Details

sample327.0ms

Algorithm

intervals

Results

23.0ms	57×	body	1280	valid
10.0ms	165×	body	80	valid
10.0ms	33×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	16×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune9.0ms

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

localize14.0ms

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)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

9.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
17.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
10.0ms	(* x (/ 1.0 (tan B)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
37.0ms	(/ 1.0 (tan B))
124.0ms	(* x (/ 1.0 (tan B)))

simplify56.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635

prune359.0ms

Filtered

129 candidates to 104 candidates (80.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	6	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0.0b

Counts

130 → 6

localize16.0ms

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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`fma-neg` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 204

Calls

4 calls:

14.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
5.0ms	(* x (cos B))
4.0ms	(/ 1 (sin B))
5.0ms	(/ (* x (cos B)) (sin B))

series244.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
40.0ms	(* x (cos B))
13.0ms	(/ 1 (sin B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify81.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	579	3808
1	2173	2513
2	5001	2510

prune334.0ms

Filtered

216 candidates to 96 candidates (44.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	215	7	222

Merged error: 0.0b

Counts

222 → 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)))

rewrite27.0ms

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` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (sin B))
7.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
7.0ms	(* x (/ 1.0 (sin B)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1.0 (sin B))
24.0ms	(/ 1.0 (sin B))
105.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
59.0ms	(* x (/ 1.0 (sin B)))

simplify50.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	325	672
1	1587	587
2	5001	587

prune321.0ms

Filtered

127 candidates to 92 candidates (72.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	128	6	134

Merged error: 0.0b

Counts

134 → 6

localize16.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 152

Calls

4 calls:

14.0ms	(* (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)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
141.0ms	(cbrt (/ 1.0 (sin B)))
135.0ms	(cbrt (/ 1.0 (sin B)))
143.0ms	(cbrt (/ 1.0 (sin B)))

simplify51.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	309	1462
1	1149	1406
2	5001	1336

prune550.0ms

Filtered

164 candidates to 130 candidates (79.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	163	7	170

Merged error: 0b

Counts

170 → 7

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

sample1.7s

Algorithm

intervals

Results

702.0ms	1707×	body	1280	valid
350.0ms	1395×	body	640	valid
291.0ms	4920×	body	80	valid
140.0ms	784×	body	320	valid
49.0ms	362×	body	160	valid