Details

Time bar (total: 20.7s)

analyze3.6s (17.3%)

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)

sample251.0ms (1.2%)

Algorithm
intervals
Results
177.0ms130×body1024valid
37.0ms50×body512valid
14.0ms68×body128valid
5.0msbody256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify49.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
046355
146355

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1
Compiler

Compiled 66 to 46 computations (30.3% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
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))))))
0.6b
(-.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)))))))

rewrite27.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 associate-*r*_binary64 associate-*l*_binary64
pow-prod-down_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64 sin-mult_binary64 *-commutative_binary64
sub-neg_binary64 asin-acos_binary64 flip3--_binary64 diff-log_binary64 cancel-sign-sub-inv_binary64 flip--_binary64
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))))))
6.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
5.0ms
(-.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))))

series719.0ms (3.5%)

Counts
4 → 12
Calls

4 calls:

340.0ms
(-.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)))))))
261.0ms
(*.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))))))
80.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
38.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify106.0ms (0.5%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
048352133
148352133

prune631.0ms (3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New571370
Fresh000
Picked011
Done000
Total571471

Merged error: 0.1b

Counts
71 → 14
Compiler

Compiled 14504 to 6438 computations (55.6% saved)

localize42.0ms (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
(*.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))))))))
0.4b
(*.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)))))))

rewrite66.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
47×pow1_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
19×pow-prod-down_binary64
12×add-sqr-sqrt_binary64 sin-mult_binary64
10×cbrt-unprod_binary64 prod-exp_binary64
*-un-lft-identity_binary64 add-cube-cbrt_binary64
associate-*r*_binary64 associate-*l*_binary64
add-log-exp_binary64
cos-mult_binary64
pow-prod-up_binary64 pow-sqr_binary64
associate-*r/_binary64 frac-sub_binary64 associate-*l/_binary64 *-commutative_binary64
pow-plus_binary64 unswap-sqr_binary64 sub-div_binary64 frac-times_binary64
sub-neg_binary64 flip3--_binary64 swap-sqr_binary64 diff-log_binary64 cancel-sign-sub-inv_binary64 sqr-cos-a_binary64 difference-of-squares_binary64 flip--_binary64 pow2_binary64 associate--l+_binary64
Counts
4 → 94
Calls

4 calls:

13.0ms
(-.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))))))))
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)))))))
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))))))
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))))))

series1.6s (7.9%)

Counts
4 → 12
Calls

4 calls:

632.0ms
(-.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))))))))
519.0ms
(*.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)))))))
247.0ms
(*.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))))))
240.0ms
(*.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))))))

simplify97.0ms (0.5%)

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049654420
149654420

prune377.0ms (1.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1033106
Fresh21012
Picked011
Done011
Total10515120

Merged error: 0.1b

Counts
120 → 15
Compiler

Compiled 11975 to 2838 computations (76.3% saved)

localize39.0ms (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
(*.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
0.6b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
3.2b
(log.f64 (exp.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

rewrite33.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
15×log-prod_binary64
14×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64 add-cube-cbrt_binary64 sin-sum_binary64
pow1_binary64
add-log-exp_binary64 associate--r+_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64
log-pow_binary64
associate-*r*_binary64 associate-*l*_binary64 exp-prod_binary64
asin-acos_binary64
pow-prod-down_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 cbrt-unprod_binary64 rem-log-exp_binary64 cancel-sign-sub-inv_binary64 exp-diff_binary64 unswap-sqr_binary64 prod-exp_binary64 sin-mult_binary64 log-div_binary64 flip--_binary64 *-commutative_binary64
Counts
4 → 67
Calls

4 calls:

9.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.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 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.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 (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))))

series1.0s (4.9%)

Counts
4 → 12
Calls

4 calls:

438.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
374.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
160.0ms
(log.f64 (exp.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
34.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify127.0ms (0.6%)

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
048393651
148393651

prune228.0ms (1.1%)

Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New77279
Fresh11112
Picked011
Done022
Total781694

Merged error: 0.0b

Counts
94 → 16
Compiler

Compiled 6317 to 1792 computations (71.6% saved)

localize49.0ms (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))))))
0.4b
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (cbrt.f64 (pow.f64 (*.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)))
0.7b
(pow.f64 (*.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)
9.4b
(cbrt.f64 (pow.f64 (*.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))

rewrite47.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
12×cbrt-prod_binary64
10×*-un-lft-identity_binary64 add-cube-cbrt_binary64
pow1_binary64 add-exp-log_binary64
cancel-sign-sub-inv_binary64
add-log-exp_binary64 add-cbrt-cube_binary64
sqr-pow_binary64
pow-unpow_binary64 associate-*r*_binary64 associate-*l*_binary64 unpow-prod-down_binary64 difference-of-squares_binary64
pow-prod-down_binary64 pow-pow_binary64 prod-exp_binary64 pow-exp_binary64
pow-to-exp_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 cbrt-unprod_binary64 pow1/3_binary64 sqr-cos-a_binary64 unswap-sqr_binary64 sin-mult_binary64 flip--_binary64 associate--l+_binary64 *-commutative_binary64
Counts
4 → 72
Calls

4 calls:

12.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (cbrt.f64 (pow.f64 (*.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)))
7.0ms
(*.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))))))
6.0ms
(pow.f64 (*.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)
3.0ms
(cbrt.f64 (pow.f64 (*.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))

series2.2s (10.6%)

Counts
4 → 12
Calls

4 calls:

832.0ms
(pow.f64 (*.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)
604.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (cbrt.f64 (pow.f64 (*.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)))
497.0ms
(cbrt.f64 (pow.f64 (*.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))
252.0ms
(*.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))))))

simplify85.0ms (0.4%)

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049663688
149663688

prune203.0ms (1%)

Pruning

17 alts after pruning (13 fresh and 4 done)

PrunedKeptTotal
New83184
Fresh01212
Picked011
Done033
Total8317100

Merged error: 0.0b

Counts
100 → 17
Compiler

Compiled 6823 to 1352 computations (80.2% saved)

regimes444.0ms (2.1%)

Compiler

Compiled 6298 to 3535 computations (43.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05755
15755

end0.0ms (0%)

sample8.6s (41.7%)

Algorithm
intervals
Results
5.8s3997×body1024valid
1.1s1364×body512valid
447.0ms2115×body128valid
262.0ms516×body256valid
28.0msbody2048valid
Compiler

Compiled 947 to 537 computations (43.3% saved)

Profiling

Loading profile data...