Details

sample198.0ms

Algorithm

intervals

Results

126.0ms	123×	body	1280	valid
40.0ms	72×	body	640	valid
9.0ms	25×	body	320	valid
5.0ms	20×	body	160	valid
2.0ms	16×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

prune3.0ms

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: 1.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

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

series196.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
95.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify108.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	249	435
1	795	394
2	2920	393
3	5001	393

prune270.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	55	12	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	12	68

Merged error: 0.8b

Counts

68 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.2b	(sin (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`sin-sum` `associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `sin-diff` `flip-+` `sin-mult`

Counts

4 → 64

Calls

4 calls:

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

series332.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (sin lambda2))
55.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
212.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
20.0ms	(sin (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	309	578
1	1149	514
2	5002	513

prune313.0ms

Filtered

76 candidates to 53 candidates (69.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 0.2b

Counts

88 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin lambda1))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`*-commutative`
2×	`associate-+r+` `distribute-rgt-neg-out` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sin-neg` `sum-log` `flip-+` `sin-mult`

Counts

4 → 69

Calls

4 calls:

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

series394.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos phi2) (sin lambda1))
45.0ms	(* (sin lambda1) (sin lambda2))
79.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
230.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	379	634
1	1565	540
2	5001	539

prune409.0ms

Filtered

81 candidates to 58 candidates (71.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 0.2b

Counts

92 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin lambda1))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (cos phi2) (cos lambda1)) (sin (- lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite22.0ms

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

Counts

4 → 70

Calls

4 calls:

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

series405.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos phi2) (sin lambda1))
47.0ms	(* (sin lambda1) (sin lambda2))
81.0ms	(* (* (cos phi2) (cos lambda1)) (sin (- lambda2)))
236.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	399	644
1	1743	550
2	5002	549

prune330.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	82	12	94

Merged error: 0.2b

Counts

94 → 12

regimes413.0ms

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	35	25
1	35	25

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.4s	3623×	body	1280	valid
1.3s	2325×	body	640	valid
317.0ms	912×	body	320	valid
101.0ms	423×	body	160	valid
77.0ms	717×	body	80	valid