Details

sample293.0ms

Algorithm

intervals

Results

212.0ms	157×	body	1280	valid
43.0ms	56×	body	640	valid
11.0ms	20×	body	320	valid
3.0ms	10×	body	160	valid
2.0ms	13×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	24
1	65	24

prune22.0ms

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: 13.5b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.5b	(sin (- lambda1 lambda2))
4.6b	(cos (- lambda1 lambda2))

rewrite26.0ms

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:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series52.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify34.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5328	642

prune180.0ms

Filtered

50 candidates to 72 candidates (-44.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	14	74

Merged error: 6.0b

Counts

74 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda2) (sin lambda1))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.6b	(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` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

7.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (cos lambda2) (sin lambda1))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series73.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (cos lambda2) (sin lambda1))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4973	871
1	4973	871

prune198.0ms

Filtered

56 candidates to 81 candidates (-44.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 0.1b

Counts

95 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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` `cbrt-unprod`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 84

Calls

4 calls:

7.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (cos lambda2) (sin lambda1))
5.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (cos lambda2) (sin lambda1))
10.0ms	(* (sin lambda1) (sin lambda2))
50.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4979	1277
1	4979	1277

prune219.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	96	14	110

Merged error: 0.0b

Counts

110 → 14

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b	(/ (* (sin phi1) (* (cos phi2) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3)))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

99×	`cos-mult`
84×	`sin-mult`
58×	`pow1`
54×	`associate-*r/`
50×	`associate-/r/`
49×	`frac-add`
48×	`associate-*l/`
42×	`frac-times`
40×	`add-exp-log` `add-cbrt-cube`
27×	`frac-sub`
26×	`pow-prod-down`
20×	`prod-exp` `cbrt-unprod`
15×	`sub-div`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cbrt-undiv` `cube-div` `pow-unpow` `flip3--` `times-frac` `div-exp` `associate-/r*` `flip--` `associate-/l/`
2×	`pow-pow` `flip3-+` `pow-plus` `associate-r` `associate-l` `pow-exp` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `cube-prod` `swap-sqr` `clear-num` `div-inv` `associate-/l*` `sqr-pow`

Counts

4 → 161

Calls

4 calls:

10.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
42.0ms	(/ (* (sin phi1) (* (cos phi2) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3)))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
10.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series337.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
279.0ms	(/ (* (sin phi1) (* (cos phi2) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3)))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
17.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
16.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify59.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5070	5888

prune247.0ms

Filtered

91 candidates to 173 candidates (-90.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	172	15	187

Merged error: 0.0b

Counts

187 → 15

regimes793.0ms

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	44	78
1	44	78

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.5s	4729×	body	1280	valid
1.5s	1890×	body	640	valid
308.0ms	563×	body	320	valid
100.0ms	619×	body	80	valid
69.0ms	199×	body	160	valid

Details

sample293.0ms

simplify3.0ms

prune22.0ms

localize24.0ms

rewrite26.0ms

series52.0ms

simplify34.0ms

prune180.0ms

localize33.0ms

rewrite26.0ms

series73.0ms

simplify42.0ms

prune198.0ms

localize33.0ms

rewrite32.0ms

series101.0ms

simplify55.0ms

prune219.0ms

localize46.0ms

rewrite79.0ms

series337.0ms

simplify59.0ms

prune247.0ms

regimes793.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.0s

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