Details

analyze2.5s

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample300.0ms

Algorithm

intervals

Results

230.0ms	157×	body	1280	valid
40.0ms	52×	body	640	valid
10.0ms	20×	body	320	valid
3.0ms	21×	body	80	valid
2.0ms	6×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 10.6b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.2b	(sin.f64 (-.f64 lambda1 lambda2))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 58

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series56.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
30.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify66.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4879	620
1	4879	620

prune126.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	56	14	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	14	71

Merged error: 6.0b

Counts

71 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite25.0ms

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`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cos-diff_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `flip--_binary64`

Counts

4 → 68

Calls

4 calls:

7.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series79.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
14.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
27.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify28.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5057	860

prune109.0ms

Filtered

56 candidates to 80 candidates (-42.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 0.1b

Counts

94 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`sin-mult_binary64`
2×	`cos-mult_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 87

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
11.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
13.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
31.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
34.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4969	943
1	4969	943

prune125.0ms

Filtered

58 candidates to 99 candidates (-70.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	96	14	110

Merged error: 0.0b

Counts

110 → 14

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
1.5b	(log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`sin-cos-mult_binary64`
3×	`log-prod_binary64` `log-pow_binary64` `sin-mult_binary64` `*-commutative_binary64`
2×	`cos-mult_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`rem-log-exp_binary64` `unswap-sqr_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 83

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
3.0ms	(log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
30.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
36.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
31.0ms	(log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5145	1014

prune63.0ms

Filtered

57 candidates to 95 candidates (-66.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	94	15	109

Merged error: 0.0b

Counts

109 → 15

regimes607.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	46
1	129	46

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.5s	4562×	body	1280	valid
1.6s	2001×	body	640	valid
305.0ms	597×	body	320	valid
100.0ms	611×	body	80	valid
75.0ms	229×	body	160	valid

Details

analyze2.5s

sample300.0ms

simplify17.0ms

prune8.0ms

localize24.0ms

rewrite24.0ms

series56.0ms

simplify66.0ms

prune126.0ms

localize34.0ms

rewrite25.0ms

series79.0ms

simplify28.0ms

prune109.0ms

localize32.0ms

rewrite33.0ms

series88.0ms

simplify53.0ms

prune125.0ms

localize39.0ms

rewrite30.0ms

series108.0ms

simplify52.0ms

prune63.0ms

regimes607.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample8.8s

Profiling