Details

sample54.0ms

Algorithm

intervals

Results

26.0ms	56×	body	2560	valid
9.0ms	39×	body	1280	valid
6.0ms	45×	body	640	valid
3.0ms	26×	body	320	valid
3.0ms	77×	body	80	valid
1.0ms	13×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize6.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
17.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune136.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.2b	(/ (- 1.0 (cos x)) x)
1.4b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 165

Calls

3 calls:

11.0ms	(/ (/ (- 1.0 (cos x)) x) x)
9.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series109.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283

prune296.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.3b	(pow (cos x) 3)
0.3b	(fma (cos x) (cos x) (* 1.0 (cos x)))
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
144×	`prod-diff`
114×	`unpow-prod-down` `*-un-lft-identity` `cube-prod`
84×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 297

Calls

4 calls:

57.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
1.0ms	(pow (cos x) 3)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
24.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series325.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
27.0ms	(pow (cos x) 3)
51.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify128.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	766	3804
1	2949	2790
2	5001	2733

prune413.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.3b	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.3b	(fma (cos x) (cos x) (* 1.0 (cos x)))
30.6b	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
18×	`unpow-prod-down` `cube-prod`
12×	`fma-neg` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`times-frac` `associate-/l*` `sqr-pow`
6×	`add-log-exp`
5×	`pow1` `cube-mult` `unpow3`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv` `expm1-udef` `associate--r-` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

1.0ms	(pow (cos x) 3)
32.0ms	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
13.0ms	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (cos x) 3)
381.0ms	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
50.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
194.0ms	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

simplify93.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	548	1814
1	2426	1305
2	5001	1293

prune363.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 29.9b

bsearch67.0ms

Steps

Iters	Range		Point
9	0.006665254470786589	7065.8830381017015	0.033493863120598724
9	-14674.600957416102	-0.00012459925560949148	-0.0343424885078094

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	32
1	39	32

end0.0ms

sample1.7s

Algorithm

intervals

Results

699.0ms	1542×	body	2560	valid
360.0ms	1501×	body	640	valid
312.0ms	1264×	body	1280	valid
92.0ms	925×	body	320	valid
68.0ms	2295×	body	80	valid
33.0ms	473×	body	160	valid