Details

Time bar (total: 26.9s)

analyze2.8s (10.5%)

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
0.8%99%0.2%11
1.2%98.6%0.2%12
1.8%98%0.2%13
2%97.7%0.2%14
Compiler

Compiled 20 to 18 computations (10% saved)

sample230.0ms (0.9%)

Algorithm
intervals
Results
163.0ms183×body1024valid
24.0ms47×body512valid
17.0msbody2048valid
4.0ms11×body256valid
1.0msbody128valid
Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify96.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
09631
19631

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
19.4b
Counts
2 → 1
Compiler

Compiled 38 to 34 computations (10.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.2b
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.0b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.9b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite326.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
3.9b
Rules
11×pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
10×add-sqr-sqrt_binary64_1464
add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
associate-*r*_binary64_1382
cos-sum_binary64_1576 add-log-exp_binary64_1481 pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 associate-*l*_binary64_1383
cos-diff_binary64_1579 cancel-sign-sub-inv_binary64_1408
*-commutative_binary64_1373
sub-neg_binary64_1435 acos-asin_binary64_1623 distribute-rgt-in_binary64_1392 distribute-lft-in_binary64_1391 cos-mult_binary64_1596 associate-*l/_binary64_1385 unswap-sqr_binary64_1410
Counts
4 → 59
Calls

4 calls:

228.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
3.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 1775 to 321 computations (81.9% saved)

series810.0ms (3%)

Error
18.2b
Counts
4 → 59
Calls

4 calls:

374.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
235.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
94.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
56.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 3621 to 2086 computations (42.4% saved)

simplify100.0ms (0.4%)

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049622893
149622893

prune146.0ms (0.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10315118
Fresh000
Picked101
Done000
Total10415119
Error
3.9b
Counts
119 → 15
Compiler

Compiled 3300 to 707 computations (78.6% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.3b
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.9b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite130.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
3.8b
Rules
20×pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
12×add-sqr-sqrt_binary64_1464
10×pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475
add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
associate-*l*_binary64_1383 associate-*r*_binary64_1382
add-log-exp_binary64_1481
sin-mult_binary64_1597 *-commutative_binary64_1373
cos-mult_binary64_1596 unswap-sqr_binary64_1410
acos-asin_binary64_1623 frac-times_binary64_1452 associate-*l/_binary64_1385 associate-*r/_binary64_1384
Counts
4 → 70
Calls

4 calls:

10.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
5.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 3146 to 420 computations (86.6% saved)

series1.1s (4%)

Error
3.9b
Counts
4 → 49
Calls

4 calls:

424.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
347.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
163.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
102.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 4808 to 2385 computations (50.4% saved)

simplify91.0ms (0.3%)

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049743434
149743434

prune156.0ms (0.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New10712119
Fresh10414
Picked101
Done000
Total11816134
Error
3.8b
Counts
134 → 16
Compiler

Compiled 4761 to 861 computations (81.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
0.4b
(exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.6b
(log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
0.9b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

rewrite108.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
3.7b
Rules
12×add-sqr-sqrt_binary64_1464
10×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
exp-prod_binary64_1494
pow1_binary64_1503 log-pow_binary64_1531
associate-*l*_binary64_1383
add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
add-log-exp_binary64_1481
acos-asin_binary64_1623 log-prod_binary64_1528 associate-*r*_binary64_1382
exp-diff_binary64_1490
log-div_binary64_1529 rem-log-exp_binary64_1483 rem-exp-log_binary64_1482 pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 unswap-sqr_binary64_1410 *-commutative_binary64_1373
Counts
4 → 58
Calls

4 calls:

6.0ms
(*.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
2.0ms
(log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
2.0ms
(exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
Compiler

Compiled 2764 to 221 computations (92% saved)

series3.1s (11.3%)

Error
3.8b
Counts
4 → 51
Calls

4 calls:

1.5s
(*.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
1.1s
(log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
255.0ms
(exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
161.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
Compiler

Compiled 5202 to 2575 computations (50.5% saved)

simplify143.0ms (0.5%)

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
048664840
148664840

prune145.0ms (0.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1018109
Fresh6915
Picked101
Done000
Total10817125
Error
3.7b
Counts
125 → 17
Compiler

Compiled 4611 to 637 computations (86.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
0.3b
(*.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
0.6b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
0.7b
(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))

rewrite142.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
3.5b
Rules
23×add-sqr-sqrt_binary64_1464
13×*-un-lft-identity_binary64_1442
add-cube-cbrt_binary64_1477 associate-*l*_binary64_1383
pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
add-log-exp_binary64_1481 associate-*r*_binary64_1382
difference-of-squares_binary64_1411
cancel-sign-sub-inv_binary64_1408
flip3--_binary64_1446 flip--_binary64_1417 times-frac_binary64_1448 distribute-lft-out--_binary64_1394 asin-acos_binary64_1622 pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 unswap-sqr_binary64_1410 associate-*l/_binary64_1385 *-commutative_binary64_1373
diff-log_binary64_1534 sub-neg_binary64_1435 associate--r-_binary64_1381 sin-mult_binary64_1597
Counts
4 → 68
Calls

4 calls:

12.0ms
(*.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
8.0ms
(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
5.0ms
(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
Compiler

Compiled 3362 to 674 computations (80% saved)

series1.0s (3.8%)

Error
3.7b
Counts
4 → 47
Calls

4 calls:

481.0ms
(*.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
229.0ms
(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
154.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
100.0ms
(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
Compiler

Compiled 4952 to 2764 computations (44.2% saved)

simplify96.0ms (0.4%)

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049714860
149714860

prune135.0ms (0.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New1069115
Fresh41216
Picked101
Done000
Total11121132
Error
3.5b
Counts
132 → 21
Compiler

Compiled 4372 to 844 computations (80.7% saved)

regimes4.5s (16.9%)

Accuracy

Total 0.6b remaining (14.7%)

Threshold costs 0.6b (14.7%)

Compiler

Compiled 76004 to 41460 computations (45.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03553
13553

end0.0ms (0%)

sample11.4s (42.4%)

Algorithm
intervals
Results
4.8s5546×body1024valid
835.0ms1476×body512valid
480.0ms242×body2048valid
165.0ms468×body256valid
53.0ms268×body128valid
2.0msbody1024invalid
Compiler

Compiled 7127 to 3886 computations (45.5% saved)

Profiling

Loading profile data...