Details

Time bar (total: 2.5min)

analyze2.7s (1.8%)

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)

sample2.0s (1.3%)

Algorithm
intervals
Results
1.8s122×body8192exit
104.0ms256×body128valid
10.0ms382×pre128true
2.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify156.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04804115
14804115

prune17.0ms (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)

localize65.0ms (0%)

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)))

rewrite165.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_1101
23×add-log-exp_binary64_1140
14×frac-add_binary64_1109
13×distribute-lft-out_binary64_1052 sum-log_binary64_1192
10×add-exp-log_binary64_1139
pow1_binary64_1162 add-cbrt-cube_binary64_1137
prod-exp_binary64_1150
flip3-+_binary64_1104 flip-+_binary64_1075
add-sqr-sqrt_binary64_1123 add-cube-cbrt_binary64_1136
associate-*r*_binary64_1041
cbrt-unprod_binary64_1134
sqrt-pow1_binary64_1119 +-commutative_binary64_1031 pow-prod-down_binary64_1172 associate-+l+_binary64_1034
*-commutative_binary64_1032 pow-exp_binary64_1169 exp-sum_binary64_1147 sqrt-prod_binary64_1117 associate-*r/_binary64_1043 pow-sub_binary64_1177 associate-*l*_binary64_1042 associate-*l/_binary64_1044 pow-to-exp_binary64_1170 pow1/2_binary64_1181
Counts
4 → 74
Calls

4 calls:

99.0ms
(+.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)))
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))

series179.0ms (0.1%)

Counts
4 → 10
Calls

4 calls:

131.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
33.0ms
(+.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))

simplify119.0ms (0.1%)

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
049123345
149123345

prune850.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New79584
Fresh101
Picked101
Done000
Total81586
Error
0.3b
Counts
86 → 5
Compiler

Compiled 7706 to 5962 computations (22.6% saved)

localize127.0ms (0.1%)

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)))))

rewrite204.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
83×associate-*r/_binary64_1043
68×frac-times_binary64_1111
64×frac-add_binary64_1109
60×flip3-+_binary64_1104 flip-+_binary64_1075
43×flip--_binary64_1076 flip3--_binary64_1105
35×associate-*l/_binary64_1044
13×add-sqr-sqrt_binary64_1123
12×add-exp-log_binary64_1139
11×*-un-lft-identity_binary64_1101 pow1_binary64_1162 add-cbrt-cube_binary64_1137
add-cube-cbrt_binary64_1136 associate-*r*_binary64_1041
prod-exp_binary64_1150
add-log-exp_binary64_1140 distribute-lft-in_binary64_1050 cancel-sign-sub-inv_binary64_1067 distribute-rgt-in_binary64_1051
cbrt-unprod_binary64_1134 associate-*l*_binary64_1042
pow-prod-down_binary64_1172
*-commutative_binary64_1032 sub-neg_binary64_1094 sqrt-pow1_binary64_1119 associate-+r+_binary64_1033 associate-+l+_binary64_1034
pow-exp_binary64_1169 exp-sum_binary64_1147 difference-of-squares_binary64_1070 sum-log_binary64_1192 distribute-lft-out--_binary64_1053 sqrt-prod_binary64_1117 +-commutative_binary64_1031 pow-sub_binary64_1177 unswap-sqr_binary64_1069 pow-to-exp_binary64_1170 pow1/2_binary64_1181
Counts
4 → 147
Calls

4 calls:

57.0ms
(*.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))
41.0ms
(+.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)))))
29.0ms
(*.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))

series205.0ms (0.1%)

Counts
4 → 10
Calls

4 calls:

120.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
49.0ms
(*.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))

simplify248.0ms (0.2%)

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0585216162

prune4.9s (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1552157
Fresh134
Picked101
Done000
Total1575162
Error
0.3b
Counts
162 → 5
Compiler

Compiled 34031 to 27804 computations (18.3% saved)

localize118.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
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))
2.0b
(+.f64 (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (*.f64 (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)) (-.f64 4 (*.f64 z z)))) (*.f64 (*.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (*.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (*.f64 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (*.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (+.f64 2 z))))

rewrite1.6s (1.1%)

Algorithm
rewrite-expression-head
Rules
1456×frac-times_binary64_1111
1197×associate-*r/_binary64_1043
706×flip--_binary64_1076 flip3--_binary64_1105
703×flip3-+_binary64_1104 flip-+_binary64_1075
676×frac-add_binary64_1109
417×associate-*l/_binary64_1044
102×cube-prod_binary64_1129 unpow-prod-down_binary64_1180
84×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
72×times-frac_binary64_1107
48×add-cube-cbrt_binary64_1136
24×difference-of-squares_binary64_1070
14×add-exp-log_binary64_1139
12×distribute-lft-in_binary64_1050 distribute-lft-out--_binary64_1053 distribute-rgt-in_binary64_1051
10×add-cbrt-cube_binary64_1137
pow1_binary64_1162
associate-/r/_binary64_1047 associate-+l+_binary64_1034
pow-exp_binary64_1169 prod-exp_binary64_1150
add-log-exp_binary64_1140
sub-neg_binary64_1094 associate-+r+_binary64_1033 div-inv_binary64_1098 associate-*r*_binary64_1041 cancel-sign-sub-inv_binary64_1067
cube-mult_binary64_1131 cbrt-unprod_binary64_1134 pow-unpow_binary64_1178 unpow3_binary64_1167 sqr-pow_binary64_1073 pow-to-exp_binary64_1170
sqrt-pow1_binary64_1119 cube-div_binary64_1130 pow-prod-down_binary64_1172
*-commutative_binary64_1032 exp-sum_binary64_1147 rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 sum-log_binary64_1192 sqrt-prod_binary64_1117 +-commutative_binary64_1031 div-exp_binary64_1152 pow-sub_binary64_1177 associate-*l*_binary64_1042 pow1/2_binary64_1181
Counts
4 → 860
Calls

4 calls:

97.0ms
(+.f64 (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (*.f64 (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)) (-.f64 4 (*.f64 z z)))) (*.f64 (*.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (*.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (*.f64 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (*.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (+.f64 2 z))))
17.0ms
(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
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))

series483.0ms (0.3%)

Counts
4 → 10
Calls

4 calls:

353.0ms
(+.f64 (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (*.f64 (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)) (-.f64 4 (*.f64 z z)))) (*.f64 (*.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (*.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (*.f64 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (*.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (+.f64 2 z))))
100.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
30.0ms
(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))

simplify5.8s (3.9%)

Algorithm
egg-herbie
Counts
870 → 870
Iterations

Useful iterations: 0 (124.0ms)

IterNodesCost
05244310084

prune2.2min (86.7%)

Profiling

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