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	77×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	13×	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: 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))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

2.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune119.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

15.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series108.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune268.0ms

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)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) x))
0.3b	(+ (cos x) 1.0)
0.3b	(pow (cos x) 3)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

48.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) x))
3.0ms	(+ (cos x) 1.0)
1.0ms	(pow (cos x) 3)
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series262.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) x))
9.0ms	(+ (cos x) 1.0)
27.0ms	(pow (cos x) 3)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	565	1583
1	2568	1474
2	5002	1430

prune308.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (cos x) 1.0)
0.3b	(pow (cos x) 3)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))
1.3b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
31×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

3.0ms	(+ (cos x) 1.0)
1.0ms	(pow (cos x) 3)
14.0ms	(- (pow 1.0 3) (pow (cos x) 3))
50.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series138.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))
49.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	673
1	1242	636
2	5001	608

prune275.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.0b

bsearch83.0ms

Steps

Iters	Range		Point
9	0.006665254470786589	7065.8830381017015	0.03227201473457714
9	-14674.600957416102	-0.00012459925560949148	-0.031162295522048522

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	55
1	61	55

end0.0ms

sample1.5s

Algorithm

intervals

Results

697.0ms	1542×	body	2560	valid
286.0ms	1264×	body	1280	valid
218.0ms	1501×	body	640	valid
97.0ms	925×	body	320	valid
68.0ms	2295×	body	80	valid
33.0ms	473×	body	160	valid