Details

sample269.0ms

Algorithm

intervals

Results

169.0ms	99×	body	1280	valid
49.0ms	53×	body	640	valid
15.0ms	25×	body	320	valid
11.0ms	64×	body	80	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

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

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(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))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite17.0ms

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

series381.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin theta) (sin delta))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
153.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify96.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (25.0ms)

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

prune404.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 0.1b

Counts

71 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.2b	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
5.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.0ms	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
156.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
177.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
7.0ms	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	326	1752
1	945	1631
2	3851	1619
3	5001	1587

prune462.0ms

Filtered

79 candidates to 57 candidates (72.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 0.1b

Counts

89 → 10

localize47.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod` `log-pow`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
12×	`pow1` `exp-prod` `sqrt-prod`
8×	`add-exp-log`
4×	`log-div` `asin-acos` `pow1/2` `exp-diff` `sqrt-div` `rem-log-exp` `add-cbrt-cube` `add-log-exp`

Counts

4 → 84

Calls

4 calls:

4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
69.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
68.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
68.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 7 (78.0ms)

Iter	Nodes	Cost
0	86	1716
1	103	1552
2	117	1552
3	152	1552
4	276	1552
5	663	1552
6	2884	1552
7	5001	1544

prune776.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	95	11	106

Merged error: 0.0b

Counts

106 → 11

localize66.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.6b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.6b	(- (log (sqrt (exp (/ PI 2)))) (log (sqrt (exp (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
28×	`log-pow`
23×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`pow1` `sqrt-pow1`
15×	`sqrt-prod`
11×	`exp-prod`
7×	`add-exp-log`
6×	`associate--l+` `associate--r+` `distribute-lft-out--`
5×	`pow1/2`
4×	`log-div` `exp-diff` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`asin-acos` `rem-log-exp`
1×	`acos-asin` `sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--` `associate--r-` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
24.0ms	(- (log (sqrt (exp (/ PI 2)))) (log (sqrt (exp (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
68.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
64.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
254.0ms	(- (log (sqrt (exp (/ PI 2)))) (log (sqrt (exp (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	210	2072
1	336	1909
2	509	1907
3	1520	1893
4	5001	1893

prune1.1s

Filtered

108 candidates to 81 candidates (75.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	108	11	119

Merged error: 0.0b

Counts

119 → 11

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 (0.0ms)

Iter	Nodes	Cost
0	53	77
1	53	77

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.2s	3144×	body	1280	valid
1.7s	1801×	body	640	valid
462.0ms	741×	body	320	valid
353.0ms	1956×	body	80	valid
161.0ms	358×	body	160	valid