Details

sample12.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 14.941406%

Results

163.0ms	96×	body	1280	valid
63.0ms	61×	body	640	valid
16.0ms	61×	body	80	valid
15.0ms	23×	body	320	valid
6.0ms	15×	body	160	valid

simplify7.0ms

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

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: 0.2b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.7b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

1.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
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)))))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
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))))
48.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify83.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	244	1107
1	692	985
2	2754	983
3	5002	983

prune138.0ms

Filtered

44 candidates to 58 candidates (-31.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	51	7	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	7	59

Merged error: 0.1b

Counts

59 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin phi1) 2)
0.2b	(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
0.3b	(* (sin delta) (* (cos phi1) (sin theta)))
0.7b	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log`
18×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
3×	`unpow-prod-down` `pow-unpow`
2×	`diff-log` `associate-r` `*-commutative`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `associate--r+` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

3.0ms	(pow (sin phi1) 2)
10.0ms	(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
6.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
7.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin phi1) 2)
26.0ms	(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
16.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
44.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	406	830
1	1609	699
2	5001	698

prune165.0ms

Filtered

53 candidates to 85 candidates (-60.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin phi1) 2)
0.2b	(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
0.3b	(* (sin delta) (* (cos phi1) (sin theta)))
0.7b	(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log`
18×	`add-cbrt-cube`
9×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
2×	`associate-r` `*-commutative`
1×	`pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-pow` `diff-log` `pow-exp` `flip--` `unpow2` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

2.0ms	(pow (sin phi1) 2)
8.0ms	(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
6.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
3.0ms	(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin phi1) 2)
25.0ms	(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
16.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
15.0ms	(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	380	597
1	1531	481
2	5002	469

prune143.0ms

Filtered

52 candidates to 82 candidates (-57.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Merged error: 0.0b

Counts

89 → 7

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.7b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
1.0b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite14.0ms

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)))))))))

series134.0ms

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))))
48.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
45.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify83.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (20.0ms)

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

prune97.0ms

Filtered

51 candidates to 69 candidates (-35.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

regimes626.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	21
1	29	21

end0.0ms

sample21.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 14.941406%

Results

5.6s	3143×	body	1280	valid
1.9s	1852×	body	640	valid
712.0ms	1971×	body	80	valid
488.0ms	743×	body	320	valid
122.0ms	291×	body	160	valid

Details

sample12.6s

simplify7.0ms

prune6.0ms

localize32.0ms

rewrite11.0ms

series100.0ms

simplify83.0ms

prune138.0ms

localize29.0ms

rewrite28.0ms

series89.0ms

simplify50.0ms

prune165.0ms

localize30.0ms

rewrite22.0ms

series60.0ms

simplify49.0ms

prune143.0ms

localize39.0ms

rewrite14.0ms

series134.0ms

simplify83.0ms

prune97.0ms

regimes626.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample21.4s

Profiling