Details

sample9.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 15.612793%

Results

218.0ms	156×	body	1280	valid
44.0ms	56×	body	640	valid
12.0ms	23×	body	320	valid
7.0ms	6×	body	160	valid
2.0ms	15×	body	80	valid

simplify8.0ms

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

prune6.0ms

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

localize26.0ms

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))

rewrite22.0ms

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:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify106.0ms

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

prune173.0ms

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

localize36.0ms

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))

rewrite21.0ms

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

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

prune161.0ms

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

localize35.0ms

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))))

rewrite26.0ms

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:

4.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin phi1) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
45.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (56.0ms)

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

prune198.0ms

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

localize48.0ms

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)

rewrite34.0ms

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)

series56.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
15.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify76.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (13.0ms)

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

prune142.0ms

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

regimes684.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	44	51
1	44	51

end0.0ms

sample17.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 15.612793%

Results

6.5s	4583×	body	1280	valid
1.6s	1981×	body	640	valid
311.0ms	565×	body	320	valid
113.0ms	655×	body	80	valid
81.0ms	216×	body	160	valid

Details

sample9.0s

simplify8.0ms

prune6.0ms

localize26.0ms

rewrite22.0ms

series47.0ms

simplify106.0ms

prune173.0ms

localize36.0ms

rewrite21.0ms

series47.0ms

simplify51.0ms

prune161.0ms

localize35.0ms

rewrite26.0ms

series71.0ms

simplify64.0ms

prune198.0ms

localize48.0ms

rewrite34.0ms

series56.0ms

simplify76.0ms

prune142.0ms

regimes684.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample17.9s

Profiling