Details

sample265.0ms

Algorithm

intervals

Results

188.0ms	148×	body	1280	valid
45.0ms	58×	body	640	valid
10.0ms	21×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	7×	body	160	valid

simplify16.0ms

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

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: 15.5b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.3b	(sin (- lambda1 lambda2))
5.3b	(cos (- 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:

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

series176.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify112.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

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

prune290.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	62	10	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	10	73

Merged error: 8.1b

Counts

73 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.3b	(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`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 68

Calls

4 calls:

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

series190.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
45.0ms	(* (sin lambda1) (cos lambda2))
86.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	333	481
1	1341	409
2	5001	409

prune393.0ms

Filtered

80 candidates to 55 candidates (68.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 0.1b

Counts

90 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

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

series294.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin lambda1) (cos lambda2))
108.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
96.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
49.0ms	(* (sin lambda1) (sin lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	409	784
1	1785	606
2	5001	604

prune424.0ms

Filtered

100 candidates to 58 candidates (58.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 0.1b

Counts

110 → 13

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
10×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`associate-*l/` `sin-mult`
2×	`unswap-sqr`
1×	`frac-times` `associate-*r/`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
5.0ms	(* (sin lambda1) (sin lambda2))

series289.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin lambda1) (cos lambda2))
110.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
94.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
43.0ms	(* (sin lambda1) (sin lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	401	741
1	1878	578
2	5002	578

prune349.0ms

Filtered

97 candidates to 59 candidates (60.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	97	13	110

Merged error: 0.1b

Counts

110 → 13

regimes474.0ms

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	29
1	35	29

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4619×	body	1280	valid
1.5s	1945×	body	640	valid
266.0ms	562×	body	320	valid
95.0ms	664×	body	80	valid
66.0ms	210×	body	160	valid