Details

analyze3.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample286.0ms

Algorithm

intervals

Results

197.0ms	153×	body	1280	valid
49.0ms	68×	body	640	valid
10.0ms	20×	body	320	valid
8.0ms	9×	body	160	valid
3.0ms	1×	body	2560	valid
1.0ms	5×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

prune16.0ms

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: 16.7b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
3.2b	(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `cos-sum` `sin-mult`

Counts

4 → 54

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0ms	(cos (- lambda1 lambda2))

series53.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
10.0ms	(* (sin phi1) (sin phi2))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune162.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	53	13	66
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	13	68

Merged error: 3.8b

Counts

68 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite15.0ms

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`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5166	1173

prune160.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 3.7b

Counts

89 → 13

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

5.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
2.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
26.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
12.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4979	1928
1	4979	1928

prune152.0ms

Filtered

42 candidates to 70 candidates (-66.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	68	15	83

Merged error: 3.7b

Counts

83 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
29.1b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
3.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series80.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
18.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
9.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify37.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4897	1250
1	4897	1250

prune93.0ms

Filtered

54 candidates to 79 candidates (-46.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	79	15	94

Merged error: 3.7b

Counts

94 → 15

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.3s	4774×	body	1280	valid
1.6s	2137×	body	640	valid
329.0ms	633×	body	320	valid
97.0ms	294×	body	160	valid
44.0ms	12×	body	2560	valid
27.0ms	150×	body	80	valid
3.0ms	2×	body	1280	invalid
1.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

Details

analyze3.0s

sample286.0ms

simplify5.0ms

prune16.0ms

localize24.0ms

rewrite13.0ms

series53.0ms

simplify57.0ms

prune162.0ms

localize32.0ms

rewrite15.0ms

series73.0ms

simplify47.0ms

prune160.0ms

localize38.0ms

rewrite12.0ms

series92.0ms

simplify68.0ms

prune152.0ms

localize34.0ms

rewrite14.0ms

series80.0ms

simplify37.0ms

prune93.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.9s

Profiling