Details

sample278.0ms

Algorithm

intervals

Results

176.0ms	111×	body	1280	valid
39.0ms	43×	body	640	valid
15.0ms	16×	body	320	valid
12.0ms	70×	body	80	valid
6.0ms	16×	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

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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 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))))
0.5b	(- (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 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)))))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
35.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
45.0ms	(- (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

prune176.0ms

Filtered

70 candidates to 51 candidates (27.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	11	71

Merged error: 0.0b

Counts

71 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.5b	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
14.6b	(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`cbrt-prod`
8×	`*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt` `add-log-exp`
3×	`pow-unpow` `difference-of-squares` `sqr-pow`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `sin-mult` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `asin-acos` `cbrt-div` `flip3--` `pow1/3` `diff-log` `pow-prod-down` `prod-exp` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
6.0ms	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
3.0ms	(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series151.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
65.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
46.0ms	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
35.0ms	(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	312	1435
1	1078	1294
2	5001	1290

prune184.0ms

Filtered

77 candidates to 56 candidates (27.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	77	11	88

Merged error: 0.0b

Counts

88 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-cbrt-cube`
3×	`pow-unpow` `difference-of-squares`
2×	`asin-acos` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `unpow-prod-down` `sqr-cos` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `flip--`

Counts

4 → 50

Calls

4 calls:

5.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 2)
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 2))

series203.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 2)
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
142.0ms	(- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	326	1111
1	1331	1021
2	5001	1006

prune167.0ms

Filtered

62 candidates to 46 candidates (25.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	62	11	73

Merged error: 0.0b

Counts

73 → 11

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin phi1) 3)
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(pow (sin phi1) 4)
0.5b	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`add-cbrt-cube`
3×	`cube-prod`
2×	`pow-to-exp` `distribute-rgt-out--` `pow-pow` `pow-exp` `sqr-pow`
1×	`cube-mult` `sub-neg` `asin-acos` `flip3--` `diff-log` `unpow3` `flip--` `rem-cube-cbrt`

Counts

4 → 62

Calls

4 calls:

3.0ms	(pow (sin phi1) 3)
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(pow (sin phi1) 4)
5.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (sin phi1) 3)
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms	(pow (sin phi1) 4)
22.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	291	484
1	1129	424
2	5001	402

prune191.0ms

Filtered

74 candidates to 47 candidates (36.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	73	12	85

Merged error: 0.0b

Counts

85 → 12

regimes701.0ms

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

sample8.4s

Algorithm

intervals

Results

5.1s	3143×	body	1280	valid
1.8s	1763×	body	640	valid
443.0ms	732×	body	320	valid
368.0ms	2025×	body	80	valid
138.0ms	337×	body	160	valid

Details

sample278.0ms

simplify6.0ms

prune7.0ms

localize32.0ms

rewrite16.0ms

series95.0ms

simplify89.0ms

prune176.0ms

localize35.0ms

rewrite17.0ms

series151.0ms

simplify42.0ms

prune184.0ms

localize41.0ms

rewrite15.0ms

series203.0ms

simplify45.0ms

prune167.0ms

localize59.0ms

rewrite13.0ms

series38.0ms

simplify42.0ms

prune191.0ms

regimes701.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.4s

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