Details

sample272.0ms

Algorithm

intervals

Results

203.0ms	158×	body	1280	valid
43.0ms	60×	body	640	valid
7.0ms	15×	body	320	valid
2.0ms	16×	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

prune4.0ms

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: 13.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))
3.6b	(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:

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))

series169.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify111.0ms

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

prune316.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	13	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 7.9b

Counts

73 → 13

localize35.0ms

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))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite26.0ms

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:

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

series281.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
42.0ms	(* (sin phi1) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	322	653
1	1423	557
2	5001	557

prune404.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.1b

Counts

95 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (cos phi2))
99.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
45.0ms	(* (sin lambda1) (sin lambda2))
114.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	388	782
1	1793	604
2	5002	604

prune449.0ms

Filtered

100 candidates to 58 candidates (58.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 0.1b

Counts

111 → 13

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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-l`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
4×	`*-commutative` `add-log-exp`
3×	`associate-*r/` `sin-cos-mult` `sin-mult`
2×	`unswap-sqr`
1×	`frac-times` `associate-*l/` `cos-mult`

Counts

4 → 85

Calls

4 calls:

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
49.0ms	(* (sin lambda1) (sin lambda2))
111.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	398	740
1	1872	577
2	5001	577

prune378.0ms

Filtered

97 candidates to 60 candidates (61.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	97	13	110

Merged error: 0.1b

Counts

110 → 13

regimes503.0ms

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	37	29
1	37	29

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4543×	body	1280	valid
1.5s	1998×	body	640	valid
288.0ms	593×	body	320	valid
93.0ms	648×	body	80	valid
75.0ms	218×	body	160	valid

Details

sample272.0ms

simplify16.0ms

prune4.0ms

localize26.0ms

rewrite20.0ms

series169.0ms

simplify111.0ms

prune316.0ms

localize35.0ms

rewrite26.0ms

series281.0ms

simplify47.0ms

prune404.0ms

localize37.0ms

rewrite30.0ms

series304.0ms

simplify59.0ms

prune449.0ms

localize37.0ms

rewrite30.0ms

series304.0ms

simplify66.0ms

prune378.0ms

regimes503.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.6s

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