Details

Time bar (total: 1.2min)

analyze1.8s (2.4%)

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)

sample1.7s (2.3%)

Algorithm
intervals
Results
1.5s138×body8192exit
84.0ms256×body128valid
7.0ms398×pre128true
1.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify140.0ms (0.2%)

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)

localize56.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b
(-.f64 (-.f64 1 z) 1)
6.5b
(-.f64 (-.f64 1 z) 1)
6.5b
(-.f64 (-.f64 1 z) 1)
6.5b
(-.f64 (-.f64 1 z) 1)

rewrite983.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
1.8b
Rules
36×*-un-lft-identity_binary64_2465
28×add-sqr-sqrt_binary64_2487
24×add-log-exp_binary64_2504 cancel-sign-sub-inv_binary64_2431
16×associate--l+_binary64_2402
12×diff-log_binary64_2557 add-cube-cbrt_binary64_2500 distribute-lft-out--_binary64_2417
sub-neg_binary64_2458 difference-of-squares_binary64_2434
pow1_binary64_2526 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 flip3--_binary64_2469 flip--_binary64_2440 difference-of-sqr-1_binary64_2435 associate--l-_binary64_2403
Counts
4 → 100
Calls

4 calls:

11.0ms
(-.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 12896 to 10998 computations (14.7% saved)

series211.0ms (0.3%)

Error
1.8b
Counts
4 → 12
Calls

4 calls:

40.0ms
(-.f64 (-.f64 1 z) 1)
39.0ms
(-.f64 (-.f64 1 z) 1)
37.0ms
(-.f64 (-.f64 1 z) 1)
37.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify77.0ms (0.1%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
05392704

prune1.4s (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Compiled 13990 to 11821 computations (15.5% saved)

localize57.0ms (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 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
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)))

rewrite469.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
1.1b
Rules
19×*-un-lft-identity_binary64_2465
18×add-log-exp_binary64_2504
10×add-exp-log_binary64_2503
sum-log_binary64_2556 pow1_binary64_2526 add-cbrt-cube_binary64_2501 distribute-lft-out_binary64_2416
frac-add_binary64_2473
prod-exp_binary64_2514
add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 flip3-+_binary64_2468 flip-+_binary64_2439
associate-*r*_binary64_2405
cbrt-unprod_binary64_2498
associate-+l+_binary64_2398 +-commutative_binary64_2395 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
pow1/2_binary64_2545 sqrt-prod_binary64_2481 pow-to-exp_binary64_2534 pow-exp_binary64_2533 pow-sub_binary64_2541 associate-*r/_binary64_2407 associate-*l/_binary64_2408 associate-*l*_binary64_2406 exp-sum_binary64_2511 *-commutative_binary64_2396
Counts
4 → 70
Calls

4 calls:

41.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
24.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 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 6200 to 4800 computations (22.6% saved)

series377.0ms (0.5%)

Error
1.1b
Counts
4 → 24
Calls

4 calls:

189.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
64.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
35.0ms
(+.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 4128 to 3310 computations (19.8% saved)

simplify67.0ms (0.1%)

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
057102881

prune514.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New89594
Fresh000
Picked101
Done011
Total90696
Error
1.1b
Counts
96 → 6
Compiler

Compiled 8129 to 6254 computations (23.1% saved)

localize64.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (/.f64 (-.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))) (-.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 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))
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)))

rewrite2.8s (3.8%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
196×*-un-lft-identity_binary64_2465
195×times-frac_binary64_2471
155×add-sqr-sqrt_binary64_2487
111×cancel-sign-sub-inv_binary64_2431
75×add-cube-cbrt_binary64_2500
43×distribute-lft-out--_binary64_2417
39×difference-of-squares_binary64_2434
15×distribute-lft-out_binary64_2416
14×pow1_binary64_2526
13×flip3-+_binary64_2468 flip-+_binary64_2439
12×associate-/r/_binary64_2411
add-log-exp_binary64_2504 frac-times_binary64_2475 frac-sub_binary64_2474
flip3--_binary64_2469 flip--_binary64_2440
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 div-inv_binary64_2462 swap-sqr_binary64_2432
associate-*l/_binary64_2408 associate-*r/_binary64_2407 associate-*l*_binary64_2406 associate-*r*_binary64_2405
distribute-rgt-in_binary64_2415 associate--l+_binary64_2402 distribute-lft-in_binary64_2414 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
diff-log_binary64_2557 sub-neg_binary64_2458 pow1/2_binary64_2545 sqrt-prod_binary64_2481 pow2_binary64_2546 pow-prod-up_binary64_2535 pow-plus_binary64_2528 prod-exp_binary64_2514 cbrt-unprod_binary64_2498 pow-sqr_binary64_2438 unswap-sqr_binary64_2433 *-commutative_binary64_2396 sum-log_binary64_2556 frac-add_binary64_2473 div-sub_binary64_2470 associate-+l-_binary64_2400 +-commutative_binary64_2395
Counts
4 → 206
Calls

