Details

Time bar (total: 1.1min)

analyze1.9s (2.8%)

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)

sample1.4s (2.1%)

Algorithm
intervals
Results
1.3s120×body8192exit
77.0ms256×body128valid
6.0ms380×pre128true
1.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify47.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04804115
14804115

prune15.0ms (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)

localize64.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b
(-.f64 (-.f64 1 z) 1)
6.2b
(-.f64 (-.f64 1 z) 1)
6.2b
(-.f64 (-.f64 1 z) 1)
6.2b
(-.f64 (-.f64 1 z) 1)

rewrite1.3s (1.8%)

Algorithm
rewrite-expression-head
Error
1.8b
Rules
36×*-un-lft-identity_binary64_3147
28×add-sqr-sqrt_binary64_3169
24×add-log-exp_binary64_3186 cancel-sign-sub-inv_binary64_3113
16×associate--l+_binary64_3084
12×diff-log_binary64_3239 add-cube-cbrt_binary64_3182 distribute-lft-out--_binary64_3099
sub-neg_binary64_3140 difference-of-squares_binary64_3116
pow1_binary64_3208 add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 flip3--_binary64_3151 flip--_binary64_3122 difference-of-sqr-1_binary64_3117 associate--l-_binary64_3085
Counts
4 → 100
Calls

4 calls:

14.0ms
(-.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)
Compiler

Compiled 11372 to 9694 computations (14.8% saved)

series227.0ms (0.3%)

Error
1.8b
Counts
4 → 12
Calls

4 calls:

50.0ms
(-.f64 (-.f64 1 z) 1)
50.0ms
(-.f64 (-.f64 1 z) 1)
50.0ms
(-.f64 (-.f64 1 z) 1)
49.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 3388 to 3009 computations (11.2% saved)

simplify76.0ms (0.1%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
05392704

prune721.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done000
Total1122114
Error
1.8b
Counts
114 → 2
Compiler

Compiled 7566 to 6377 computations (15.7% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b
(+.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))
2.5b
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite489.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
1.1b
Rules
19×*-un-lft-identity_binary64_3147
18×add-log-exp_binary64_3186
10×add-exp-log_binary64_3185
sum-log_binary64_3238 pow1_binary64_3208 add-cbrt-cube_binary64_3183 distribute-lft-out_binary64_3098
frac-add_binary64_3155
prod-exp_binary64_3196
add-cube-cbrt_binary64_3182 add-sqr-sqrt_binary64_3169 flip3-+_binary64_3150 flip-+_binary64_3121
associate-*r*_binary64_3087
cbrt-unprod_binary64_3180
associate-+l+_binary64_3080 +-commutative_binary64_3077 pow-prod-down_binary64_3218 sqrt-pow1_binary64_3165
pow1/2_binary64_3227 sqrt-prod_binary64_3163 pow-to-exp_binary64_3216 pow-exp_binary64_3215 pow-sub_binary64_3223 associate-*r/_binary64_3089 associate-*l/_binary64_3090 associate-*l*_binary64_3088 exp-sum_binary64_3193 *-commutative_binary64_3078
Counts
4 → 70
Calls

4 calls:

37.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
23.0ms
(+.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)))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 5591 to 4335 computations (22.5% saved)

series591.0ms (0.9%)

Error
1.1b
Counts
4 → 30
Calls

4 calls:

312.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
94.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
82.0ms
(+.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 4348 to 3504 computations (19.4% saved)

simplify67.0ms (0.1%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
057602977

prune458.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New955100
Fresh000
Picked101
Done011
Total966102
Error
1.1b
Counts
102 → 6
Compiler

Compiled 6806 to 5257 computations (22.8% saved)

localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b
(+.f64 (/.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 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 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))

rewrite1.1s (1.6%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
21×associate-*r/_binary64_3089
17×frac-add_binary64_3155
16×flip3-+_binary64_3150 flip-+_binary64_3121
10×add-exp-log_binary64_3185
pow1_binary64_3208 add-cbrt-cube_binary64_3183
add-log-exp_binary64_3186 frac-times_binary64_3157
*-un-lft-identity_binary64_3147 prod-exp_binary64_3196
flip3--_binary64_3151 flip--_binary64_3122
add-cube-cbrt_binary64_3182 add-sqr-sqrt_binary64_3169 associate-*l/_binary64_3090
associate-*r*_binary64_3087
cbrt-unprod_binary64_3180
sum-log_binary64_3238 distribute-rgt-in_binary64_3097 associate-+l+_binary64_3080 distribute-lft-in_binary64_3096 associate-+r+_binary64_3079 +-commutative_binary64_3077 pow-prod-down_binary64_3218 sqrt-pow1_binary64_3165
pow1/2_binary64_3227 sqrt-prod_binary64_3163 pow-to-exp_binary64_3216 pow-exp_binary64_3215 pow-sub_binary64_3223 associate-*l*_binary64_3088 exp-sum_binary64_3193 *-commutative_binary64_3078 distribute-lft-out_binary64_3098
Counts
4 → 76
Calls

