Details

analyze2.6s

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

sample303.0ms

Algorithm

intervals

Results

226.0ms	153×	body	1280	valid
47.0ms	58×	body	640	valid
9.0ms	15×	body	320	valid
4.0ms	24×	body	80	valid
2.0ms	6×	body	160	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune7.0ms

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: 12.5b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.1b	(sin.f64 (-.f64 lambda1 lambda2))
2.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms

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` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 57

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
27.0ms	(.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))

simplify69.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4809	577
1	4809	577

prune85.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	11	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Merged error: 6.0b

Counts

70 → 11

localize32.0ms

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))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite27.0ms

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:

8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
7.0ms	(*.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))

series68.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
9.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
25.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify29.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5057	860

prune79.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 0.1b

Counts

91 → 11

localize32.0ms

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`associate-r/_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`flip3-+_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`

Counts

4 → 84

Calls

4 calls:

9.0ms	(.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))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
9.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
46.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4993	1277
1	4993	1277

prune100.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.0b

Counts

107 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 lambda2))
0.3b	(cbrt.f64 (cos.f64 lambda2))
0.3b	(cbrt.f64 (cos.f64 lambda2))
0.3b	(*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

2.0ms	(cbrt.f64 (cos.f64 lambda2))
2.0ms	(cbrt.f64 (cos.f64 lambda2))
1.0ms	(cbrt.f64 (cos.f64 lambda2))
6.0ms	(*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 (cos.f64 lambda2))
14.0ms	(cbrt.f64 (cos.f64 lambda2))
14.0ms	(cbrt.f64 (cos.f64 lambda2))
23.0ms	(*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2)))

simplify47.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5038	469

prune39.0ms

Filtered

55 candidates to 85 candidates (-54.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

regimes394.0ms

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	139	47
1	139	47

end0.0ms

sample9.4s

Algorithm

intervals

Results

7.1s	4712×	body	1280	valid
1.5s	1856×	body	640	valid
325.0ms	588×	body	320	valid
110.0ms	659×	body	80	valid
64.0ms	185×	body	160	valid

Details

analyze2.6s

sample303.0ms

simplify25.0ms

prune7.0ms

localize30.0ms

rewrite23.0ms

series45.0ms

simplify69.0ms

prune85.0ms

localize32.0ms

rewrite27.0ms

series68.0ms

simplify29.0ms

prune79.0ms

localize32.0ms

rewrite33.0ms

series95.0ms

simplify56.0ms

prune100.0ms

localize36.0ms

rewrite13.0ms

series65.0ms

simplify47.0ms

prune39.0ms

regimes394.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample9.4s

Profiling