4 calls:

136.0ms
(+.f64 (/.f64 (-.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))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
67.0ms
(-.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))))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 24366 to 19316 computations (20.7% saved)

series341.0ms (0.5%)

Error
1.1b
Counts
4 → 30
Calls

4 calls:

125.0ms
(+.f64 (/.f64 (-.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))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
66.0ms
(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
50.0ms
(-.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 5000 to 3987 computations (20.3% saved)

simplify135.0ms (0.2%)

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
052827811

prune2.5s (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2333236
Fresh134
Picked101
Done011
Total2357242
Error
0.3b
Counts
242 → 7
Compiler

Compiled 25909 to 20316 computations (21.6% saved)

localize72.0ms (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 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z)))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.6b
(-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))

rewrite4.9s (6.6%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
320×times-frac_binary64_2471
296×sqrt-prod_binary64_2481
252×add-sqr-sqrt_binary64_2487
237×*-un-lft-identity_binary64_2465
198×cancel-sign-sub-inv_binary64_2431
134×add-cube-cbrt_binary64_2500
55×difference-of-squares_binary64_2434
50×distribute-lft-out--_binary64_2417
18×associate-/r/_binary64_2411
11×add-log-exp_binary64_2504
10×add-exp-log_binary64_2503 flip3--_binary64_2469 flip--_binary64_2440
pow1_binary64_2526 add-cbrt-cube_binary64_2501 div-inv_binary64_2462
prod-exp_binary64_2514
associate-*r*_binary64_2405
cbrt-unprod_binary64_2498
sum-log_binary64_2556 diff-log_binary64_2557 flip3-+_binary64_2468 frac-sub_binary64_2474 flip-+_binary64_2439 sqrt-div_binary64_2482 distribute-lft-out_binary64_2416 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
sub-neg_binary64_2458 associate--l+_binary64_2402 pow1/2_binary64_2545 frac-add_binary64_2473 +-commutative_binary64_2395 pow-to-exp_binary64_2534 pow-exp_binary64_2533 pow-sub_binary64_2541 associate-*r/_binary64_2407 associate-*l/_binary64_2408 associate-*l*_binary64_2406 exp-sum_binary64_2511 *-commutative_binary64_2396
Counts
4 → 267
Calls

4 calls:

211.0ms
(+.f64 (/.f64 (*.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z)))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
95.0ms
(-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.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 35469 to 28391 computations (20% saved)

series423.0ms (0.6%)

Error
0.3b
Counts
4 → 24
Calls

4 calls:

198.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
72.0ms
(+.f64 (/.f64 (*.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z)))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
47.0ms
(-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 5164 to 4192 computations (18.8% saved)

simplify162.0ms (0.2%)

Algorithm
egg-herbie
Counts
291 → 291
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0495112467
1495112467

prune4.3s (5.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2910291
Fresh055
Picked011
Done011
Total2917298
Error
0.3b
Counts
298 → 7
Compiler

Compiled 36582 to 29097 computations (20.5% saved)

regimes652.0ms (0.9%)

Accuracy

Total 0.2b remaining (42.3%)

Threshold costs 0.2b (42.3%)

Compiler

Compiled 9768 to 8172 computations (16.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0144177
1144177

end0.0ms (0%)

sample49.4s (67.2%)

Algorithm
intervals
Results
42.6s3846×body8192exit
2.5s8000×body128valid
224.0ms11926×pre128true
27.0ms80×body128invalid
Compiler

Compiled 5000 to 4183 computations (16.3% saved)

Profiling

Loading profile data...