Details

analyze2.2s

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample183.0ms

Algorithm

intervals

Results

106.0ms	112×	body	1280	valid
41.0ms	73×	body	640	valid
10.0ms	27×	body	320	valid
4.0ms	30×	body	80	valid
3.0ms	14×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

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: 0.9b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))
4.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `associate-+r+_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 38

Calls

4 calls:

1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
27.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify83.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4859	567
1	4859	567

prune118.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	37	13	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	13	51

Merged error: 0.7b

Counts

51 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `cos-diff_binary64`
2×	`associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 47

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series57.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
12.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
29.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify77.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4777	706
1	4777	706

prune102.0ms

Filtered

45 candidates to 59 candidates (-31.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 0.1b

Counts

72 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.4b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite18.0ms

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×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
12.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
17.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
66.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4976	985
1	4976	985

prune96.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 0.0b

Counts

80 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.6b	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.6b	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.6b	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
3.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
3.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
3.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
24.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
24.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
26.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5154	519

prune61.0ms

Filtered

48 candidates to 70 candidates (-45.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 0.0b

Counts

80 → 11

regimes523.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	49
1	62	49

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	3508×	body	1280	valid
1.3s	2331×	body	640	valid
381.0ms	1027×	body	320	valid
105.0ms	442×	body	160	valid
83.0ms	692×	body	80	valid

Details

analyze2.2s

sample183.0ms

simplify20.0ms

prune4.0ms

localize21.0ms

rewrite15.0ms

series51.0ms

simplify83.0ms

prune118.0ms

localize28.0ms

rewrite15.0ms

series57.0ms

simplify77.0ms

prune102.0ms

localize30.0ms

rewrite18.0ms

series107.0ms

simplify51.0ms

prune96.0ms

localize35.0ms

rewrite18.0ms

series115.0ms

simplify56.0ms

prune61.0ms

regimes523.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample5.7s

Profiling