Details

sample142.0ms

Algorithm

intervals

Results

77.0ms	57×	body	2560	valid
36.0ms	80×	body	1280	valid
13.0ms	58×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	10×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 1.0 (cos x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune177.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	59	15	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	15	75

Merged error: 0.3b

Counts

75 → 15

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series174.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
122.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify34.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	61	148
1	188	130
2	1009	130
3	5002	130

prune106.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	26	15	41

Merged error: 0.3b

Counts

41 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.2b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series139.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune311.0ms

Filtered

144 candidates to 102 candidates (70.8%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	142	17	159

Merged error: 0.2b

Counts

159 → 17

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.2b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 177

Calls

3 calls:

8.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series92.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify69.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	572	1779
1	2636	1549
2	5001	1441

prune214.0ms

Filtered

186 candidates to 95 candidates (51.1%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	0	14	14
Picked	1	0	1
Done	0	2	2
Total	185	18	203

Merged error: 0.2b

Counts

203 → 18

regimes173.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 31.8b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	32
1	35	32

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	1543×	body	2560	valid
1.5s	2760×	body	1280	valid
458.0ms	1940×	body	640	valid
147.0ms	897×	body	320	valid
63.0ms	486×	body	160	valid
24.0ms	373×	body	80	valid
3.0ms	1×	body	5120	valid