Details

sample54.0ms

Algorithm

intervals

Results

25.0ms	58×	body	2560	valid
9.0ms	36×	body	1280	valid
8.0ms	54×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	73×	body	80	valid
1.0ms	11×	body	160	valid

simplify7.0ms

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: 32.9b

localize7.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
17.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

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

prune131.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(* 1/24 (pow x 2))
13.7b	(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:

5.0ms	(* 1/24 (pow x 2))
1.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series69.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
44.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify101.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	139	203
1	565	171
2	2616	171
3	5001	170

prune111.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

6.0ms	(cbrt (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series178.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify97.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	208	863
1	622	569
2	2937	535
3	5002	482

prune240.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.8b	(- (pow 1.0 3) (pow (cos x) 3))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

162×	`prod-diff`
121×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
93×	`add-cube-cbrt`
87×	`unpow-prod-down` `cube-prod`
33×	`sqr-pow`
25×	`cube-mult` `unpow3`
18×	`fma-neg` `difference-of-squares`
12×	`add-log-exp`
7×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `sqr-cos` `associate-+l+` `distribute-rgt-out` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 264

Calls

4 calls:

5.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
16.0ms	(- (pow 1.0 3) (pow (cos x) 3))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series128.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify141.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	641	2981
1	2525	2020
2	5001	2008

prune478.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

regimes56.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.3b

bsearch96.0ms

Steps

Iters	Range		Point
9	1.2358748968334836e-07	0.22405535791780642	0.03173609678414467
9	-0.11986014733990268	-1.6789357321840064e-10	-0.03018149556589929

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	57
1	50	57

end0.0ms

sample1.6s

Algorithm

intervals

Results

774.0ms	1673×	body	2560	valid
301.0ms	1285×	body	1280	valid
229.0ms	1497×	body	640	valid
100.0ms	852×	body	320	valid
70.0ms	2215×	body	80	valid
35.0ms	478×	body	160	valid