Details

sample299.0ms

Algorithm

intervals

Results

222.0ms	153×	body	1280	valid
42.0ms	54×	body	640	valid
7.0ms	14×	body	320	valid
4.0ms	25×	body	80	valid
3.0ms	10×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune15.0ms

Filtered

1 candidates to 1 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: 12.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2)))))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
3.6b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`cos-diff`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate--r+`
3×	`sub-neg` `associate-r` `associate-l`
2×	`cos-sum` `sin-sum`
1×	`flip3--` `diff-log` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `sin-cos-mult` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* (cos phi1) (sin phi2)) (* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2)))))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5484	785

prune164.0ms

Filtered

54 candidates to 69 candidates (-27.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	13	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	13	71

Merged error: 7.0b

Counts

71 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`cos-diff`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate--r+`
2×	`sub-neg` `cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `diff-log` `sin-cos-mult` `flip--`

Counts

4 → 65

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
36.0ms	(- (* (cos phi1) (sin phi2)) (* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2)))))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5769	836

prune154.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 0.1b

Counts

90 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`*-commutative`
2×	`sin-mult` `associate--r+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `associate-*r/` `flip--`

Counts

4 → 70

Calls

4 calls:

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

series106.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* (cos phi1) (sin phi2)) (* (cos phi2) (+ (* (cos lambda1) (* (cos lambda2) (sin phi1))) (* (sin lambda1) (* (sin lambda2) (sin phi1))))))
8.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
9.0ms	(* (sin lambda2) (sin phi1))

simplify29.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5159	956

prune162.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 0.0b

Counts

92 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

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

series117.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* (cos phi1) (sin phi2)) (* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
8.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
27.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5006	1219

prune98.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Merged error: 0.0b

Counts

99 → 11

regimes601.0ms

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	135	38
1	135	38

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.8s	4667×	body	1280	valid
1.5s	1882×	body	640	valid
295.0ms	562×	body	320	valid
116.0ms	694×	body	80	valid
67.0ms	195×	body	160	valid

Details

sample299.0ms

simplify13.0ms

prune15.0ms

localize24.0ms

rewrite22.0ms

series54.0ms

simplify48.0ms

prune164.0ms

localize36.0ms

rewrite20.0ms

series64.0ms

simplify52.0ms

prune154.0ms

localize37.0ms

rewrite21.0ms

series106.0ms

simplify29.0ms

prune162.0ms

localize37.0ms

rewrite24.0ms

series117.0ms

simplify48.0ms

prune98.0ms

regimes601.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.3s

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