Details

sample9.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 15.612793%

Results

228.0ms	156×	body	1280	valid
52.0ms	56×	body	640	valid
14.0ms	23×	body	320	valid
3.0ms	15×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

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

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0b	(sin (- lambda1 lambda2))
5.0b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
22.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune171.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	14	73

Merged error: 8.7b

Counts

73 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0b	(cos (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative` `sin-cos-mult`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series43.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (sin phi1) (cos phi2))
22.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	308	486
1	1294	414
2	5002	414

prune159.0ms

Filtered

56 candidates to 81 candidates (-44.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 0.1b

Counts

95 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 84

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin phi1) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
40.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	474	790
1	2287	685
2	5001	684

prune197.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	95	13	108

Merged error: 0.1b

Counts

108 → 13

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.6b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`cos-mult` `sin-mult`
4×	`pow-pow` `pow-plus` `pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

9.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
8.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series57.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
15.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify73.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	450	568
1	2270	531
2	5001	531

prune140.0ms

Filtered

62 candidates to 132 candidates (-112.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	132	13	145

Merged error: 0.1b

Counts

145 → 13

regimes704.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	51
1	44	51

end0.0ms

sample19.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 15.612793%

Results

6.9s	4583×	body	1280	valid
1.7s	1981×	body	640	valid
312.0ms	565×	body	320	valid
112.0ms	655×	body	80	valid
76.0ms	216×	body	160	valid

Details

sample9.7s

simplify9.0ms

prune5.0ms

localize33.0ms

rewrite24.0ms

series45.0ms

simplify104.0ms

prune171.0ms

localize37.0ms

rewrite20.0ms

series43.0ms

simplify38.0ms

prune159.0ms

localize34.0ms

rewrite27.0ms

series66.0ms

simplify65.0ms

prune197.0ms

localize51.0ms

rewrite30.0ms

series57.0ms

simplify73.0ms

prune140.0ms

regimes704.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample19.0s

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