4 calls:

81.0ms
(+.f64 (/.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))
17.0ms
(*.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 10790 to 8699 computations (19.4% saved)

series781.0ms (1.1%)

Error
1.1b
Counts
4 → 24
Calls

4 calls:

314.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
259.0ms
(+.f64 (/.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
86.0ms
(+.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 4514 to 3666 computations (18.8% saved)

simplify96.0ms (0.1%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
051086361

prune943.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New964100
Fresh044
Picked101
Done011
Total979106
Error
0.3b
Counts
106 → 9
Compiler

Compiled 11911 to 9552 computations (19.8% saved)

localize83.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (*.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))) (*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
1.0b
(*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
1.0b
(sqrt.f64 (*.f64 2 PI.f64))
2.6b
(+.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))

rewrite1.7s (2.5%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
40×add-exp-log_binary64_3185
28×prod-exp_binary64_3196
24×cbrt-prod_binary64_3178
23×pow1_binary64_3208
22×add-sqr-sqrt_binary64_3169
20×associate-*r/_binary64_3089
16×frac-add_binary64_3155
15×flip3-+_binary64_3150 flip-+_binary64_3121
14×add-cube-cbrt_binary64_3182 *-un-lft-identity_binary64_3147 cbrt-unprod_binary64_3180 associate-*r*_binary64_3087
13×add-cbrt-cube_binary64_3183
pow-prod-down_binary64_3218
frac-times_binary64_3157 associate-*l*_binary64_3088
associate-*l/_binary64_3090 swap-sqr_binary64_3114
add-log-exp_binary64_3186 flip3--_binary64_3151 flip--_binary64_3122 pow1/3_binary64_3229
exp-sum_binary64_3193
unswap-sqr_binary64_3115
distribute-rgt-in_binary64_3097 associate-+l+_binary64_3080 distribute-lft-in_binary64_3096 associate-+r+_binary64_3079 sqrt-pow1_binary64_3165 pow-prod-up_binary64_3217 pow-sqr_binary64_3120 *-commutative_binary64_3078 pow-to-exp_binary64_3216 pow-exp_binary64_3215
sum-log_binary64_3238 +-commutative_binary64_3077 pow1/2_binary64_3227 sqrt-prod_binary64_3163 pow2_binary64_3228 pow-plus_binary64_3210 pow-sub_binary64_3223
Counts
4 → 119
Calls

4 calls:

33.0ms
(+.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))
30.0ms
(*.f64 (*.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))) (*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
13.0ms
(*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
2.0ms
(sqrt.f64 (*.f64 2 PI.f64))
Compiler

Compiled 16046 to 12915 computations (19.5% saved)

series785.0ms (1.1%)

Error
0.3b
Counts
4 → 18
Calls

4 calls:

307.0ms
(*.f64 (*.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))) (*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
259.0ms
(*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
93.0ms
(+.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))
0.0ms
(sqrt.f64 (*.f64 2 PI.f64))
Compiler

Compiled 5039 to 4159 computations (17.5% saved)

simplify98.0ms (0.1%)

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
052526209

prune1.7s (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1361137
Fresh167
Picked011
Done011
Total1379146
Error
0.3b
Counts
146 → 9
Compiler

Compiled 14001 to 11229 computations (19.8% saved)

regimes7.4s (10.8%)

Accuracy

Total 0.2b remaining (38.7%)

Threshold costs 0.2b (38.7%)

Compiler

Compiled 97726 to 82044 computations (16% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0131196
1131196

end7.0ms (0%)

Compiler

Compiled 125 to 103 computations (17.6% saved)

sample46.7s (67.8%)

Algorithm
intervals
Results
42.2s3809×body8192exit
2.4s8000×body128valid
219.0ms11902×pre128true
30.0ms93×body128invalid
Compiler

Compiled 1485 to 1265 computations (14.8% saved)

Profiling

Loading profile data...