Details

analyze2.8s

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

sample561.0ms

Algorithm

intervals

Results

194.0ms	147×	body	1280	valid
53.0ms	73×	body	640	valid
11.0ms	23×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	6×	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

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 16.6b

Counts

2 → 1

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
3.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
15.0b	(cos (- lambda1 lambda2))

rewrite17.0ms

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:

8.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0ms	(cos (- lambda1 lambda2))

series47.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
25.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune179.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	50	16	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	16	67

Merged error: 3.2b

Counts

67 → 16

localize146.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
3.1b	(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:

4.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
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 phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
12.0ms	(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

prune208.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	60	16	76
Fresh	13	2	15
Picked	1	0	1
Done	0	0	0
Total	74	18	92

Merged error: 3.0b

Counts

92 → 18

localize216.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
3.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
36.9b	(log (pow (exp (sin lambda1)) (sin lambda2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series91.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
46.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
22.0ms	(log (pow (exp (sin lambda1)) (sin lambda2)))

simplify32.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5009	1204

prune192.0ms

Filtered

53 candidates to 75 candidates (-41.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	76	17	93

Merged error: 3.0b

Counts

93 → 17

localize314.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
0.4b	(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
0.7b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
3.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series96.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
12.0ms	(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
32.0ms	(log (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)))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4866	1908
1	4866	1908

prune68.0ms

Filtered

39 candidates to 69 candidates (-76.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	69	17	86

Merged error: 3.0b

Counts

86 → 17

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	30
1	34	30

end0.0ms

sample19.8s

Algorithm

intervals

Results

6.1s	4715×	body	1280	valid
1.6s	2141×	body	640	valid
349.0ms	697×	body	320	valid
103.0ms	294×	body	160	valid
25.0ms	146×	body	80	valid
24.0ms	7×	body	2560	valid

Details

analyze2.8s

sample561.0ms

simplify5.0ms

prune13.0ms

localize96.0ms

rewrite17.0ms

series47.0ms

simplify56.0ms

prune179.0ms

localize146.0ms

rewrite15.0ms

series73.0ms

simplify47.0ms

prune208.0ms

localize216.0ms

rewrite14.0ms

series91.0ms

simplify32.0ms

prune192.0ms

localize314.0ms

rewrite12.0ms

series96.0ms

simplify70.0ms

prune68.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample19.8s

Profiling