Details

Time bar (total: 10.5s)

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

sample171.0ms

Algorithm
intervals
Results
112.0ms140×body1024valid
24.0ms58×body512valid
12.0ms7×body2048valid
7.0ms28×body256valid
3.0ms23×body128valid

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
027132
127132

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

localize21.0ms

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)))))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.1b
(sin.f64 (-.f64 lambda1 lambda2))
5.1b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite18.0ms

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))))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))

series354.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
216.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
36.0ms
(sin.f64 (-.f64 lambda1 lambda2))
33.0ms
(cos.f64 (-.f64 lambda1 lambda2))

simplify63.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
04909950
14909950

prune73.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New381250
Fresh000
Picked101
Done000
Total391251

Merged error: 0.4b

Counts
51 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
5.1b
(sin.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms

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
2×associate-+r+_binary64
1×pow-prod-down_binary64 flip3-+_binary64 sin-diff_binary64 sub-neg_binary64 cbrt-unprod_binary64 sin-sum_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 sin-mult_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 48
Calls
4 calls:
5.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 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)))))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

series657.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
97.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
448.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
35.0ms
(sin.f64 (-.f64 lambda1 lambda2))

simplify114.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
049481388
149481388

prune73.0ms

Filtered
47 candidates to 60 candidates (-27.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New59160
Fresh11011
Picked101
Done000
Total611172

Merged error: 0.1b

Counts
72 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b
(*.f64 (sin.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))))))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite23.0ms

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 sin-cos-mult_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 58
Calls
4 calls:
5.0ms
(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
5.0ms
(*.f64 (sin.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)))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
64.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
115.0ms
(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))))))
441.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050301640

prune84.0ms

Filtered
52 candidates to 70 candidates (-34.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New69170
Fresh1910
Picked011
Done000
Total701181

Merged error: 0.1b

Counts
81 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
5.1b
(sin.f64 (-.f64 lambda1 lambda2))
5.1b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod_binary64
8×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 associate-+r+_binary64
6×add-log-exp_binary64
5×pow1_binary64
4×log-pow_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 cos-diff_binary64
3×sub-neg_binary64 exp-sum_binary64 exp-prod_binary64
2×cos-sum_binary64
1×flip3-+_binary64 sin-diff_binary64 rem-log-exp_binary64 sin-sum_binary64 exp-diff_binary64 log-div_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 54
Calls
4 calls:
6.0ms
(log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))))
8.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))

series460.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))))
308.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
31.0ms
(sin.f64 (-.f64 lambda1 lambda2))
29.0ms
(cos.f64 (-.f64 lambda1 lambda2))

simplify88.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
04889951
14889951

prune55.0ms

Filtered
53 candidates to 66 candidates (-24.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh099
Picked011
Done011
Total661177

Merged error: 0.1b

Counts
77 → 11

regimes181.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05756
15756

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.5s4452×body1024valid
813.0ms1772×body512valid
198.0ms719×body256valid
184.0ms103×body2048valid
133.0ms954×body128valid

Profiling

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