Details

Time bar (total: 1.1min)

analyze1.7s (2.5%)

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%)

Algorithm
intervals
Results
1.3s114×body8192exit
76.0ms256×body128valid
7.0ms375×pre128true
2.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify136.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04804115
14804115

prune13.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 271 to 232 computations (14.4% saved)

localize55.0ms (0.1%)

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)))

rewrite165.0ms (0.2%)

Algorithm
rewrite-expression-head
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 flip3-+_binary64_2127 flip-+_binary64_2098 add-cbrt-cube_binary64_2160
prod-exp_binary64_2173
add-cube-cbrt_binary64_2159 add-sqr-sqrt_binary64_2146
associate-*r*_binary64_2064
cbrt-unprod_binary64_2157
pow-prod-down_binary64_2195 sqrt-pow1_binary64_2142 +-commutative_binary64_2054 associate-+l+_binary64_2057
pow-exp_binary64_2192 *-commutative_binary64_2055 pow-sub_binary64_2200 sqrt-prod_binary64_2140 associate-*l*_binary64_2065 associate-*l/_binary64_2067 pow1/2_binary64_2204 pow-to-exp_binary64_2193 associate-*r/_binary64_2066 exp-sum_binary64_2170
Counts
4 → 86
Calls

4 calls:

95.0ms
(+.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)))
22.0ms
(*.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))

series159.0ms (0.2%)

Counts
4 → 10
Calls

4 calls:

98.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
45.0ms
(+.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)))
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))

simplify112.0ms (0.2%)

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049537992
149537992

prune829.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New90696
Fresh101
Picked101
Done000
Total92698
Error
0.2b
Counts
98 → 6
Compiler

Compiled 11580 to 9123 computations (21.2% saved)

localize102.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite156.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×add-log-exp_binary64_2163 *-un-lft-identity_binary64_2124
12×sum-log_binary64_2215 distribute-lft-out_binary64_2075
flip3-+_binary64_2127 flip-+_binary64_2098 frac-add_binary64_2132
pow1_binary64_2185 associate-+r+_binary64_2056 add-cube-cbrt_binary64_2159 +-commutative_binary64_2054 add-sqr-sqrt_binary64_2146 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
Counts
4 → 68
Calls

4 calls:

27.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
24.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series71.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

22.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
17.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
16.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
15.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify78.0ms (0.1%)

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049622204
149622204

prune3.6s (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New80080
Fresh055
Picked011
Done000
Total80686
Error
0.2b
Counts
86 → 6
Compiler

Compiled 32802 to 27104 computations (17.4% saved)

localize59.0ms (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
(exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))))))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.6b
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite172.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity_binary64_2124
44×frac-add_binary64_2132
31×distribute-lft-out_binary64_2075
14×exp-diff_binary64_2172 log-div_binary64_2211
11×exp-sum_binary64_2170
10×pow1_binary64_2185 log-prod_binary64_2210 add-exp-log_binary64_2162
add-log-exp_binary64_2163 flip3-+_binary64_2127 flip-+_binary64_2098 add-cbrt-cube_binary64_2160
add-cube-cbrt_binary64_2159 prod-exp_binary64_2173 add-sqr-sqrt_binary64_2146
exp-prod_binary64_2176 associate-*r*_binary64_2064
sum-log_binary64_2215 cbrt-unprod_binary64_2157
pow-prod-down_binary64_2195 sqrt-pow1_binary64_2142
pow-exp_binary64_2192 log-pow_binary64_2213 *-commutative_binary64_2055 pow-sub_binary64_2200 sqrt-prod_binary64_2140 associate-+r+_binary64_2056 associate-*l*_binary64_2065 associate-*l/_binary64_2067 rem-exp-log_binary64_2164 +-commutative_binary64_2054 pow1/2_binary64_2204 pow-to-exp_binary64_2193 associate-*r/_binary64_2066
Counts
4 → 85
Calls

4 calls:

99.0ms
(exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))))))
24.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 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))

series170.0ms (0.3%)

Counts
4 → 10
Calls

4 calls:

94.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
59.0ms
(exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))))))
17.0ms
(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))

simplify116.0ms (0.2%)

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049797722
149797722

prune747.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New94195
Fresh044
Picked011
Done011
Total947101
Error
0.2b
Counts
101 → 7
Compiler

Compiled 11236 to 8860 computations (21.1% saved)

localize102.0ms (0.2%)

Local error

Found 4 expressions with local error:

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
(*.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 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite409.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
83×associate-*r/_binary64_2066
68×frac-times_binary64_2134
64×frac-add_binary64_2132
60×flip3-+_binary64_2127 flip-+_binary64_2098
43×flip--_binary64_2099 flip3--_binary64_2128
35×associate-*l/_binary64_2067
13×add-sqr-sqrt_binary64_2146
12×add-exp-log_binary64_2162
11×pow1_binary64_2185 *-un-lft-identity_binary64_2124 add-cbrt-cube_binary64_2160
add-cube-cbrt_binary64_2159 associate-*r*_binary64_2064
prod-exp_binary64_2173
cancel-sign-sub-inv_binary64_2090 add-log-exp_binary64_2163 distribute-rgt-in_binary64_2074 distribute-lft-in_binary64_2073
associate-*l*_binary64_2065 cbrt-unprod_binary64_2157
pow-prod-down_binary64_2195
sqrt-pow1_binary64_2142 *-commutative_binary64_2055 associate-+r+_binary64_2056 sub-neg_binary64_2117 associate-+l+_binary64_2057
difference-of-squares_binary64_2093 unswap-sqr_binary64_2092 sum-log_binary64_2215 distribute-lft-out--_binary64_2076 pow-exp_binary64_2192 pow-sub_binary64_2200 sqrt-prod_binary64_2140 +-commutative_binary64_2054 pow1/2_binary64_2204 pow-to-exp_binary64_2193 exp-sum_binary64_2170
Counts
4 → 147
Calls

4 calls:

222.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
39.0ms
(*.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))
31.0ms
(+.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))

series183.0ms (0.3%)

Counts
4 → 10
Calls

4 calls:

107.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
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))
36.0ms
(+.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))

simplify234.0ms (0.3%)

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
0489615864
1489615864

prune6.6s (9.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1543157
Fresh044
Picked101
Done112
Total1568164
Error
0.2b
Counts
164 → 8
Compiler

Compiled 50038 to 40629 computations (18.8% saved)

regimes556.0ms (0.8%)

Accuracy

Total 0.2b remaining (41.9%)

Threshold costs 0.2b (41.9%)

Compiler

Compiled 8060 to 6728 computations (16.5% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0205589
1205589

end0.0ms (0%)

sample49.7s (73.5%)

Algorithm
intervals
Results
43.8s3998×body8192exit
2.4s8000×body128valid
228.0ms12082×pre128true
26.0ms84×body128invalid
Compiler

Compiled 4422 to 3693 computations (16.5% saved)

Profiling

Loading profile data...