Details

sample260.0ms

Algorithm

intervals

Results

162.0ms	103×	body	1280	valid
48.0ms	50×	body	640	valid
16.0ms	27×	body	320	valid
11.0ms	67×	body	80	valid
4.0ms	9×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	22
1	61	22
2	71	22
3	72	22
4	72	22

prune5.0ms

Filtered

1 candidates to 0 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: 0.2b

Counts

2 → 1

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (sin delta)) (cos theta))
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))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* (* (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)))))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* (cos phi1) (sin delta)) (cos theta))
152.0ms	(* (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))))
176.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1246
1	1294	1093
2	5001	1088

prune441.0ms

Filtered

83 candidates to 65 candidates (78.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 0.1b

Counts

84 → 8

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `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 → 70

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(pow (cos delta) 3)
6.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series272.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
28.0ms	(pow (cos delta) 3)
231.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	260	852
1	1060	748
2	5002	744

prune535.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 0.1b

Counts

90 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.6b	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.7b	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `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×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `prod-diff`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `asin-acos` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 78

Calls

4 calls:

2.0ms	(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
3.0ms	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
2.0ms	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series226.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
173.0ms	(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
35.0ms	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0ms	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify172.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	258	1606
1	863	1462
2	4709	1451
3	5001	1450

prune450.0ms

Filtered

90 candidates to 56 candidates (62.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 0.1b

Counts

100 → 10

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `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 → 70

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(pow (cos delta) 3)
6.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series269.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
27.0ms	(pow (cos delta) 3)
229.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	260	856
1	1058	748
2	5001	744

prune493.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	82	10	92

Merged error: 0.1b

Counts

92 → 10

regimes442.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	42	58
1	42	58

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.0s	3143×	body	1280	valid
1.7s	1848×	body	640	valid
457.0ms	757×	body	320	valid
316.0ms	1957×	body	80	valid
115.0ms	295×	body	160	valid