Details

sample299.0ms

Algorithm

intervals

Results

197.0ms	147×	body	1280	valid
40.0ms	54×	body	640	valid
9.0ms	20×	body	320	valid
4.0ms	25×	body	80	valid
3.0ms	10×	body	160	valid

simplify10.0ms

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: 14.0b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(sin (- lambda1 lambda2))
3.9b	(cos (- 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`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify114.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune159.0ms

Filtered

71 candidates to 50 candidates (29.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 7.3b

Counts

72 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 67

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (cos phi1) (sin phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	331	476
1	1299	404
2	5002	404

prune143.0ms

Filtered

79 candidates to 54 candidates (31.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 0.1b

Counts

90 → 9

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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

Counts

4 → 87

Calls

4 calls:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
26.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
29.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	420	777
1	1833	599
2	5001	599

prune162.0ms

Filtered

99 candidates to 57 candidates (42.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Merged error: 0.0b

Counts

108 → 12

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

8.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
1.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))

series79.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
18.0ms	(cbrt (sin lambda1))
19.0ms	(cbrt (sin lambda1))
19.0ms	(cbrt (sin lambda1))

simplify120.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	161	512
1	596	460
2	3671	403
3	5002	397

prune115.0ms

Filtered

85 candidates to 60 candidates (29.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

regimes660.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	39
1	43	39

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.6s	4731×	body	1280	valid
1.5s	1894×	body	640	valid
307.0ms	576×	body	320	valid
96.0ms	583×	body	80	valid
70.0ms	216×	body	160	valid

Details

sample299.0ms

simplify10.0ms

prune5.0ms

localize31.0ms

rewrite20.0ms

series42.0ms

simplify114.0ms

prune159.0ms

localize35.0ms

rewrite22.0ms

series45.0ms

simplify43.0ms

prune143.0ms

localize36.0ms

rewrite29.0ms

series73.0ms

simplify57.0ms

prune162.0ms

localize40.0ms

rewrite15.0ms

series79.0ms

simplify120.0ms

prune115.0ms

regimes660.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.0s

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