Details

sample280.0ms

Algorithm

intervals

Results

197.0ms	149×	body	1280	valid
58.0ms	71×	body	640	valid
4.0ms	10×	body	320	valid
3.0ms	21×	body	80	valid
2.0ms	5×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 12.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite21.0ms

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:

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

series171.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin phi1) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify111.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune302.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Merged error: 6.2b

Counts

73 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite23.0ms

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:

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

series195.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
42.0ms	(* (sin lambda1) (cos lambda2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

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

prune382.0ms

Filtered

81 candidates to 56 candidates (69.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 0.1b

Counts

89 → 8

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (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 phi1) (cos phi2))
5.0ms	(* (sin lambda1) (cos lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
45.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (sin lambda1) (sin lambda2))
171.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify68.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (57.0ms)

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

prune452.0ms

Filtered

96 candidates to 64 candidates (66.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.1b

Counts

104 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

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

series302.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
45.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (sin lambda1) (sin lambda2))
170.0ms	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	430	710
1	1776	605
2	5001	605

prune391.0ms

Filtered

93 candidates to 63 candidates (67.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	91	11	102

Merged error: 0.1b

Counts

102 → 11

regimes431.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	27
1	36	27

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.2s	4577×	body	1280	valid
1.5s	1982×	body	640	valid
282.0ms	552×	body	320	valid
104.0ms	665×	body	80	valid
71.0ms	224×	body	160	valid

Details

sample280.0ms

simplify9.0ms

prune4.0ms

localize26.0ms

rewrite21.0ms

series171.0ms

simplify111.0ms

prune302.0ms

localize35.0ms

rewrite23.0ms

series195.0ms

simplify40.0ms

prune382.0ms

localize37.0ms

rewrite27.0ms

series304.0ms

simplify68.0ms

prune452.0ms

localize37.0ms

rewrite28.0ms

series302.0ms

simplify52.0ms

prune391.0ms

regimes431.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.5s

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