Details

Time bar (total: 2.5min)

analyze1.9s (1.2%)

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)

sample1.5s (1%)

Algorithm
intervals
Results
1.3s121×body8192exit
77.0ms256×body128valid
7.0ms380×pre128true
1.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify49.0ms (0%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04804115
14804115

prune18.0ms (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)

localize54.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 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)))

rewrite1.0s (0.7%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
45×*-un-lft-identity_binary64_2124
44×add-log-exp_binary64_2163 frac-add_binary64_2132
31×sum-log_binary64_2215 distribute-lft-out_binary64_2075
10×add-exp-log_binary64_2162
pow1_binary64_2185 add-cbrt-cube_binary64_2160 flip3-+_binary64_2127 flip-+_binary64_2098
prod-exp_binary64_2173
add-cube-cbrt_binary64_2159 add-sqr-sqrt_binary64_2146
associate-*r*_binary64_2064
cbrt-unprod_binary64_2157
associate-+l+_binary64_2057 +-commutative_binary64_2054 pow-prod-down_binary64_2195 sqrt-pow1_binary64_2142
pow1/2_binary64_2204 sqrt-prod_binary64_2140 pow-to-exp_binary64_2193 pow-exp_binary64_2192 pow-sub_binary64_2200 associate-*r/_binary64_2066 associate-*l/_binary64_2067 associate-*l*_binary64_2065 exp-sum_binary64_2170 *-commutative_binary64_2055
Counts
4 → 86
Calls

4 calls:

93.0ms
(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 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)))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 10066 to 7936 computations (21.2% saved)

series512.0ms (0.3%)

Error
0.3b
Counts
4 → 22
Calls

4 calls:

254.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
122.0ms
(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
50.0ms
(+.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 3444 to 2750 computations (20.2% saved)

simplify89.0ms (0.1%)

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
051898306

prune980.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1026108
Fresh101
Picked101
Done000
Total1046110
Error
0.2b
Counts
110 → 6
Compiler

Compiled 11706 to 9157 computations (21.8% saved)

localize61.0ms (0%)

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)))

rewrite2.6s (1.7%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
183×times-frac_binary64_2130
162×*-un-lft-identity_binary64_2124
156×add-sqr-sqrt_binary64_2146
111×cancel-sign-sub-inv_binary64_2090
76×add-cube-cbrt_binary64_2159
39×difference-of-squares_binary64_2093
36×distribute-lft-out--_binary64_2076
16×pow1_binary64_2185
12×add-exp-log_binary64_2162 flip3-+_binary64_2127 flip-+_binary64_2098 associate-/r/_binary64_2070
11×add-cbrt-cube_binary64_2160
frac-times_binary64_2134 frac-sub_binary64_2133 prod-exp_binary64_2173 associate-*r*_binary64_2064
flip3--_binary64_2128 flip--_binary64_2099
add-log-exp_binary64_2163 div-inv_binary64_2121 swap-sqr_binary64_2091 distribute-lft-out_binary64_2075
associate-*l/_binary64_2067 associate-*r/_binary64_2066 associate-*l*_binary64_2065
cbrt-unprod_binary64_2157
pow-prod-down_binary64_2195
distribute-rgt-in_binary64_2074 associate--l+_binary64_2061 distribute-lft-in_binary64_2073 sqrt-pow1_binary64_2142 *-commutative_binary64_2055
diff-log_binary64_2216 sub-neg_binary64_2117 pow1/2_binary64_2204 sqrt-prod_binary64_2140 pow-to-exp_binary64_2193 pow-exp_binary64_2192 pow-sub_binary64_2200 exp-sum_binary64_2170 pow2_binary64_2205 pow-prod-up_binary64_2194 pow-plus_binary64_2187 pow-sqr_binary64_2097 unswap-sqr_binary64_2092
Counts
4 → 207
Calls

4 calls:

65.0ms
(-.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)))
25.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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 24141 to 19104 computations (20.9% saved)

series565.0ms (0.4%)

Error
0.2b
Counts
4 → 24
Calls

4 calls:

265.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
88.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
83.0ms
(-.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 5536 to 4492 computations (18.9% saved)

simplify120.0ms (0.1%)

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049407481
149407481

prune2.6s (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2292231
Fresh235
Picked101
Done000
Total2325237
Error
0.2b
Counts
237 → 5
Compiler

Compiled 25996 to 20427 computations (21.4% saved)

localize75.0ms (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 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
1.0b
(+.f64 (*.f64 (-.f64 2 z) (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))))) (*.f64 (*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))))

rewrite1.7min (68.8%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
1088×times-frac_binary64_2130
976×add-sqr-sqrt_binary64_2146
960×*-un-lft-identity_binary64_2124
900×frac-times_binary64_2134
815×flip3--_binary64_2128 flip--_binary64_2099
696×cancel-sign-sub-inv_binary64_2090
654×distribute-rgt-in_binary64_2074 distribute-lft-in_binary64_2073
604×associate-+l+_binary64_2057
452×associate-*l/_binary64_2067
442×frac-add_binary64_2132
392×add-cube-cbrt_binary64_2159
376×difference-of-squares_binary64_2093
372×associate-*r/_binary64_2066
192×distribute-lft-out--_binary64_2076
64×associate-/r/_binary64_2070
32×div-inv_binary64_2121
21×pow1_binary64_2185
16×swap-sqr_binary64_2091
12×associate-*l*_binary64_2065 associate-*r*_binary64_2064
add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 sub-neg_binary64_2117
add-log-exp_binary64_2163
pow-prod-down_binary64_2195
sqrt-pow1_binary64_2142 pow2_binary64_2205 pow-prod-up_binary64_2194 pow-plus_binary64_2187 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 pow-sqr_binary64_2097 unswap-sqr_binary64_2092 *-commutative_binary64_2055
sum-log_binary64_2215 flip3-+_binary64_2127 flip-+_binary64_2098 +-commutative_binary64_2054 pow1/2_binary64_2204 sqrt-prod_binary64_2140
Counts
4 → 1256
Calls

4 calls:

202.0ms
(+.f64 (*.f64 (-.f64 2 z) (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))))) (*.f64 (*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))))
38.0ms
(*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
32.0ms
(*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 269088 to 218212 computations (18.9% saved)

series485.0ms (0.3%)

Error
0.2b
Counts
4 → 24
Calls

4 calls:

131.0ms
(+.f64 (*.f64 (-.f64 2 z) (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))))) (*.f64 (*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))))
110.0ms
(*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
85.0ms
(*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 6916 to 5629 computations (18.6% saved)

simplify1.6s (1%)

Algorithm
egg-herbie
Counts
1280 → 1280
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
05673168176

prune32.7s (21.8%)

Profiling

Loading profile data...