Details

Time bar (total: 12.2s)

analyze2.1s (16.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
0.8%98.9%0.3%13
1.2%98.5%0.3%14
Compiler

Compiled 38 to 31 computations (18.4% saved)

sample39.0ms (0.3%)

Algorithm
intervals
Results
23.0ms256×body128valid
2.0ms22×body128invalid
Compiler

Compiled 75 to 67 computations (10.7% saved)

simplify277.0ms (2.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (114.0ms)

IterNodesCost
0497155
1497155

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 28.7b

Counts
2 → 1
Compiler

Compiled 74 to 60 computations (18.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
0.1b
(*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
2.9b
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
27.2b
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

rewrite87.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_5490
15×add-exp-log_binary64_5504 add-cbrt-cube_binary64_5502
12×add-cube-cbrt_binary64_5501 *-un-lft-identity_binary64_5469
10×pow1_binary64_5527
associate-*r*_binary64_5411 associate-*l*_binary64_5412
flip-+_binary64_5443 flip3-+_binary64_5472
associate-*l/_binary64_5414 cbrt-unprod_binary64_5499 associate-*r/_binary64_5413 add-log-exp_binary64_5505 prod-exp_binary64_5515
pow-prod-down_binary64_5537 associate-/r*_binary64_5415 unswap-sqr_binary64_5437 *-commutative_binary64_5402 times-frac_binary64_5475
associate-/l/_binary64_5418 cbrt-undiv_binary64_5500 associate-/r/_binary64_5417 div-exp_binary64_5517
clear-num_binary64_5468 distribute-lft-in_binary64_5420 associate-/l*_binary64_5416 div-inv_binary64_5466 frac-2neg_binary64_5480 distribute-rgt-in_binary64_5421
Counts
4 → 87
Calls

4 calls:

36.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
18.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
12.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
8.0ms
(*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)

series1.3s (11%)

Counts
4 → 12
Calls

4 calls:

897.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
323.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
84.0ms
(*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
37.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)

simplify99.0ms (0.8%)

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
051213027

prune252.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91899
Fresh000
Picked101
Done000
Total928100

Merged error: 0.5b

Counts
100 → 8
Compiler

Compiled 4895 to 3293 computations (32.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t))
0.1b
(*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656))
0.2b
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496)))
26.8b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))

rewrite103.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64_5490
24×add-cube-cbrt_binary64_5501 *-un-lft-identity_binary64_5469
21×associate-*r*_binary64_5411
19×times-frac_binary64_5475
15×add-exp-log_binary64_5504 add-cbrt-cube_binary64_5502
10×pow1_binary64_5527
associate-*l*_binary64_5412
flip-+_binary64_5443 associate-*r/_binary64_5413 flip3-+_binary64_5472
cbrt-unprod_binary64_5499 associate-/r/_binary64_5417 unswap-sqr_binary64_5437 add-log-exp_binary64_5505 prod-exp_binary64_5515
pow-prod-down_binary64_5537 associate-/r*_binary64_5415 associate-/l*_binary64_5416 *-commutative_binary64_5402
associate-/l/_binary64_5418 cbrt-undiv_binary64_5500 distribute-lft-in_binary64_5420 div-inv_binary64_5466 div-exp_binary64_5517 distribute-rgt-in_binary64_5421
clear-num_binary64_5468 frac-2neg_binary64_5480
Counts
4 → 109
Calls

4 calls:

34.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))
33.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496)))
12.0ms
(*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t))
8.0ms
(*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656))

series1.3s (10.8%)

Counts
4 → 12
Calls

4 calls:

902.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496)))
309.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))
73.0ms
(*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656))
36.0ms
(*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t))

simplify122.0ms (1%)

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
050294972

prune313.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1192121
Fresh077
Picked101
Done000
Total1209129

