Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	45×	body	2560	valid
8.0ms	39×	body	1280	valid
6.0ms	42×	body	640	valid
3.0ms	89×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	16×	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: 28.4b

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
12.8b	(/ (- 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:

4.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

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

prune132.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
46×	`times-frac`
36×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `prod-diff`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `fma-neg` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 132

Calls

3 calls:

17.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
7.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series107.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
42.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify72.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	582	999
1	2640	823
2	5001	787

prune258.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite27.0ms

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:

9.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series107.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (/ (- 1.0 (cos x)) x) x)
47.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify65.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (46.0ms)

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

prune310.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (expm1 (log1p (- 1.0 (cos x)))) x)
0.1b	(log1p (- 1.0 (cos x)))
0.3b	(expm1 (log1p (- 1.0 (cos x))))
1.5b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

3.0ms	(/ (expm1 (log1p (- 1.0 (cos x)))) x)
1.0ms	(log1p (- 1.0 (cos x)))
1.0ms	(expm1 (log1p (- 1.0 (cos x))))
5.0ms	(- 1.0 (cos x))

series491.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (expm1 (log1p (- 1.0 (cos x)))) x)
106.0ms	(log1p (- 1.0 (cos x)))
154.0ms	(expm1 (log1p (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	298	624
1	933	479
2	5001	448

prune196.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.5b

bsearch78.0ms

Steps

Iters	Range		Point
10	9.598072339636849e-08	814.2255113159289	0.03176890082881835
11	-402.67606408878214	-1.1015269942960052e-19	-0.034487839009759345

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

779.0ms	1666×	body	2560	valid
286.0ms	1211×	body	1280	valid
219.0ms	1506×	body	640	valid
96.0ms	926×	body	320	valid
70.0ms	2227×	body	80	valid
40.0ms	464×	body	160	valid