Details

analyze2.9s

Algorithm

Search

True	Other	False	Iter
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
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample460.0ms

Algorithm

intervals

Results

374.0ms	153×	body	1280	valid
51.0ms	65×	body	640	valid
12.0ms	25×	body	320	valid
4.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.3b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite16.0ms

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×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `acos-asin_binary64` `cos-diff_binary64` `sin-mult_binary64` `cos-sum_binary64`

Counts

4 → 54

Calls

4 calls:

4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
8.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify62.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune149.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	49	17	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	17	67

Merged error: 4.0b

Counts

67 → 17

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (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

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`sin-mult_binary64`
1×	`acos-asin_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
46.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
16.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5164	1173

prune157.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	63	13	76
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	73	20	93

Merged error: 3.9b

Counts

93 → 20

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.9b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
5×	`add-log-exp_binary64`
4×	`log-pow_binary64`
3×	`acos-asin_binary64` `associate-r_binary64` `log-prod_binary64` `associate-l_binary64`
2×	`exp-diff_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `log-div_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
29.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
14.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
14.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5198	1366

prune150.0ms

Filtered

44 candidates to 67 candidates (-52.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	6	13	19
Picked	1	0	1
Done	0	0	0
Total	67	20	87

Merged error: 3.8b

Counts

87 → 20

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.9b	(log.f64 (exp.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
1.4b	(acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
4.0b	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`log-pow_binary64` `exp-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `log-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`acos-asin_binary64`
2×	`rem-log-exp_binary64` `exp-diff_binary64`
1×	`rem-exp-log_binary64` `log-div_binary64` `exp-to-pow_binary64`

Counts

4 → 50

Calls

4 calls:

4.0ms	(exp.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
4.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
2.0ms	(acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
3.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(exp.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
14.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
14.0ms	(acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
10.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4989	1338
1	4989	1338

prune45.0ms

Filtered

41 candidates to 62 candidates (-51.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	19	19
Picked	0	1	1
Done	0	0	0
Total	62	20	82

Merged error: 3.8b

Counts

82 → 20

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	30
1	34	30

end0.0ms

sample9.1s

Algorithm

intervals

Results

6.6s	4755×	body	1280	valid
1.6s	2106×	body	640	valid
369.0ms	698×	body	320	valid
103.0ms	304×	body	160	valid
24.0ms	7×	body	2560	valid
24.0ms	130×	body	80	valid
11.0ms	5×	body	1280	invalid
1.0ms	1×	body	320	invalid

Details

analyze2.9s

sample460.0ms

simplify8.0ms

prune4.0ms

localize29.0ms

rewrite16.0ms

series51.0ms

simplify62.0ms

prune149.0ms

localize30.0ms

rewrite17.0ms

series81.0ms

simplify52.0ms

prune157.0ms

localize36.0ms

rewrite14.0ms

series68.0ms

simplify58.0ms

prune150.0ms

localize40.0ms

rewrite13.0ms

series70.0ms

simplify64.0ms

prune45.0ms

regimes1.2s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.1s

Profiling