Details

analyze3.0s

Algorithm: search

sample296.0ms

Algorithm

intervals

Results

203.0ms	147×	body	1280	valid
58.0ms	74×	body	640	valid
12.0ms	23×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune10.0ms

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: 17.0b

Counts

2 → 1

localize26.0ms

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)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.5b	(cos (- lambda1 lambda2))

rewrite14.0ms

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×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

4.0ms	(* (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))

series49.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
26.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
8.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569

prune145.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	56	11	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	11	68

Merged error: 3.6b

Counts

68 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite16.0ms

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:

6.0ms	(* (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))))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	260	929
1	831	774
2	1930	774
3	3056	774
4	5001	774

prune156.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 3.5b

Counts

87 → 12

localize39.0ms

Local error

Found 4 expressions with local error:

1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
7.5b	(cbrt (* (sin lambda1) (sin lambda2)))
7.5b	(cbrt (* (sin lambda1) (sin lambda2)))
7.5b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
1×	`acos-asin`

Counts

4 → 38

Calls

4 calls:

1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
23.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify192.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	159	662
1	388	577
2	1141	571
3	4721	507
4	5002	507

prune139.0ms

Filtered

39 candidates to 50 candidates (-28.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	50	12	62

Merged error: 3.5b

Counts

62 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.0b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
4×	`difference-of-squares`
2×	`asin-acos` `flip3--` `times-frac` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`sub-neg` `diff-log` `sin-mult` `associate--r-`

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
1.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
7.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin lambda1) (sin lambda2))
68.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
13.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
24.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	282	1489
1	859	1348
2	3189	1342
3	5001	1342

prune95.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	9	78
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	73	17	90

Merged error: 3.3b

Counts

90 → 17

regimes1.8s

Accuracy

0% (0.6b remaining)

Error of 3.9b against oracle of 3.3b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

analyze2.9s

Algorithm: search

sample9.4s

Algorithm

intervals

Results

6.7s	4728×	body	1280	valid
1.8s	2121×	body	640	valid
403.0ms	708×	body	320	valid
110.0ms	292×	body	160	valid
42.0ms	11×	body	2560	valid
28.0ms	140×	body	80	valid
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	640	invalid

Details

analyze3.0s

sample296.0ms

simplify6.0ms

prune10.0ms

localize26.0ms

rewrite14.0ms

series49.0ms

simplify48.0ms

prune145.0ms

localize32.0ms

rewrite16.0ms

series76.0ms

simplify78.0ms

prune156.0ms

localize39.0ms

rewrite12.0ms

series82.0ms

simplify192.0ms

prune139.0ms

localize35.0ms

rewrite26.0ms

series114.0ms

simplify78.0ms

prune95.0ms

regimes1.8s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.9s

sample9.4s

Profiling