Details

sample283.0ms

Algorithm

intervals

Results

163.0ms	104×	body	1280	valid
66.0ms	73×	body	640	valid
15.0ms	16×	body	320	valid
9.0ms	52×	body	80	valid
8.0ms	11×	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: 0.2b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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))
6.0ms	(* (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))))
9.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin theta) (sin delta))
154.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
187.0ms	(- (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 (27.0ms)

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

prune375.0ms

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

localize35.0ms

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))))
0.6b	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
1.9b	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `add-log-exp`
4×	`log-pow`
3×	`associate-r` `associate-l` `associate--r+`
2×	`distribute-lft-out--`
1×	`sub-neg` `asin-acos` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `difference-of-squares` `unswap-sqr`

Counts

4 → 59

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))))
6.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (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))))
188.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
160.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify81.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	250	1229
1	686	1110
2	2590	1106
3	5002	1106

prune368.0ms

Filtered

71 candidates to 53 candidates (74.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 0.1b

Counts

80 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
2.7b	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sin-sum`
8×	`*-un-lft-identity` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-rgt-in` `acos-asin` `add-cube-cbrt` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `associate--r+`
5×	`associate--r-`
3×	`associate-r` `associate-l`
2×	`flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

12.0ms	(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
1.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
8.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
12.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
192.0ms	(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
36.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify138.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	311	1574
1	910	1389
2	3654	1325
3	5001	1306

prune415.0ms

Filtered

79 candidates to 57 candidates (72.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	78	10	88

Merged error: 0.1b

Counts

88 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
12.0b	(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
58.2b	(cos (/ PI 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
2×	`acos-asin`
1×	`cos-diff` `sub-neg` `flip3--` `cos-PI/2` `diff-log` `cos-acos` `flip--`

Counts

4 → 37

Calls

4 calls:

1.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
2.0ms	(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
2.0ms	(cos (/ PI 2))

series314.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
183.0ms	(- (cos delta) (* (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
123.0ms	(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.0ms	(cos (/ PI 2))

simplify81.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	207	712
1	486	618
2	1834	600
3	5001	600

prune302.0ms

Filtered

47 candidates to 39 candidates (83.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	47	10	57

Merged error: 0.1b

Counts

57 → 10

regimes404.0ms

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	32	24
1	32	24

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.2s	3166×	body	1280	valid
1.9s	1847×	body	640	valid
448.0ms	718×	body	320	valid
359.0ms	1956×	body	80	valid
126.0ms	313×	body	160	valid

Details

sample283.0ms

simplify8.0ms

prune5.0ms

localize33.0ms

rewrite23.0ms

series399.0ms

simplify96.0ms

prune375.0ms

localize35.0ms

rewrite18.0ms

series517.0ms

simplify81.0ms

prune368.0ms

localize40.0ms

rewrite28.0ms

series394.0ms

simplify138.0ms

prune415.0ms

localize44.0ms

rewrite10.0ms

series314.0ms

simplify81.0ms

prune302.0ms

regimes404.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.4s

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