_3227 associate-*l*_binary64_3088 associate-*r/_binary64_3089 sqrt-prod_binary64_3163
Counts
4 → 74
Calls

4 calls:

52.0ms
(+.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)))
22.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
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)))
3.0ms
(sqrt.f64 (*.f64 PI.f64 2))

series143.0ms (0.2%)

Counts
4 → 10
Calls

4 calls:

101.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
26.0ms
(+.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)))
15.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))

simplify84.0ms (0.1%)

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049123345
149123345

prune435.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New77784
Fresh000
Picked101
Done011
Total78886

Merged error: 0.3b

Counts
86 → 8
Compiler

Compiled 7910 to 6133 computations (22.5% 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 (*.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))))) (-.f64 3 z))
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)))))

rewrite162.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
83×associate-*r/_binary64_3089
68×frac-times_binary64_3157
64×frac-add_binary64_3155
60×flip-+_binary64_3121 flip3-+_binary64_3150
43×flip--_binary64_3122 flip3--_binary64_3151
35×associate-*l/_binary64_3090
13×add-sqr-sqrt_binary64_3169
12×add-exp-log_binary64_3185
11×*-un-lft-identity_binary64_3147 add-cbrt-cube_binary64_3183 pow1_binary64_3208
associate-*r*_binary64_3087 add-cube-cbrt_binary64_3182
prod-exp_binary64_3196
cancel-sign-sub-inv_binary64_3113 distribute-lft-in_binary64_3096 add-log-exp_binary64_3186 distribute-rgt-in_binary64_3097
cbrt-unprod_binary64_3180 associate-*l*_binary64_3088
pow-prod-down_binary64_3218
*-commutative_binary64_3078 associate-+l+_binary64_3080 sub-neg_binary64_3140 associate-+r+_binary64_3079 sqrt-pow1_binary64_3165
pow-exp_binary64_3215 pow-sub_binary64_3223 unswap-sqr_binary64_3115 exp-sum_binary64_3193 pow-to-exp_binary64_3216 distribute-lft-out--_binary64_3099 +-commutative_binary64_3077 difference-of-squares_binary64_3116 pow1/2_binary64_3227 sqrt-prod_binary64_3163 sum-log_binary64_3238
Counts
4 → 147
Calls

4 calls:

38.0ms
(*.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))))) (-.f64 3 z))
30.0ms
(+.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)))))
21.0ms
(*.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))

series173.0ms (0.3%)

Counts
4 → 10
Calls

4 calls:

89.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
44.0ms
(+.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)))))
40.0ms
(*.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))))) (-.f64 3 z))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))

simplify198.0ms (0.3%)

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0585216162

prune4.3s (6.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1516157
Fresh246
Picked101
Done011
Total15411165

Merged error: 0.2b

Counts
165 → 11
Compiler

Compiled 34904 to 28541 computations (18.2% saved)

localize78.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (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)) (-.f64 3 z))
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)))))

rewrite209.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
102×associate-*r/_binary64_3089
80×frac-add_binary64_3155
76×frac-times_binary64_3157
75×flip-+_binary64_3121 flip3-+_binary64_3150
72×cube-div_binary64_3176
54×cbrt-div_binary64_3179
49×flip--_binary64_3122 flip3--_binary64_3151
38×associate-*l/_binary64_3090
25×add-sqr-sqrt_binary64_3169
16×*-un-lft-identity_binary64_3147 cbrt-prod_binary64_3178
15×associate-*l*_binary64_3088
14×add-cube-cbrt_binary64_3182
10×pow1_binary64_3208
unpow-prod-down_binary64_3226 add-exp-log_binary64_3185 cube-prod_binary64_3175
cancel-sign-sub-inv_binary64_3113 add-cbrt-cube_binary64_3183 distribute-lft-in_binary64_3096 add-log-exp_binary64_3186 distribute-rgt-in_binary64_3097
unswap-sqr_binary64_3115 associate-*r*_binary64_3087
sqr-pow_binary64_3119 pow-unpow_binary64_3224
pow-prod-down_binary64_3218 associate-+l+_binary64_3080 sub-neg_binary64_3140 associate-+r+_binary64_3079 cube-mult_binary64_3177 sqrt-pow1_binary64_3165 unpow3_binary64_3213
*-commutative_binary64_3078 pow-exp_binary64_3215 rem-cube-cbrt_binary64_3170 pow-to-exp_binary64_3216 distribute-lft-out--_binary64_3099 +-commutative_binary64_3077 prod-exp_binary64_3196 difference-of-squares_binary64_3116 pow1/2_binary64_3227 cbrt-unprod_binary64_3180 pow-pow_binary64_3219 sqrt-prod_binary64_3163 sum-log_binary64_3238
Counts
4 → 183
Calls

4 calls:

43.0ms
(*.f64 (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)) (-.f64 3 z))
35.0ms
(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)
30.0ms
(+.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))

series127.0ms (0.2%)

Counts
4 → 10
Calls

4 calls:

44.0ms
(+.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)))))
42.0ms
(*.f64 (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)) (-.f64 3 z))
41.0ms
(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)
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))

simplify261.0ms (0.4%)

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0503520887

prune5.1s (7.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1921193
Fresh189
Picked011
Done011
Total19311204

Merged error: 0.2b

Counts
204 → 11
Compiler

Compiled 41897 to 34329 computations (18.1% saved)

regimes643.0ms (1%)

Compiler

Compiled 9752 to 8234 computations (15.6% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0168364
1168364

end0.0ms (0%)

sample48.0s (74%)

Algorithm
intervals
Results
41.8s3775×body8192exit
2.5s8000×body128valid
233.0ms11857×pre128true
27.0ms82×body128invalid
Compiler

Compiled 5118 to 4321 computations (15.6% saved)

Profiling

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