Details

Time bar (total: 32.0s)

analyze3.4s (10.6%)

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)

sample273.0ms (0.9%)

Algorithm
intervals
Results
192.0ms185×body1024valid
26.0ms11×body2048valid
24.0ms37×body512valid
4.0ms11×body256valid
3.0ms12×body128valid
1.0msbody1024invalid
Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify124.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
09631
19631

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
18.1b
Counts
2 → 1
Compiler

Compiled 38 to 34 computations (10.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
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)
1.6b
(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))

rewrite103.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
4.2b
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 unswap-sqr_binary64_1410 distribute-rgt-in_binary64_1392 distribute-lft-in_binary64_1391 cos-mult_binary64_1596 associate-*l/_binary64_1385
Counts
4 → 59
Calls

4 calls:

7.0ms
(*.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)

series1.2s (3.6%)

Error
17.3b
Counts
4 → 58
Calls

4 calls:

511.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
391.0ms
(*.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)
122.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
65.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 3539 to 2037 computations (42.4% saved)

simplify121.0ms (0.4%)

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
049702837
149702837

prune174.0ms (0.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10314117
Fresh000
Picked101
Done000
Total10414118
Error
4.2b
Counts
118 → 14
Compiler

Compiled 3239 to 684 computations (78.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.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)
1.6b
(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))))))

rewrite156.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
4.1b
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
*-commutative_binary64_1373 sin-mult_binary64_1597
unswap-sqr_binary64_1410 cos-mult_binary64_1596
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)))
8.0ms
(*.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)

series1.5s (4.7%)

Error
4.2b
Counts
4 → 50
Calls

4 calls:

588.0ms
(*.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)
524.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
181.0ms
(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))))))
150.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 4874 to 2394 computations (50.9% saved)

simplify108.0ms (0.3%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049433489
149433489

prune199.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11010120
Fresh9413
Picked101
Done000
Total12014134
Error
4.1b
Counts
134 → 14
Compiler

Compiled 4717 to 823 computations (82.6% saved)

localize33.0ms (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 (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))))))))
0.9b
(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)))))))))
1.6b
(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)))))))

rewrite133.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
4.1b
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)
3.0ms
(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)

series3.7s (11.5%)

Error
4.1b
Counts
4 → 51
Calls

4 calls:

1.8s
(*.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)
1.3s
(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)))))))))
341.0ms
(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))))))))
219.0ms
(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)

simplify198.0ms (0.6%)

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (133.0ms)

IterNodesCost
048664840
148664840

prune180.0ms (0.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1045109
Fresh01313
Picked101
Done000
Total10518123
Error
4.1b
Counts
123 → 18
Compiler

Compiled 4635 to 655 computations (85.9% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))
0.3b
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)
1.6b
(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)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)))))
26.9b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))

rewrite163.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
4.1b
Rules
23×pow1_binary64_1503 add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
12×pow-prod-down_binary64_1513 prod-exp_binary64_1491 cbrt-unprod_binary64_1475
cbrt-prod_binary64_1473
add-cube-cbrt_binary64_1477 add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442
associate-*r/_binary64_1384
add-log-exp_binary64_1481 pow-pow_binary64_1514 pow-exp_binary64_1510 rem-cube-cbrt_binary64_1465
cos-mult_binary64_1596 pow-unpow_binary64_1519 associate-*l*_binary64_1383
cube-div_binary64_1471 unpow-prod-down_binary64_1521 unpow3_binary64_1508 cube-mult_binary64_1472 cube-prod_binary64_1470 sqr-pow_binary64_1414
pow1/3_binary64_1524 cbrt-div_binary64_1474 rem-cbrt-cube_binary64_1466 acos-asin_binary64_1623 pow-to-exp_binary64_1511 associate-*r*_binary64_1382 *-commutative_binary64_1373
Counts
4 → 77
Calls

4 calls:

10.0ms
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)
10.0ms
(*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))
4.0ms
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))
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)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)))))
Compiler

Compiled 3574 to 811 computations (77.3% saved)

series2.3s (7.2%)

Error
4.1b
Counts
4 → 60
Calls

4 calls:

970.0ms
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)
532.0ms
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))
517.0ms
(*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))
181.0ms
(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)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)))))
Compiler

Compiled 6569 to 3650 computations (44.4% saved)

simplify107.0ms (0.3%)

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
054233470

prune178.0ms (0.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New1361137
Fresh11617
Picked011
Done000
Total13718155
Error
4.1b
Counts
155 → 18
Compiler

Compiled 5271 to 1072 computations (79.7% saved)

regimes4.6s (14.2%)

Accuracy

Total 0.4b remaining (10.7%)

Threshold costs 0.4b (10.7%)

Compiler

Compiled 57468 to 32562 computations (43.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03347
13347

end0.0ms (0%)

sample13.1s (40.9%)

Algorithm
intervals
Results
6.1s5531×body1024valid
938.0ms1441×body512valid
542.0ms232×body2048valid
218.0ms509×body256valid
58.0ms287×body128valid
3.0msbody1024invalid
1.0msbody512invalid
0.0msbody256invalid
Compiler

Compiled 5306 to 3020 computations (43.1% saved)

Profiling

Loading profile data...