Details

sample313.0ms

Algorithm

intervals

Results

20.0ms	49×	body	1280	valid
14.0ms	55×	body	640	valid
11.0ms	165×	body	80	valid
3.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid

simplify18.0ms

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)))

rewrite43.0ms

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:

8.0ms	(+ (- (* 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)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
34.0ms	(/ 1.0 (tan B))
126.0ms	(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (43.0ms)

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

prune330.0ms

Filtered

129 candidates to 104 candidates (80.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Merged error: 0.0b

Counts

130 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

20.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (* x 1.0) (tan B))

series241.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
109.0ms	(/ (* x 1.0) (tan B))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	350	492
1	1353	445
2	5002	440

prune224.0ms

Filtered

100 candidates to 81 candidates (81.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	100	9	109

Merged error: 0.0b

Counts

109 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series741.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt x) (cbrt x))
178.0ms	(cbrt x)
182.0ms	(cbrt x)
179.0ms	(cbrt x)

simplify95.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune251.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 0.0b

Counts

102 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:

3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
13.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (/ 1.0 (sin B)))
135.0ms	(cbrt (/ 1.0 (sin B)))
141.0ms	(cbrt (/ 1.0 (sin B)))
181.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify50.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	309	1462
1	1156	1406
2	5001	1336

prune473.0ms

Filtered

164 candidates to 130 candidates (79.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	163	10	173

Merged error: 0b

Counts

173 → 10

regimes84.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	20	7
2	20	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

745.0ms	1745×	body	1280	valid
376.0ms	1436×	body	640	valid
301.0ms	4934×	body	80	valid
120.0ms	640×	body	320	valid
45.0ms	351×	body	160	valid