Details

sample264.0ms

Algorithm

intervals

Results

191.0ms	153×	body	1280	valid
40.0ms	59×	body	640	valid
12.0ms	18×	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: 13.9b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite23.0ms

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	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series198.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

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

prune337.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	13	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 7.0b

Counts

73 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite25.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series286.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (cos lambda2))
134.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	378	674
1	1662	581
2	5001	580

prune481.0ms

Filtered

82 candidates to 59 candidates (72.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.0b

Counts

95 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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`
5×	`sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`associate-*l/` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 90

Calls

4 calls:

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

series411.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (cos lambda2))
132.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
182.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	533	1120
1	2470	977
2	5001	975

prune623.0ms

Filtered

102 candidates to 77 candidates (75.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	11	102
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`sub-neg` `*-commutative` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`associate-*l/` `cos-mult`
1×	`flip3--` `flip3-+` `sin-neg` `distribute-rgt-neg-out` `frac-sub` `sin-cos-mult` `flip--` `flip-+` `sub-div`

Counts

4 → 89

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (cos lambda2))
131.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
57.0ms	(* (sin lambda1) (sin (- lambda2)))
184.0ms	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	487	1051
1	2034	899
2	5002	897

prune522.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Merged error: 0.0b

Counts

112 → 10

regimes329.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	45
1	39	45

end0.0ms

sample8.1s

Algorithm

intervals

Results

6.0s	4697×	body	1280	valid
1.3s	1857×	body	640	valid
279.0ms	566×	body	320	valid
98.0ms	692×	body	80	valid
66.0ms	188×	body	160	valid