Details

sample349.0ms

Algorithm

intervals

Results

167.0ms	97×	body	1280	valid
54.0ms	60×	body	640	valid
14.0ms	23×	body	320	valid
12.0ms	66×	body	80	valid
4.0ms	10×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	56	22
2	59	22
3	59	22

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.1b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos delta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

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`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `sin-cos-mult` `flip--` `sin-mult`

Counts

4 → 58

Calls

4 calls:

5.0ms	(* (sin phi1) (cos delta))
9.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos delta))
38.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
46.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	290	931
1	891	843
2	3724	841
3	5002	841

prune136.0ms

Filtered

70 candidates to 51 candidates (27.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0.0b

Counts

71 → 4

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin phi1)) (cbrt (sin phi1)))
0.6b	(cbrt (sin phi1))
0.6b	(cbrt (sin phi1))
0.6b	(cbrt (sin phi1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt (sin phi1)) (cbrt (sin phi1)))
1.0ms	(cbrt (sin phi1))
1.0ms	(cbrt (sin phi1))
2.0ms	(cbrt (sin phi1))

series79.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (sin phi1)) (cbrt (sin phi1)))
18.0ms	(cbrt (sin phi1))
18.0ms	(cbrt (sin phi1))
18.0ms	(cbrt (sin phi1))

simplify116.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	161	512
1	598	454
2	3692	400
3	5001	394

prune121.0ms

Filtered

85 candidates to 60 candidates (29.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.6b	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `asin-acos` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

series178.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
44.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
46.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
82.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	288	1796
1	1015	1670
2	5002	1664

prune115.0ms

Filtered

80 candidates to 50 candidates (37.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	80	4	84

Merged error: 0.0b

Counts

84 → 4

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.8b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
46.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
44.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	253	1234
1	764	1106
2	2949	1102
3	5001	1102

prune97.0ms

Filtered

69 candidates to 50 candidates (27.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

regimes385.0ms

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	34	29
1	34	29

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.0s	3054×	body	1280	valid
1.7s	1843×	body	640	valid
467.0ms	717×	body	320	valid
391.0ms	2059×	body	80	valid
133.0ms	327×	body	160	valid

Details

sample349.0ms

simplify8.0ms

prune6.0ms

localize32.0ms

rewrite20.0ms

series99.0ms

simplify97.0ms

prune136.0ms

localize40.0ms

rewrite12.0ms

series79.0ms

simplify116.0ms

prune121.0ms

localize35.0ms

rewrite15.0ms

series178.0ms

simplify46.0ms

prune115.0ms

localize37.0ms

rewrite15.0ms

series131.0ms

simplify86.0ms

prune97.0ms

regimes385.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.3s

Profiling