Details

Time bar (total: 52.9s)

analyze5.2s (9.8%)

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)

sample438.0ms (0.8%)

Algorithm
intervals
Results
293.0ms183×body1024valid
49.0ms50×body512valid
42.0ms10×body2048valid
4.0msbody256valid
2.0msbody128valid
Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify195.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
09631
19631

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
19.0b
Counts
2 → 1
Compiler

Compiled 38 to 34 computations (10.5% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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)
0.3b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.6b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite181.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
1.7b
Rules
13×add-sqr-sqrt_binary64_1464
add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
associate-*l*_binary64_1383 associate-*r*_binary64_1382
cos-sum_binary64_1576 add-log-exp_binary64_1481
cancel-sign-sub-inv_binary64_1408
pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 unswap-sqr_binary64_1410 *-commutative_binary64_1373
cos-diff_binary64_1579 sub-neg_binary64_1435 acos-asin_binary64_1623 sin-mult_binary64_1597
Counts
4 → 57
Calls

4 calls:

11.0ms
(cos.f64 (-.f64 lambda1 lambda2))
10.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
7.0ms
(*.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)
2.0ms
(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 1667 to 309 computations (81.5% saved)

series963.0ms (1.8%)

Error
18.2b
Counts
4 → 47
Calls

4 calls:

439.0ms
(*.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)
184.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
165.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
101.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 2726 to 1652 computations (39.4% saved)

simplify159.0ms (0.3%)

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (114.0ms)

IterNodesCost
050452315

prune227.0ms (0.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New8915104
Fresh000
Picked101
Done000
Total9015105
Error
1.7b
Counts
105 → 15
Compiler

Compiled 2932 to 665 computations (77.3% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite246.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
1.6b
Rules
13×pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478 add-sqr-sqrt_binary64_1464
add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442 associate-*r*_binary64_1382
associate-*l*_binary64_1383
cos-mult_binary64_1596
pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475
add-log-exp_binary64_1481
*-commutative_binary64_1373 sin-mult_binary64_1597 frac-times_binary64_1452 associate-*r/_binary64_1384
unswap-sqr_binary64_1410 frac-add_binary64_1450 flip3-+_binary64_1445 flip-+_binary64_1416
acos-asin_binary64_1623 distribute-rgt-in_binary64_1392 distribute-lft-in_binary64_1391 associate-*l/_binary64_1385
Counts
4 → 72
Calls

4 calls:

21.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
9.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
7.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
2.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 2888 to 416 computations (85.6% saved)

series2.4s (4.6%)

Error
1.7b
Counts
4 → 57
Calls

4 calls:

1.2s
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
665.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
265.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
190.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
Compiler

Compiled 5252 to 2690 computations (48.8% saved)

simplify174.0ms (0.3%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (94.0ms)

IterNodesCost
051294512

prune299.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11613129
Fresh13114
Picked101
Done000
Total13014144
Error
1.6b
Counts
144 → 14
Compiler

Compiled 4893 to 891 computations (81.8% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
0.3b
(log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
0.3b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
0.4b
(exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

rewrite180.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
1.5b
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
rem-exp-log_binary64_1482 log-div_binary64_1529 rem-log-exp_binary64_1483 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:

11.0ms
(*.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
8.0ms
(log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
4.0ms
(exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
2.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
Compiler

Compiled 2764 to 221 computations (92% saved)

series5.7s (10.8%)

Error
1.6b
Counts
4 → 51
Calls

4 calls:

2.9s
(*.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
1.9s
(log.f64 (exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
482.0ms
(exp.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
291.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
Compiler

Compiled 5202 to 2575 computations (50.5% saved)

simplify277.0ms (0.5%)

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (197.0ms)

IterNodesCost
048664840
148664840

prune238.0ms (0.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1054109
Fresh11213
Picked011
Done000
Total10617123
Error
1.5b
Counts
123 → 17
Compiler

Compiled 4551 to 621 computations (86.4% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b
(*.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
0.4b
(-.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

rewrite250.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
1.5b
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:

20.0ms
(*.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
16.0ms
(-.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
13.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
2.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
Compiler

Compiled 3362 to 617 computations (81.6% saved)

series1.9s (3.5%)

Error
1.5b
Counts
4 → 48
Calls

4 calls:

859.0ms
(*.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
425.0ms
(-.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
299.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
183.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
Compiler

Compiled 5008 to 2777 computations (44.5% saved)

simplify179.0ms (0.3%)

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
052244893

prune241.0ms (0.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New1106116
Fresh31215
Picked011
Done101
Total11419133
Error
1.5b
Counts
133 → 19
Compiler

Compiled 4419 to 803 computations (81.8% saved)

regimes9.8s (18.6%)

Accuracy

Total 0.6b remaining (16%)

Threshold costs 0.6b (16%)

Compiler

Compiled 70352 to 40246 computations (42.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03143
13143

end0.0ms (0%)

sample23.4s (44.3%)

Algorithm
intervals
Results
8.7s5467×body1024valid
1.5s1458×body512valid
997.0ms272×body2048valid
338.0ms514×body256valid
90.0ms289×body128valid
1.0msbody1024invalid
1.0msbody512invalid
Compiler

Compiled 6623 to 3785 computations (42.9% saved)

Profiling

Loading profile data...