Details

sample268.0ms

Algorithm

intervals

Results

181.0ms	136×	body	1280	valid
51.0ms	70×	body	640	valid
11.0ms	23×	body	320	valid
3.0ms	19×	body	80	valid
2.0ms	8×	body	160	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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 12.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(cos (- lambda1 lambda2))
4.1b	(sin (- lambda1 lambda2))

rewrite20.0ms

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify101.0ms

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

prune177.0ms

Filtered

72 candidates to 51 candidates (29.2%)

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: 5.2b

Counts

73 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)))
3.8b	(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` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `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))

series63.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	348	646
1	1462	557
2	5001	557

prune161.0ms

Filtered

82 candidates to 56 candidates (31.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

7.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
9.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	433	949
1	2002	747
2	5001	747

prune149.0ms

Filtered

101 candidates to 59 candidates (41.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Merged error: 0.0b

Counts

111 → 8

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))))
0.6b	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

13.0ms	(* (cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))))
4.0ms	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
5.0ms	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))))
33.0ms	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
35.0ms	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
33.0ms	(cbrt (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))

simplify144.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	258	1840
1	902	1674
2	4859	1592
3	5001	1592

prune134.0ms

Filtered

99 candidates to 71 candidates (28.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

regimes599.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	48
1	39	48

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.4s	4653×	body	1280	valid
1.5s	1946×	body	640	valid
292.0ms	569×	body	320	valid
89.0ms	627×	body	80	valid
81.0ms	205×	body	160	valid

Details

sample268.0ms

simplify8.0ms

prune5.0ms

localize25.0ms

rewrite20.0ms

series46.0ms

simplify101.0ms

prune177.0ms

localize34.0ms

rewrite23.0ms

series63.0ms

simplify45.0ms

prune161.0ms

localize36.0ms

rewrite31.0ms

series91.0ms

simplify61.0ms

prune149.0ms

localize42.0ms

rewrite29.0ms

series143.0ms

simplify144.0ms

prune134.0ms

regimes599.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.8s

Profiling