Details

Time bar (total: 18.6s)

analyze3.8s

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

sample270.0ms

Algorithm
intervals
Results
154.0ms88×body1280valid
67.0ms69×body640valid
16.0ms26×body320valid
12.0ms64×body80valid
4.0msbody160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
046455
146455

prune4.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.1b

Counts
2 → 1

localize35.0ms

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))))
0.5b
(-.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)))))))

rewrite18.0ms

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 flip--_binary64
Counts
4 → 57
Calls
4 calls:
5.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
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)))))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
160.0ms
(*.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))))))
28.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
216.0ms
(-.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)))))))

simplify94.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
050602029

prune112.0ms

Filtered
55 candidates to 69 candidates (-25.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New62769
Fresh000
Picked101
Done000
Total63770

Merged error: 0.0b

Counts
70 → 7

localize33.0ms

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))))
0.5b
(-.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)))))))))
3.6b
(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))))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
pow1_binary64 add-cube-cbrt_binary64
add-log-exp_binary64 log-prod_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
log-pow_binary64
associate--r+_binary64 associate-*r*_binary64 associate-*l*_binary64
distribute-lft-out--_binary64
pow-prod-down_binary64 sub-neg_binary64 asin-acos_binary64 flip3--_binary64 diff-log_binary64 cbrt-unprod_binary64 rem-log-exp_binary64 unswap-sqr_binary64 prod-exp_binary64 difference-of-squares_binary64 sin-mult_binary64 flip--_binary64 exp-to-pow_binary64 exp-prod_binary64 *-commutative_binary64
Counts
4 → 58
Calls
4 calls:
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))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
7.0ms
(-.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)))))))))
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))))))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(*.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))))))
23.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
217.0ms
(-.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)))))))))
165.0ms
(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))))))))

simplify98.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
050542611

prune95.0ms

Filtered
58 candidates to 70 candidates (-20.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New69170
Fresh066
Picked011
Done000
Total69877

Merged error: 0.0b

Counts
77 → 8

localize41.0ms

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 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (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 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2)))) (+.f64 (cos.f64 delta) (*.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 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (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 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
times-frac_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64
associate-/r*_binary64 associate-/l*_binary64
associate-/l/_binary64 asin-acos_binary64 flip3--_binary64 associate-/r/_binary64 flip--_binary64
flip3-+_binary64 sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 sqr-cos-a_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64 associate--l+_binary64
Counts
4 → 60
Calls
4 calls:
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))))
15.0ms
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (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 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2)))) (+.f64 (cos.f64 delta) (*.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))))))))
8.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (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 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2))))

series2.6s

Counts
4 → 12
Calls
4 calls:
25.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
25.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
1.7s
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (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 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2)))) (+.f64 (cos.f64 delta) (*.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))))))))
836.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (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 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2))))

simplify106.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050226910

prune176.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New70272
Fresh156
Picked101
Done011
Total72880

Merged error: 0.0b

Counts
80 → 8

localize34.0ms

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
(pow.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)))))) 3)
0.5b
(-.f64 (cos.f64 delta) (cbrt.f64 (pow.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)))))) 3)))
17.0b
(cbrt.f64 (pow.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)))))) 3))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
10×cbrt-prod_binary64
*-un-lft-identity_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 add-cube-cbrt_binary64
pow-unpow_binary64 sqr-pow_binary64 difference-of-squares_binary64
pow-pow_binary64 cube-div_binary64 rem-cube-cbrt_binary64 unpow-prod-down_binary64 sin-mult_binary64 cube-prod_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64
cbrt-div_binary64 pow-to-exp_binary64 pow-prod-down_binary64 sub-neg_binary64 rem-cbrt-cube_binary64 asin-acos_binary64 flip3--_binary64 diff-log_binary64 cbrt-unprod_binary64 pow1/3_binary64 prod-exp_binary64 distribute-lft-out--_binary64 flip--_binary64
Counts
4 → 64
Calls
4 calls:
1.0ms
(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 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
6.0ms
(-.f64 (cos.f64 delta) (cbrt.f64 (pow.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)))))) 3)))
3.0ms
(cbrt.f64 (pow.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)))))) 3))

series752.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
355.0ms
(pow.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)))))) 3)
211.0ms
(-.f64 (cos.f64 delta) (cbrt.f64 (pow.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)))))) 3)))
160.0ms
(cbrt.f64 (pow.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)))))) 3))

simplify103.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
049492996
149492996

prune83.0ms

Filtered
57 candidates to 76 candidates (-33.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New76076
Fresh066
Picked011
Done011
Total76884

Merged error: 0.0b

Counts
84 → 8

regimes152.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04359
14359

end0.0ms

sample8.9s

Algorithm
intervals
Results
5.6s3192×body1280valid
1.9s1843×body640valid
465.0ms696×body320valid
396.0ms1942×body80valid
145.0ms327×body160valid

Profiling

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