Merged error: 0.5b

Counts
129 → 9
Compiler

Compiled 6519 to 4403 computations (32.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 z)
0.6b
(cbrt.f64 z)
0.6b
(cbrt.f64 z)
26.8b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t) (cbrt.f64 z))) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))

rewrite57.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
15×add-cube-cbrt_binary64_5501 *-un-lft-identity_binary64_5469 add-sqr-sqrt_binary64_5490
cbrt-prod_binary64_5497 times-frac_binary64_5475
add-exp-log_binary64_5504 add-cbrt-cube_binary64_5502
pow1_binary64_5527 add-log-exp_binary64_5505
associate-/r*_binary64_5415 associate-/l*_binary64_5416 pow1/3_binary64_5548
associate-/l/_binary64_5418 flip-+_binary64_5443 associate-/r/_binary64_5417 flip3-+_binary64_5472
clear-num_binary64_5468 cbrt-undiv_binary64_5500 div-inv_binary64_5466 div-exp_binary64_5517 frac-2neg_binary64_5480
Counts
4 → 64
Calls

4 calls:

42.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t) (cbrt.f64 z))) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))
2.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 z)

series910.0ms (7.5%)

Counts
4 → 12
Calls

4 calls:

447.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t) (cbrt.f64 z))) a)) b) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))
160.0ms
(cbrt.f64 z)
154.0ms
(cbrt.f64 z)
149.0ms
(cbrt.f64 z)

simplify85.0ms (0.7%)

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049712448
149712448

prune182.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh088
Picked011
Done000
Total76985

Merged error: 0.5b

Counts
85 → 9
Compiler

Compiled 4309 to 2732 computations (36.6% saved)

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.9b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))
8.9b
(sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
18.8b
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b))
20.2b
(/.f64 (*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b)) (sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496)))

rewrite150.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64_5490
26×times-frac_binary64_5475
24×add-cube-cbrt_binary64_5501 *-un-lft-identity_binary64_5469 associate-*l*_binary64_5412
22×sqrt-prod_binary64_5484
18×add-exp-log_binary64_5504 add-cbrt-cube_binary64_5502
flip-+_binary64_5443 sqrt-div_binary64_5485 pow1_binary64_5527 flip3-+_binary64_5472
associate-/r*_binary64_5415
associate-/l/_binary64_5418 cbrt-undiv_binary64_5500 div-exp_binary64_5517
frac-times_binary64_5479 cbrt-unprod_binary64_5499 associate-/r/_binary64_5417 associate-*r/_binary64_5413 add-log-exp_binary64_5505 prod-exp_binary64_5515
associate-*r*_binary64_5411 unswap-sqr_binary64_5437
rem-sqrt-square_binary64_5482 associate-*l/_binary64_5414 pow1/2_binary64_5546 div-inv_binary64_5466 sqrt-pow1_binary64_5486
clear-num_binary64_5468 pow-prod-down_binary64_5537 distribute-lft-in_binary64_5420 associate-/l*_binary64_5416 frac-2neg_binary64_5480 *-commutative_binary64_5402 distribute-rgt-in_binary64_5421
Counts
4 → 116
Calls

4 calls:

54.0ms
(/.f64 (*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b)) (sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496)))
44.0ms
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b))
15.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))
14.0ms
(sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

series1.9s (15.8%)

Counts
4 → 12
Calls

4 calls:

959.0ms
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b))
880.0ms
(/.f64 (*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))) (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656)) t)) a)) b)) (sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496)))
44.0ms
(sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
44.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496))

simplify118.0ms (1%)

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049706868
149706868

prune466.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1271128
Fresh077
Picked101
Done011
Total1289137

Merged error: 0.5b

Counts
137 → 9
Compiler

Compiled 8565 to 5962 computations (30.4% saved)

regimes505.0ms (4.1%)

Compiler

Compiled 2370 to 1980 computations (16.5% saved)

bsearch85.0ms (0.7%)

Steps
ItersRangePoint
10
7.317459805983961e+27
4.072634537553549e+40
4.974259772593562e+39
7
-1.6442048761342146e+69
-4.647464072227077e+67
-4.702036921833592e+67
Compiler

Compiled 1 to 6 computations (-500% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0100123
1100123

end0.0ms (0%)

sample1.6s (12.8%)

Algorithm
intervals
Results
754.0ms8000×body128valid
86.0ms883×body128invalid
Compiler

Compiled 592 to 468 computations (20.9% saved)

Profiling

Loading profile data...