Details

sample281.0ms

Algorithm

intervals

Results

187.0ms	141×	body	1280	valid
49.0ms	67×	body	640	valid
8.0ms	17×	body	320	valid
4.0ms	27×	body	80	valid
1.0ms	4×	body	160	valid

simplify9.0ms

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

prune7.0ms

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: 14.1b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.5b	(cos (- lambda1 lambda2))
4.6b	(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:

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

series221.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin phi1) (cos phi2))
111.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify115.0ms

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

prune418.0ms

Filtered

72 candidates to 51 candidates (29.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	9	73

Merged error: 6.7b

Counts

73 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.5b	(cos (- lambda1 lambda2))

rewrite24.0ms

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

Counts

4 → 64

Calls

4 calls:

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

series376.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
56.0ms	(* (sin phi1) (cos phi2))
112.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	303	610
1	1314	544
2	5001	544

prune435.0ms

Filtered

76 candidates to 54 candidates (28.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 0.1b

Counts

85 → 9

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
5.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))

series385.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin lambda1) (cos lambda2))
56.0ms	(* (sin phi1) (cos phi2))
213.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
59.0ms	(* (sin lambda1) (sin lambda2))

simplify66.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	474	790
1	2287	685
2	5001	684

prune758.0ms

Filtered

96 candidates to 65 candidates (32.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Merged error: 0.1b

Counts

105 → 12

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
9×	`associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`sin-cos-mult`

Counts

4 → 86

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin lambda1) (cos lambda2))
171.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
61.0ms	(* (sin lambda1) (sin lambda2))
213.0ms	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	418	922
1	1864	791
2	5001	791

prune679.0ms

Filtered

98 candidates to 67 candidates (31.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	97	13	110

Merged error: 0.1b

Counts

110 → 13

regimes863.0ms

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	33	25
1	33	25

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.6s	4694×	body	1280	valid
1.4s	1870×	body	640	valid
284.0ms	572×	body	320	valid
97.0ms	672×	body	80	valid
59.0ms	192×	body	160	valid

Details

sample281.0ms

simplify9.0ms

prune7.0ms

localize27.0ms

rewrite21.0ms

series221.0ms

simplify115.0ms

prune418.0ms

localize37.0ms

rewrite24.0ms

series376.0ms

simplify48.0ms

prune435.0ms

localize38.0ms

rewrite26.0ms

series385.0ms

simplify66.0ms

prune758.0ms

localize36.0ms

rewrite33.0ms

series503.0ms

simplify58.0ms

prune679.0ms

regimes863.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.9s

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