Details

sample62.0ms

Algorithm

intervals

Results

24.0ms	57×	body	1280	valid
10.0ms	165×	body	80	valid
9.0ms	33×	body	640	valid
6.0ms	31×	body	320	valid
2.0ms	16×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

7.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
107.0ms	(* x (/ 1.0 (tan B)))

simplify48.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604

prune291.0ms

Filtered

115 candidates to 90 candidates (78.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	6	116

Merged error: 0.0b

Counts

116 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

9.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
4.0ms	(* x (cos B))
4.0ms	(/ 1 (sin B))
5.0ms	(/ (* x (cos B)) (sin B))

series229.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
37.0ms	(* x (cos B))
12.0ms	(/ 1 (sin B))
92.0ms	(/ (* x (cos B)) (sin B))

simplify43.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	309	612
1	1342	540
2	5002	535

prune206.0ms

Filtered

104 candidates to 65 candidates (62.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	103	7	110

Merged error: 0.0b

Counts

110 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

3.0ms	(/ 1.0 (sin B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
7.0ms	(* x (/ 1.0 (sin B)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
21.0ms	(/ 1.0 (sin B))
98.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
55.0ms	(* x (/ 1.0 (sin B)))

simplify48.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	315	645
1	1562	560
2	5001	560

prune273.0ms

Filtered

119 candidates to 84 candidates (70.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Merged error: 0.0b

Counts

126 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

15.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
133.0ms	(cbrt (/ 1.0 (sin B)))
131.0ms	(cbrt (/ 1.0 (sin B)))
132.0ms	(cbrt (/ 1.0 (sin B)))

simplify50.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	301	1430
1	1123	1366
2	5002	1300

prune501.0ms

Filtered

156 candidates to 122 candidates (78.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	155	8	163

Merged error: 0b

Counts

163 → 8

regimes68.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

736.0ms	1707×	body	1280	valid
381.0ms	1395×	body	640	valid
312.0ms	4920×	body	80	valid
149.0ms	784×	body	320	valid
48.0ms	362×	body	160	valid