Details

sample281.0ms

Algorithm

intervals

Results

194.0ms	140×	body	1280	valid
55.0ms	74×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	20×	body	80	valid
1.0ms	4×	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

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: 13.8b

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)))
2.7b	(cos (- lambda1 lambda2))
2.7b	(sin (- 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 (- lambda1 lambda2)) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series49.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
6.0ms	(sin (- lambda1 lambda2))

simplify103.0ms

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

prune158.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	12	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	12	73

Merged error: 6.9b

Counts

73 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(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` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
7.0ms	(* (- (* (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	(* (cos phi1) (sin phi2))
27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	357	648
1	1484	552
2	5002	552

prune167.0ms

Filtered

56 candidates to 81 candidates (-44.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 0.1b

Counts

93 → 12

localize37.0ms

Local error

Found 4 expressions with local error:

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

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

series89.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	433	949
1	2002	747
2	5002	747

prune178.0ms

Filtered

59 candidates to 101 candidates (-71.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Merged error: 0.0b

Counts

113 → 14

localize41.0ms

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))

rewrite12.0ms

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:

6.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
1.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))

series82.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
18.0ms	(cbrt (sin lambda1))
17.0ms	(cbrt (sin lambda1))
20.0ms	(cbrt (sin lambda1))

simplify120.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (113.0ms)

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

prune100.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	85	14	99

Merged error: 0.0b

Counts

99 → 14

regimes710.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	39	36
1	39	36

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.4s	4621×	body	1280	valid
1.5s	1959×	body	640	valid
277.0ms	550×	body	320	valid
94.0ms	648×	body	80	valid
68.0ms	222×	body	160	valid

Details

sample281.0ms

simplify8.0ms

prune5.0ms

localize25.0ms

rewrite21.0ms

series49.0ms

simplify103.0ms

prune158.0ms

localize33.0ms

rewrite23.0ms

series63.0ms

simplify41.0ms

prune167.0ms

localize37.0ms

rewrite31.0ms

series89.0ms

simplify58.0ms

prune178.0ms

localize41.0ms

rewrite12.0ms

series82.0ms

simplify120.0ms

prune100.0ms

regimes710.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.7s

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