Details

Time bar (total: 17.2s)

analyze3.6s (21%)

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)

sample230.0ms (1.3%)

Algorithm
intervals
Results
154.0ms117×body1024valid
36.0ms41×body512valid
16.0ms82×body128valid
7.0ms16×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify212.0ms (1.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
046355
146355

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.1b

Counts
2 → 1
Compiler

Compiled 66 to 46 computations (30.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))))
0.3b
(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)))))))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_1446
add-cube-cbrt_binary64_1457 add-cbrt-cube_binary64_1458 pow1_binary64_1483 add-exp-log_binary64_1460 *-un-lft-identity_binary64_1425
associate-*l*_binary64_1368 associate-*r*_binary64_1367 add-log-exp_binary64_1461
unswap-sqr_binary64_1393 prod-exp_binary64_1471 cbrt-unprod_binary64_1455 sin-mult_binary64_1577 *-commutative_binary64_1358 pow-prod-down_binary64_1493
flip--_binary64_1400 diff-log_binary64_1514 sub-neg_binary64_1418 asin-acos_binary64_1602 flip3--_binary64_1429
Counts
4 → 57
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))))))
6.0ms
(*.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))))

series674.0ms (3.9%)

Counts
4 → 12
Calls

4 calls:

326.0ms
(-.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)))))))
238.0ms
(*.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))))))
73.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
36.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify106.0ms (0.6%)

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
048572099
148572099

prune130.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New60969
Fresh000
Picked101
Done000
Total61970

Merged error: 0.0b

Counts
70 → 9
Compiler

Compiled 3243 to 589 computations (81.8% saved)

localize35.0ms (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))))
0.4b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3)))))
0.5b
(pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3)
10.2b
(cbrt.f64 (pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3))

rewrite22.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod_binary64_1453
10×add-cube-cbrt_binary64_1457 add-sqr-sqrt_binary64_1446 *-un-lft-identity_binary64_1425
unpow-prod-down_binary64_1501 cube-prod_binary64_1450 add-log-exp_binary64_1461
add-cbrt-cube_binary64_1458 pow1_binary64_1483 add-exp-log_binary64_1460
pow-unpow_binary64_1499
unpow3_binary64_1488 cube-mult_binary64_1452 sqr-pow_binary64_1397
flip--_binary64_1400 diff-log_binary64_1514 pow-pow_binary64_1494 pow-to-exp_binary64_1491 sub-neg_binary64_1418 asin-acos_binary64_1602 pow-exp_binary64_1490 rem-cube-cbrt_binary64_1447 pow1/3_binary64_1504 flip3--_binary64_1429 rem-cbrt-cube_binary64_1448
Counts
4 → 63
Calls

4 calls:

4.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3)))))
4.0ms
(pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3)
3.0ms
(cbrt.f64 (pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3))
2.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series623.0ms (3.6%)

Counts
4 → 12
Calls

4 calls:

338.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3)))))
211.0ms
(pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3)
38.0ms
(cbrt.f64 (pow.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))) 3))
35.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify98.0ms (0.6%)

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
048832726
148832726

prune125.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh088
Picked011
Done000
Total75984

Merged error: 0.0b

Counts
84 → 9
Compiler

Compiled 3682 to 801 computations (78.2% saved)

localize40.0ms (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
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b
(*.f64 (*.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)))))) (*.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)))))))
0.4b
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.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)))))) (*.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))))))))

rewrite47.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
43×pow1_binary64_1483
17×pow-prod-down_binary64_1493
16×add-cbrt-cube_binary64_1458 add-exp-log_binary64_1460
10×sin-mult_binary64_1577
prod-exp_binary64_1471 cbrt-unprod_binary64_1455
add-log-exp_binary64_1461
cos-mult_binary64_1576
add-cube-cbrt_binary64_1457 add-sqr-sqrt_binary64_1446 pow-sqr_binary64_1398 *-un-lft-identity_binary64_1425 pow-prod-up_binary64_1492
associate-*r/_binary64_1369 frac-sub_binary64_1434 associate-*l/_binary64_1370
pow-plus_binary64_1485 asin-acos_binary64_1602 sub-div_binary64_1432 frac-times_binary64_1435
flip--_binary64_1400 diff-log_binary64_1514 associate-*l*_binary64_1368 sub-neg_binary64_1418 pow2_binary64_1503 associate--l+_binary64_1364 associate-*r*_binary64_1367 difference-of-squares_binary64_1394 swap-sqr_binary64_1392 sqr-cos-a_binary64_1571 flip3--_binary64_1429 *-commutative_binary64_1358
Counts
4 → 71
Calls

4 calls:

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

series1.2s (7%)

Counts
4 → 12
Calls

4 calls:

626.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.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)))))) (*.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))))))))
504.0ms
(*.f64 (*.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)))))) (*.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)))))))
37.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
36.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify85.0ms (0.5%)

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
050073409

prune182.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh167
Picked011
Done011
Total83992

Merged error: 0.0b

Counts
92 → 9
Compiler

Compiled 6693 to 845 computations (87.4% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))))))
0.3b
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b
(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (*.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)))))))))
2.9b
(log.f64 (exp.f64 (*.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))))))))

rewrite29.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_1446
11×*-un-lft-identity_binary64_1425
add-cube-cbrt_binary64_1457 pow1_binary64_1483
add-cbrt-cube_binary64_1458 log-prod_binary64_1508 add-exp-log_binary64_1460 add-log-exp_binary64_1461
log-pow_binary64_1511
associate-*l*_binary64_1368 associate-*r*_binary64_1367 associate--r+_binary64_1363
distribute-lft-out--_binary64_1379
flip--_binary64_1400 diff-log_binary64_1514 unswap-sqr_binary64_1393 prod-exp_binary64_1471 exp-to-pow_binary64_1484 sub-neg_binary64_1418 cbrt-unprod_binary64_1455 asin-acos_binary64_1602 exp-prod_binary64_1474 difference-of-squares_binary64_1394 rem-log-exp_binary64_1463 flip3--_binary64_1429 sin-mult_binary64_1577 *-commutative_binary64_1358 pow-prod-down_binary64_1493
Counts
4 → 58
Calls

4 calls:

10.0ms
(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (*.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))))))
3.0ms
(log.f64 (exp.f64 (*.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))))

series1.2s (7%)

Counts
4 → 12
Calls

4 calls:

510.0ms
(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (*.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)))))))))
432.0ms
(log.f64 (exp.f64 (*.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))))))))
226.0ms
(*.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))))))
35.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify112.0ms (0.7%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
049082712
149082712

prune95.0ms (0.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New69170
Fresh156
Picked011
Done022
Total70979

Merged error: 0.0b

Counts
79 → 9
Compiler

Compiled 3062 to 419 computations (86.3% saved)

regimes182.0ms (1.1%)

Compiler

Compiled 2385 to 1285 computations (46.1% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06060
16060

end0.0ms (0%)

sample8.0s (46.8%)

Algorithm
intervals
Results
5.4s3966×body1024valid
1.0s1279×body512valid
450.0ms2193×body128valid
275.0ms551×body256valid
47.0ms11×body2048valid
Compiler

Compiled 545 to 302 computations (44.6% saved)

Profiling

Loading profile data...