Details

analyze3.8s

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
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

sample310.0ms

Algorithm

intervals

Results

187.0ms	101×	body	1280	valid
61.0ms	59×	body	640	valid
16.0ms	23×	body	320	valid
13.0ms	63×	body	80	valid
5.0ms	10×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	33
1	44	33

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: 0.1b

Counts

2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin 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)))))))

rewrite16.0ms

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` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

5.0ms	(* (sin theta) (sin delta))
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)))))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
33.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(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)))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4929	1209
1	4929	1209

prune163.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	6	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.0b

Counts

71 → 7

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b	(pow (cos delta) 3)
0.5b	(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`pow-unpow`
4×	`unpow-prod-down` `cube-prod` `add-log-exp`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `asin-acos` `unpow3` `sqr-pow`
1×	`cube-div` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`

Counts

4 → 62

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
2.0ms	(pow (cos delta) 3)
5.0ms	(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)

series83.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(pow (cos delta) 3)
67.0ms	(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)

simplify40.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5234	1027

prune158.0ms

Filtered

50 candidates to 74 candidates (-48.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Merged error: 0.0b

Counts

81 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
34.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
44.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4969	1260
1	4969	1260

prune132.0ms

Filtered

51 candidates to 69 candidates (-35.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(/ (- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`asin-acos` `associate-/r` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 56

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
10.0ms	(/ (- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
275.0ms	(/ (- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	2941
1	4939	2941

prune127.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 0.0b

Counts

75 → 7

regimes517.0ms

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	43	86
1	43	86

end0.0ms

analyze4.0s

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
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

sample9.4s

Algorithm

intervals

Results

5.9s	3180×	body	1280	valid
1.9s	1783×	body	640	valid
515.0ms	694×	body	320	valid
412.0ms	2013×	body	80	valid
161.0ms	330×	body	160	valid

Details

analyze3.8s

sample310.0ms

simplify3.0ms

prune22.0ms

localize35.0ms

rewrite16.0ms

series94.0ms

simplify80.0ms

prune163.0ms

localize50.0ms

rewrite12.0ms

series83.0ms

simplify40.0ms

prune158.0ms

localize34.0ms

rewrite17.0ms

series99.0ms

simplify67.0ms

prune132.0ms

localize44.0ms

rewrite15.0ms

series291.0ms

simplify69.0ms

prune127.0ms

regimes517.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze4.0s

sample9.4s

Profiling