Details

Time bar (total: 21.7s)

analyze3.7s (16.9%)

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)

sample233.0ms (1.1%)

Algorithm
intervals
Results
160.0ms134×body1024valid
26.0ms38×body512valid
20.0ms71×body128valid
6.0ms13×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify136.0ms (0.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
046355
146355

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.1b
Counts
2 → 1
Compiler

Compiled 66 to 46 computations (30.3% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
0.2b
(*.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))))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b
(-.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)))))))

rewrite124.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
12×add-sqr-sqrt_binary64_1464
pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
add-log-exp_binary64_1481 associate-*l*_binary64_1383 associate-*r*_binary64_1382
sin-mult_binary64_1597 pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 unswap-sqr_binary64_1410 *-commutative_binary64_1373
diff-log_binary64_1534 flip3--_binary64_1446 sub-neg_binary64_1435 flip--_binary64_1417 cancel-sign-sub-inv_binary64_1408 asin-acos_binary64_1622
Counts
4 → 58
Calls

4 calls:

6.0ms
(*.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))))))
5.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
4.0ms
(-.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)))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
Compiler

Compiled 2653 to 371 computations (86% saved)

series1.0s (4.8%)

Error
0.1b
Counts
4 → 41
Calls

4 calls:

443.0ms
(-.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)))))))
346.0ms
(*.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))))))
115.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
83.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
Compiler

Compiled 4081 to 1941 computations (52.4% saved)

simplify90.0ms (0.4%)

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
048622949
148622949

prune155.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91899
Fresh000
Picked101
Done000
Total928100
Error
0.0b
Counts
100 → 8
Compiler

Compiled 4264 to 647 computations (84.8% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite209.0ms (1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
43×pow1_binary64_1503
17×pow-prod-down_binary64_1513
16×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
10×sin-mult_binary64_1597
prod-exp_binary64_1491 cbrt-unprod_binary64_1475
add-log-exp_binary64_1481
cos-mult_binary64_1596
add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442 pow-prod-up_binary64_1512 pow-sqr_binary64_1415
frac-sub_binary64_1451 associate-*l/_binary64_1385 associate-*r/_binary64_1384
frac-times_binary64_1452 sub-div_binary64_1449 pow-plus_binary64_1505 asin-acos_binary64_1622
diff-log_binary64_1534 flip3--_binary64_1446 sub-neg_binary64_1435 flip--_binary64_1417 difference-of-squares_binary64_1411 cancel-sign-sub-inv_binary64_1408 sqr-cos-a_binary64_1591 associate--l+_binary64_1379 pow2_binary64_1523 swap-sqr_binary64_1409 associate-*l*_binary64_1383 associate-*r*_binary64_1382 *-commutative_binary64_1373
Counts
4 → 72
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
10.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 6994 to 552 computations (92.1% saved)

series1.6s (7.6%)

Error
0.0b
Counts
4 → 41
Calls

4 calls:

782.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
603.0ms
(*.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
96.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
95.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 8306 to 2561 computations (69.2% saved)

simplify97.0ms (0.4%)

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049714409
149714409

prune223.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1112113
Fresh077
Picked101
Done000
Total1129121
Error
0.0b
Counts
121 → 9
Compiler

Compiled 8923 to 1065 computations (88.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
0.3b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
3.3b
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))

rewrite192.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
20×sin-sum_binary64_1575
18×add-sqr-sqrt_binary64_1464
16×cancel-sign-sub-inv_binary64_1408
13×*-un-lft-identity_binary64_1442
11×add-cube-cbrt_binary64_1477
10×distribute-rgt-in_binary64_1392 associate--r+_binary64_1378 distribute-lft-in_binary64_1391
add-log-exp_binary64_1481
pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478 sub-neg_binary64_1435 acos-asin_binary64_1623
associate--r-_binary64_1381
associate-*l*_binary64_1383 associate-*r*_binary64_1382
diff-log_binary64_1534 flip3--_binary64_1446 flip--_binary64_1417 difference-of-squares_binary64_1411
times-frac_binary64_1448 distribute-lft-out--_binary64_1394 sin-mult_binary64_1597 pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 unswap-sqr_binary64_1410 *-commutative_binary64_1373
Counts
4 → 77
Calls

4 calls:

14.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
9.0ms
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
6.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
1.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 4926 to 1122 computations (77.2% saved)

series1.2s (5.7%)

Error
0.0b
Counts
4 → 41
Calls

4 calls:

538.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
438.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
129.0ms
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
81.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 4571 to 2538 computations (44.5% saved)

simplify136.0ms (0.6%)

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
048644503
148644503

prune183.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1171118
Fresh088
Picked101
Done000
Total1189127
Error
0.0b
Counts
127 → 9
Compiler

Compiled 5780 to 1279 computations (77.9% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b
(pow.f64 (cos.f64 delta) 3)
0.4b
(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)

rewrite185.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442 pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
pow-unpow_binary64_1519
unpow-prod-down_binary64_1521 add-log-exp_binary64_1481 cube-prod_binary64_1470
pow-pow_binary64_1514 pow-exp_binary64_1510 rem-cube-cbrt_binary64_1465
pow-to-exp_binary64_1511 unpow3_binary64_1508 cube-mult_binary64_1472 sqr-pow_binary64_1414 asin-acos_binary64_1622
pow-prod-down_binary64_1513 prod-exp_binary64_1491 sin-mult_binary64_1597 cube-div_binary64_1471 cbrt-unprod_binary64_1475
Counts
4 → 62
Calls

4 calls:

6.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
4.0ms
(pow.f64 (cos.f64 delta) 3)
2.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
2.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 6003 to 772 computations (87.1% saved)

series1.1s (5.2%)

Error
0.0b
Counts
4 → 34
Calls

4 calls:

771.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
107.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
104.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
59.0ms
(pow.f64 (cos.f64 delta) 3)
Compiler

Compiled 8543 to 2547 computations (70.2% saved)

simplify69.0ms (0.3%)

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049522299
149522299

prune225.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New93396
Fresh178
Picked101
Done000
Total9510105
Error
0.0b
Counts
105 → 10
Compiler

Compiled 8725 to 1026 computations (88.2% saved)

regimes1.3s (6.1%)

Accuracy

Total 0.1b remaining (62.8%)

Threshold costs 0.1b (62.8%)

Compiler

Compiled 24694 to 10787 computations (56.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
053178
153178

end0.0ms (0%)

sample9.2s (42.6%)

Algorithm
intervals
Results
5.0s3879×body1024valid
995.0ms1311×body512valid
496.0ms2265×body128valid
261.0ms537×body256valid
21.0msbody2048valid
Compiler

Compiled 3648 to 1583 computations (56.6% saved)

Profiling

Loading profile data...