Details

sample275.0ms

Algorithm

intervals

Results

173.0ms	99×	body	1280	valid
50.0ms	53×	body	640	valid
15.0ms	25×	body	320	valid
11.0ms	64×	body	80	valid
6.0ms	15×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize33.0ms

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

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

Counts

4 → 72

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)))))))

series377.0ms

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))))
150.0ms	(* (sin phi1) (sin (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)))))))

simplify113.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	322	1198
1	1021	1064
2	4124	1059
3	5001	1054

prune489.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	10	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.1b

Counts

85 → 10

localize37.0ms

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))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sin-sum`
7×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `associate--r+` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l` `prod-diff`
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 → 81

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
8.0ms	(- (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))))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
151.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
179.0ms	(- (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))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	359	2066
1	1073	1898
2	4511	1881
3	5001	1874

prune535.0ms

Filtered

93 candidates to 73 candidates (78.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	92	11	103

Merged error: 0.1b

Counts

103 → 11

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)))))))

rewrite22.0ms

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×	`expm1-log1p-u` `log-div` `asin-acos` `pow1/2` `exp-diff` `sqrt-div` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 92

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)))))))
8.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
66.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
66.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
61.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 7 (83.0ms)

Iter	Nodes	Cost
0	90	1828
1	113	1664
2	128	1664
3	163	1664
4	288	1664
5	687	1664
6	2989	1664
7	5001	1656

prune790.0ms

Filtered

104 candidates to 80 candidates (76.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	104	11	115

Merged error: 0.0b

Counts

115 → 11

localize69.0ms

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))))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

302×	`log-pow`
232×	`sqrt-pow1`
198×	`exp-prod`
171×	`prod-diff`
141×	`*-un-lft-identity`
137×	`add-sqr-sqrt`
135×	`add-cube-cbrt`
90×	`times-frac`
74×	`pow1`
34×	`pow1/2`
30×	`log-prod`
19×	`fma-neg`
15×	`sqrt-prod`
10×	`div-inv`
7×	`add-exp-log`
6×	`associate--l+` `associate--r+` `distribute-lft-out--`
4×	`expm1-log1p-u` `log-div` `exp-diff` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `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 → 294

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)))))))
26.0ms	(- (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:

63.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
67.0ms	(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)))))))
255.0ms	(- (log (sqrt (exp (/ PI 2)))) (log (sqrt (exp (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify246.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	699	15094
1	1436	9175
2	4937	8574
3	5001	8574

prune1.6s

Filtered

306 candidates to 130 candidates (42.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	306	11	317

Merged error: 0.0b

Counts

317 → 11

regimes484.0ms

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

sample8.7s

Algorithm

intervals

Results

5.5s	3144×	body	1280	valid
1.8s	1801×	body	640	valid
495.0ms	741×	body	320	valid
393.0ms	1956×	body	80	valid
168.0ms	358×	body	160	valid