Details

analyze3.5s

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

sample361.0ms

Algorithm

intervals

Results

255.0ms	151×	body	1280	valid
58.0ms	69×	body	640	valid
13.0ms	24×	body	320	valid
4.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify149.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune9.0ms

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: 15.3b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.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)
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_559`
8×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
6×	`associate-l_binary64_634` `associate-r_binary64_633`
4×	`add-log-exp_binary64_539`
2×	`unswap-sqr_binary64_602` `cbrt-unprod_binary64_543` `*-commutative_binary64_642` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
1×	`cos-sum_binary64_424` `sub-neg_binary64_578` `sin-mult_binary64_445` `acos-asin_binary64_408` `cos-diff_binary64_427`

Counts

4 → 54

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.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)
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)))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series229.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
116.0ms	(.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)
51.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5630	1438

prune386.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	52	14	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	14	67

Merged error: 2.7b

Counts

67 → 14

localize45.0ms

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 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.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)
0.8b	(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))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-sqr-sqrt_binary64_559` `add-exp-log_binary64_538`
9×	`-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `associate-r*_binary64_633`
7×	`associate-l_binary64_634`
6×	`cos-mult_binary64_444`
5×	`cbrt-unprod_binary64_543` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
4×	`add-log-exp_binary64_539`
3×	`frac-times_binary64_566` `sin-mult_binary64_445` `-commutative_binary64_642` `associate-r/_binary64_635`
2×	`unswap-sqr_binary64_602` `flip3-+_binary64_572` `flip-+_binary64_599` `frac-add_binary64_564`
1×	`distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `associate-*l/_binary64_636` `acos-asin_binary64_408`

Counts

4 → 72

Calls

4 calls:

15.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.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)
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))))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
38.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
186.0ms	(.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)
63.0ms	(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))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5110	2773

prune457.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	14	84
Fresh	12	1	13
Picked	1	0	1
Done	0	0	0
Total	83	15	98

Merged error: 2.6b

Counts

98 → 15

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (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)))))))) R)
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)))))))
0.6b	(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))))))))
0.8b	(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

12×	`add-sqr-sqrt_binary64_559`
10×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
9×	`exp-prod_binary64_528`
8×	`pow1_binary64_520` `log-pow_binary64_495`
7×	`associate-l_binary64_634`
6×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
5×	`add-log-exp_binary64_539`
3×	`log-prod_binary64_492` `associate-r_binary64_633` `acos-asin_binary64_408`
2×	`exp-diff_binary64_535`
1×	`log-div_binary64_493` `unswap-sqr_binary64_602` `cbrt-unprod_binary64_543` `rem-exp-log_binary64_536` `rem-log-exp_binary64_537` `*-commutative_binary64_642` `pow-prod-down_binary64_501` `prod-exp_binary64_525`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (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)))))))) R)
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))))))))
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))))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(.f64 (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)))))))) R)
118.0ms	(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)))))))
55.0ms	(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))))))))
62.0ms	(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))))))

simplify110.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5214	3227

prune568.0ms

Filtered

41 candidates to 70 candidates (-70.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	68	17	85

Merged error: 2.5b

Counts

85 → 17

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.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	(log.f64 (exp.f64 (.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

13×	`add-sqr-sqrt_binary64_559`
9×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `pow1_binary64_520`
8×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
6×	`associate-l_binary64_634` `associate-r_binary64_633`
5×	`log-prod_binary64_492` `add-log-exp_binary64_539`
3×	`log-pow_binary64_495`
2×	`exp-sum_binary64_533` `unswap-sqr_binary64_602` `cbrt-unprod_binary64_543` `*-commutative_binary64_642` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
1×	`exp-prod_binary64_528` `exp-to-pow_binary64_514` `distribute-lft-in_binary64_616` `rem-log-exp_binary64_537` `distribute-rgt-in_binary64_617` `sin-mult_binary64_445` `acos-asin_binary64_408`

Counts

4 → 61

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.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 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
195.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
55.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
216.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5587	2321

prune257.0ms

Filtered

51 candidates to 73 candidates (-43.1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	70	20	90

Merged error: 2.5b

Counts

90 → 20

regimes1.9s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	47
1	33	47

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.6s	4836×	body	1280	valid
1.6s	2107×	body	640	valid
379.0ms	683×	body	320	valid
96.0ms	250×	body	160	valid
36.0ms	10×	body	2560	valid
21.0ms	114×	body	80	valid
1.0ms	1×	body	1280	invalid

Details

analyze3.5s

sample361.0ms

simplify149.0ms

prune9.0ms

localize34.0ms

rewrite15.0ms

series229.0ms

simplify107.0ms

prune386.0ms

localize45.0ms

rewrite27.0ms

series502.0ms

simplify101.0ms

prune457.0ms

localize51.0ms

rewrite13.0ms

series424.0ms

simplify110.0ms

prune568.0ms

localize49.0ms

rewrite14.0ms

series504.0ms

simplify97.0ms

prune257.0ms

regimes1.9s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample9.3s

Profiling