Details

analyze3.1s

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

sample282.0ms

Algorithm

intervals

Results

198.0ms	145×	body	1280	valid
44.0ms	58×	body	640	valid
17.0ms	34×	body	320	valid
4.0ms	11×	body	160	valid
1.0ms	8×	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

prune10.0ms

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: 14.6b

Counts

2 → 1

localize24.0ms

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))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.5b	(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))

series50.0ms

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))

simplify65.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune91.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	54	12	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	12	67

Merged error: 4.1b

Counts

67 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.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))
1.0b	(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))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
6×	`cos-mult_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `sin-mult_binary64` `frac-times_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64`
1×	`acos-asin_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.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	(.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))))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
49.0ms	(.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))
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))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5064	1677

prune110.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	71	13	84
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	80	16	96

Merged error: 4.0b

Counts

96 → 16

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(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)))))))
0.7b	(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))))))))
1.0b	(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))))))

rewrite13.0ms

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:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
2.0ms	(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))))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
33.0ms	(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)))))))
15.0ms	(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))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5198	1366

prune98.0ms

Filtered

44 candidates to 67 candidates (-52.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	66	17	83

Merged error: 3.9b

Counts

83 → 17

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.3b	(/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1_binary64`
59×	`cos-mult_binary64`
42×	`sin-mult_binary64`
38×	`associate-*r/_binary64`
37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
34×	`pow-prod-down_binary64` `frac-times_binary64`
33×	`associate-/l/_binary64`
23×	`associate-*l/_binary64`
19×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-sub_binary64`
11×	`sub-div_binary64`
8×	`pow-prod-up_binary64` `pow-sqr_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `pow-plus_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `times-frac_binary64` `div-exp_binary64` `flip--_binary64`
2×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`acos-asin_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 142

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
30.0ms	(/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
169.0ms	(/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
14.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
41.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5463	2796

prune89.0ms

Filtered

95 candidates to 154 candidates (-62.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	154	17	171

Merged error: 3.9b

Counts

171 → 17

regimes823.0ms

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	50
1	69	50

end0.0ms

sample9.1s

Algorithm

intervals

Results

6.4s	4758×	body	1280	valid
1.7s	2064×	body	640	valid
385.0ms	747×	body	320	valid
110.0ms	290×	body	160	valid
34.0ms	9×	body	2560	valid
30.0ms	132×	body	80	valid
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	320	invalid

Details

analyze3.1s

sample282.0ms

simplify8.0ms

prune10.0ms

localize24.0ms

rewrite16.0ms

series50.0ms

simplify65.0ms

prune91.0ms

localize33.0ms

rewrite23.0ms

series123.0ms

simplify55.0ms

prune110.0ms

localize37.0ms

rewrite13.0ms

series70.0ms

simplify57.0ms

prune98.0ms

localize36.0ms

rewrite60.0ms

series238.0ms

simplify45.0ms

prune89.0ms

regimes823.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.1s

Profiling