Details

sample264.0ms

Algorithm

intervals

Results

162.0ms	99×	body	1280	valid
62.0ms	67×	body	640	valid
12.0ms	71×	body	80	valid
8.0ms	15×	body	320	valid
1.0ms	4×	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

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: 0.1b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.2b	(* (sin theta) (sin delta))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (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 → 58

Calls

4 calls:

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

series450.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
49.0ms	(* (sin theta) (sin delta))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
245.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify99.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	289	930
1	894	837
2	3513	835
3	5002	835

prune382.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Merged error: 0.1b

Counts

71 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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	(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)))))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
178.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
243.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)
179.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	288	1800
1	1010	1672
2	5001	1664

prune371.0ms

Filtered

80 candidates to 50 candidates (62.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 0.1b

Counts

89 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin phi1) 2)
0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.6b	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log`
15×	`add-cbrt-cube`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
4×	`associate-r`
3×	`unpow-prod-down` `pow-unpow`
2×	`diff-log` `*-commutative`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `sin-mult` `associate--r+` `distribute-lft-out--` `unpow2` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

2.0ms	(pow (sin phi1) 2)
5.0ms	(* (sin theta) (sin delta))
9.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
7.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sin phi1) 2)
43.0ms	(* (sin theta) (sin delta))
91.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
307.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	400	786
1	1562	674
2	5001	673

prune339.0ms

Filtered

86 candidates to 54 candidates (62.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	88	8	96

Merged error: 0.0b

Counts

96 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.6b	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
0.8b	(log (exp (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
15×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l` `log-pow`
5×	`log-prod` `exp-prod`
4×	`associate-r`
2×	`sub-neg` `diff-log` `exp-sum` `*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`log-div` `flip3--` `exp-diff` `rem-log-exp` `sum-log` `flip--` `sin-mult` `associate--r+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

4.0ms	(* (sin theta) (sin delta))
9.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
7.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
10.0ms	(log (exp (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin theta) (sin delta))
91.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
177.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
177.0ms	(log (exp (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	360	1114
1	1370	967
2	5001	966

prune361.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	87	9	96

Merged error: 0.0b

Counts

96 → 9

regimes349.0ms

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	33	24
1	33	24

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.1s	3194×	body	1280	valid
1.6s	1766×	body	640	valid
426.0ms	703×	body	320	valid
351.0ms	2027×	body	80	valid
116.0ms	310×	body	160	valid