Details

sample270.0ms

Algorithm

intervals

Results

170.0ms	105×	body	1280	valid
53.0ms	58×	body	640	valid
14.0ms	23×	body	320	valid
10.0ms	60×	body	80	valid
4.0ms	10×	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

localize42.0ms

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)))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

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

series417.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin theta) (sin delta))
164.0ms	(* (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))))
195.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	296	1030
1	898	937
2	3397	935
3	5001	935

prune344.0ms

Filtered

74 candidates to 53 candidates (71.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	10	75

Merged error: 0.1b

Counts

75 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

144×	`add-sqr-sqrt`
59×	`unswap-sqr`
45×	`difference-of-squares`
32×	`*-un-lft-identity`
27×	`swap-sqr`
14×	`*-commutative`
13×	`associate-l`
10×	`distribute-lft-out--`
6×	`sin-mult` `add-log-exp`
5×	`cos-mult`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`asin-acos` `frac-sub`
2×	`associate-r/` `associate-l/` `sub-div`
1×	`frac-times` `sub-neg` `sqr-cos` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

4 → 97

Calls

4 calls:

3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
51.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
522.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	424	3797
1	1633	3248
2	5001	3215

prune419.0ms

Filtered

109 candidates to 51 candidates (46.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	110	9	119

Merged error: 0.1b

Counts

119 → 9

localize57.0ms

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) 3)
0.5b	(pow (sin phi1) 4)
0.5b	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
56×	`unpow-prod-down`
52×	`difference-of-squares`
48×	`unswap-sqr`
45×	`sqr-pow`
27×	`unpow2`
22×	`*-un-lft-identity`
12×	`add-cube-cbrt` `distribute-rgt-out--`
10×	`associate-r`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`add-cbrt-cube`
2×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `unpow3` `associate-l` `flip--` `rem-cube-cbrt`

Counts

4 → 122

Calls

4 calls:

3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(pow (sin phi1) 3)
2.0ms	(pow (sin phi1) 4)
23.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
35.0ms	(pow (sin phi1) 3)
34.0ms	(pow (sin phi1) 4)
100.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	605	1443
1	1722	1224
2	5001	1184

prune755.0ms

Filtered

134 candidates to 63 candidates (47.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 0.0b

Counts

143 → 8

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.6b	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
5.6b	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
59×	`unswap-sqr`
45×	`difference-of-squares`
37×	`*-un-lft-identity`
27×	`swap-sqr`
14×	`*-commutative`
13×	`associate-l`
10×	`distribute-lft-out--`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`unpow-prod-down` `sin-mult` `add-log-exp`
5×	`pow1` `add-exp-log` `cos-mult` `add-cbrt-cube`
4×	`pow-unpow`
3×	`frac-sub`
2×	`unpow3` `associate-r/` `associate-l/` `rem-cbrt-cube` `sub-div` `sqr-pow`
1×	`frac-times` `pow-to-exp` `sub-neg` `asin-acos` `sqr-cos` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `associate--l+` `flip--` `rem-cube-cbrt`

Counts

4 → 118

Calls

4 calls:

3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
53.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
8.0ms	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
3.0ms	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series571.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
522.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
34.0ms	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0ms	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify85.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	500	4099
1	1979	3561
2	5002	3551

prune483.0ms

Filtered

130 candidates to 56 candidates (43.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Merged error: 0.0b

Counts

138 → 8

regimes437.0ms

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	48	56
1	48	56

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.9s	3049×	body	1280	valid
1.9s	1838×	body	640	valid
409.0ms	713×	body	320	valid
334.0ms	2061×	body	80	valid
131.0ms	339×	body	160	valid