Details

sample288.0ms

Algorithm

intervals

Results

171.0ms	104×	body	1280	valid
60.0ms	58×	body	640	valid
15.0ms	24×	body	320	valid
10.0ms	59×	body	80	valid
5.0ms	11×	body	160	valid

simplify6.0ms

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

prune8.0ms

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

localize38.0ms

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

rewrite15.0ms

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:

4.0ms	(* (sin theta) (sin delta))
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))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin theta) (sin delta))
144.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
170.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (24.0ms)

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

prune492.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.0b

Counts

71 → 7

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.9b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

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))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
168.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
168.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify85.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	253	1234
1	764	1106
2	2949	1102
3	5001	1102

prune484.0ms

Filtered

69 candidates to 50 candidates (72.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (sin (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))
0.6b	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

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	(- (cos delta) (* (sin phi1) (sin (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)

series566.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
164.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
166.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
227.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

simplify43.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	288	1796
1	1015	1670
2	5002	1664

prune500.0ms

Filtered

80 candidates to 49 candidates (61.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	79	8	87

Merged error: 0.0b

Counts

87 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(pow (sin phi1) 2)
0.3b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.4b	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite24.0ms

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:

4.0ms	(* (sin theta) (sin delta))
2.0ms	(pow (sin phi1) 2)
8.0ms	(* (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))))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin theta) (sin delta))
18.0ms	(pow (sin phi1) 2)
88.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
171.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (42.0ms)

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

prune439.0ms

Filtered

86 candidates to 54 candidates (62.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	87	7	94

Merged error: 0.0b

Counts

94 → 7

regimes558.0ms

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	29	21
1	29	21

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.1s	3105×	body	1280	valid
1.7s	1737×	body	640	valid
468.0ms	750×	body	320	valid
376.0ms	2101×	body	80	valid
125.0ms	307×	body	160	valid

Details

sample288.0ms

simplify6.0ms

prune8.0ms

localize38.0ms

rewrite15.0ms

series362.0ms

simplify89.0ms

prune492.0ms

localize39.0ms

rewrite15.0ms

series483.0ms

simplify85.0ms

prune484.0ms

localize36.0ms

rewrite14.0ms

series566.0ms

simplify43.0ms

prune500.0ms

localize28.0ms

rewrite24.0ms

series322.0ms

simplify49.0ms

prune439.0ms

regimes558.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.3s

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