Details

Time bar (total: 9.5s)

analyze2.1s

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
9.4%90.4%0.2%9
9.4%90.4%0.2%10
10.9%88.9%0.2%11
10.9%88.9%0.2%12
10.9%88.9%0.2%13
10.9%88.9%0.2%14

sample188.0ms

Algorithm
intervals
Results
110.0ms116×body1280valid
44.0ms75×body640valid
9.0ms26×body320valid
4.0ms16×body160valid
3.0ms23×body80valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
027020
127020

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.3b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.5b
(cos.f64 (-.f64 lambda1 lambda2))
3.7b
(sin.f64 (-.f64 lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp_binary64
4×*-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64
3×cos-diff_binary64
2×sub-neg_binary64 associate-+r+_binary64
1×flip3-+_binary64 sin-diff_binary64 sin-sum_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 cos-sum_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 38
Calls
4 calls:
1.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

series45.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
26.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
5.0ms
(sin.f64 (-.f64 lambda1 lambda2))

simplify55.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04947591
14947591

prune125.0ms

Filtered
42 candidates to 50 candidates (-19.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New341650
Fresh000
Picked101
Done000
Total351651

Merged error: 1.0b

Counts
51 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.5b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64
6×*-un-lft-identity_binary64 add-log-exp_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×associate-*r*_binary64 associate-*l*_binary64 cos-diff_binary64
2×associate-+r+_binary64
1×pow-prod-down_binary64 flip3-+_binary64 sub-neg_binary64 cbrt-unprod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 cos-sum_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 47
Calls
4 calls:
5.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
1.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
11.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
27.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

simplify79.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
05109730

prune106.0ms

Filtered
46 candidates to 59 candidates (-28.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New58159
Fresh21315
Picked101
Done000
Total611475

Merged error: 0.1b

Counts
75 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
8×*-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
6×add-log-exp_binary64 associate-*r*_binary64 associate-*l*_binary64
2×pow-prod-down_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64 associate-+r+_binary64 *-commutative_binary64
1×flip3-+_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 sin-mult_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 57
Calls
4 calls:
6.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
1.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
5.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series90.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
15.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
56.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
04961985
14961985

prune113.0ms

Filtered
50 candidates to 69 candidates (-38.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New65469
Fresh21113
Picked101
Done000
Total681583

Merged error: 0.0b

Counts
83 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
0.6b
(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
3.5b
(cos.f64 (-.f64 lambda1 lambda2))
3.7b
(sin.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity_binary64 add-log-exp_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
5×pow1_binary64
4×log-prod_binary64 log-pow_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×exp-prod_binary64
2×sub-neg_binary64
1×flip3-+_binary64 sin-diff_binary64 rem-log-exp_binary64 sin-sum_binary64 cos-diff_binary64 exp-sum_binary64 cos-sum_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 45
Calls
4 calls:
5.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
5.0ms
(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

series61.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
26.0ms
(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
5.0ms
(sin.f64 (-.f64 lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
04892602
14892602

prune54.0ms

Filtered
44 candidates to 57 candidates (-29.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New55257
Fresh11314
Picked101
Done000
Total571572

Merged error: 0.0b

Counts
72 → 15

regimes600.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03325
13325

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.3s3455×body1280valid
1.3s2434×body640valid
380.0ms995×body320valid
105.0ms401×body160valid
80.0ms715×body80valid

Profiling

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