Details

sample73.0ms

Algorithm

intervals

Results

25.0ms	46×	body	2560	valid
16.0ms	39×	body	1280	valid
13.0ms	60×	body	640	valid
5.0ms	34×	body	320	valid
5.0ms	70×	body	80	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.3b

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
13.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

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))

series64.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 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

prune122.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
13.2b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

6.0ms	(* 1/24 (pow x 2))
0.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series70.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
46.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify103.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	139	194
1	532	171
2	2601	171
3	5001	170

prune104.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`times-frac`
40×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 158

Calls

4 calls:

12.0ms	(/ (sqrt (- 1.0 (cos x))) x)
8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sqrt (- 1.0 (cos x))) x)
92.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify179.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 3 (166.0ms)

Iter	Nodes	Cost
0	301	1368
1	936	1148
2	4953	1118
3	5001	1112

prune352.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (- 1.0 (cos x)) 3)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`prod-diff`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
8×	`add-log-exp`
6×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 116

Calls

4 calls:

5.0ms	(pow (- 1.0 (cos x)) 3)
5.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series101.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (- 1.0 (cos x)) 3)
23.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	295	803
1	1139	612
2	5001	606

prune267.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes81.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch97.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.028129396018266136
10	-1.7081313977704333	-1.7977825652338532e-10	-0.03302109030086143

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	24
1	38	24

end0.0ms

sample2.1s

Algorithm

intervals

Results

924.0ms	1625×	body	2560	valid
412.0ms	1261×	body	1280	valid
318.0ms	1436×	body	640	valid
146.0ms	914×	body	320	valid
141.0ms	2294×	body	80	valid
59.0ms	470×	body	160	valid