Details

Time bar (total: 24.2s)

analyze5.2s (21.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
1.2%98.6%0.2%11
1.4%98.4%0.2%12
10.8%88.9%0.2%13
10.8%88.9%0.2%14
Compiler

Compiled 34 to 24 computations (29.4% saved)

sample293.0ms (1.2%)

Algorithm
intervals
Results
189.0ms117×body1024valid
48.0ms49×body512valid
26.0ms75×body128valid
8.0ms15×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify201.0ms (0.8%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
046355
146355

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.2b
Counts
2 → 1
Compiler

Compiled 66 to 46 computations (30.3% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite46.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_2487
*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 pow1_binary64_2526
add-log-exp_binary64_2504 associate-*r*_binary64_2405 associate-*l*_binary64_2406
sin-mult_binary64_2620 *-commutative_binary64_2396 unswap-sqr_binary64_2433 prod-exp_binary64_2514 pow-prod-down_binary64_2536 cbrt-unprod_binary64_2498
flip--_binary64_2440 asin-acos_binary64_2645 sub-neg_binary64_2458 cancel-sign-sub-inv_binary64_2431 diff-log_binary64_2557 flip3--_binary64_2469
Counts
4 → 58
Calls

4 calls:

11.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
10.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
8.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
2.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series639.0ms (2.6%)

Counts
4 → 12
Calls

4 calls:

323.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
226.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
64.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
26.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify142.0ms (0.6%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (113.0ms)

IterNodesCost
048682133
148682133

prune183.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New591170
Fresh000
Picked101
Done000
Total601171
Error
0.1b
Counts
71 → 11
Compiler

Compiled 3409 to 653 computations (80.8% saved)

localize53.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.7b
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

rewrite31.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64_2487
*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500
pow1_binary64_2526
add-log-exp_binary64_2504 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
log-prod_binary64_2551
log-pow_binary64_2554
associate-*r*_binary64_2405 exp-prod_binary64_2517 associate-*l*_binary64_2406
sub-neg_binary64_2458 cancel-sign-sub-inv_binary64_2431 exp-sum_binary64_2511
log-div_binary64_2552 sin-mult_binary64_2620 *-commutative_binary64_2396 flip--_binary64_2440 asin-acos_binary64_2645 unswap-sqr_binary64_2433 diff-log_binary64_2557 prod-exp_binary64_2514 pow-prod-down_binary64_2536 flip3--_binary64_2469 rem-log-exp_binary64_2506 exp-diff_binary64_2513 cbrt-unprod_binary64_2498
Counts
4 → 57
Calls

4 calls:

8.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
8.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
6.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.0s (4.1%)

Counts
4 → 12
Calls

4 calls:

489.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
254.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
237.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
25.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify176.0ms (0.7%)

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (148.0ms)

IterNodesCost
050602817

prune185.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New67269
Fresh01010
Picked101
Done000
Total681280
Error
0.1b
Counts
80 → 12
Compiler

Compiled 3689 to 704 computations (80.9% saved)

localize50.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
0.7b
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
3.8b
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite40.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_2487
11×*-un-lft-identity_binary64_2465 cancel-sign-sub-inv_binary64_2431
10×associate--r+_binary64_2401 sin-sum_binary64_2598
add-cube-cbrt_binary64_2500
add-log-exp_binary64_2504
distribute-lft-in_binary64_2414 log-prod_binary64_2551 sub-neg_binary64_2458 distribute-rgt-in_binary64_2415 pow1_binary64_2526
log-pow_binary64_2554 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 acos-asin_binary64_2646
associate--r-_binary64_2404 exp-prod_binary64_2517
difference-of-squares_binary64_2434 flip--_binary64_2440 diff-log_binary64_2557 exp-sum_binary64_2511 flip3--_binary64_2469
log-div_binary64_2552 times-frac_binary64_2471 distribute-lft-out--_binary64_2417 rem-log-exp_binary64_2506 exp-diff_binary64_2513
Counts
4 → 66
Calls

4 calls:

17.0ms
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
7.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
4.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
1.0ms
(acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.0s (4.3%)

Counts
4 → 12
Calls

4 calls:

580.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
375.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
61.0ms
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
26.0ms
(acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify137.0ms (0.6%)

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (103.0ms)

IterNodesCost
049063230
149063230

prune187.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New77178
Fresh2911
Picked011
Done000
Total791190
Error
0.1b
Counts
90 → 11
Compiler

Compiled 4452 to 1068 computations (76% saved)

localize64.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.6b
(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3)
16.6b
(cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite27.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod_binary64_2496
10×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
add-log-exp_binary64_2504 cube-prod_binary64_2493 unpow-prod-down_binary64_2544
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 pow1_binary64_2526
cube-div_binary64_2494
flip--_binary64_2440 pow-unpow_binary64_2542 flip3--_binary64_2469 cos-diff_binary64_2602 acos-asin_binary64_2646
associate--r+_binary64_2401 unpow3_binary64_2531 cbrt-div_binary64_2497 cube-mult_binary64_2495 sqr-pow_binary64_2437
rem-cube-cbrt_binary64_2488 distribute-lft-in_binary64_2414 pow-exp_binary64_2533 sub-neg_binary64_2458 pow-to-exp_binary64_2534 pow1/3_binary64_2547 distribute-rgt-in_binary64_2415 cancel-sign-sub-inv_binary64_2431 cos-acos_binary64_2631 diff-log_binary64_2557 pow-pow_binary64_2537 rem-cbrt-cube_binary64_2489
Counts
4 → 71
Calls

4 calls:

5.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
5.0ms
(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3)
4.0ms
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3))
3.0ms
(cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

series1.2s (5.1%)

Counts
4 → 12
Calls

4 calls:

626.0ms
(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3)
298.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
191.0ms
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3))
131.0ms
(cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

simplify104.0ms (0.4%)

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049923993
149923993

prune205.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New81283
Fresh189
Picked101
Done011
Total831194
Error
0.1b
Counts
94 → 11
Compiler

Compiled 3981 to 572 computations (85.6% saved)

regimes996.0ms (4.1%)

Accuracy

Total 0.1b remaining (62.1%)

Threshold costs 0.1b (62.1%)

Compiler

Compiled 10064 to 5873 computations (41.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05755
15755

end0.0ms (0%)

sample11.9s (49.1%)

Algorithm
intervals
Results
7.2s3992×body1024valid
1.5s1351×body512valid
632.0ms2097×body128valid
381.0ms552×body256valid
30.0msbody2048valid
Compiler

Compiled 1485 to 871 computations (41.3% saved)

Profiling

Loading profile data...