Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	54×	body	2560	valid
8.0ms	39×	body	1280	valid
6.0ms	47×	body	640	valid
3.0ms	32×	body	320	valid
2.0ms	66×	body	80	valid
1.0ms	18×	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: 30.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.1b	(- 1.0 (cos x))
14.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite30.0ms

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:

10.0ms	(- 1.0 (cos x))
19.0ms	(/ (- 1.0 (cos x)) (* x x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
38.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

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

prune111.0ms

Pruning

9 alts after pruning (9 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)
0.1b	(/ (- 1.0 (cos x)) x)
1.1b	(- 1.0 (cos x))

rewrite51.0ms

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:

20.0ms	(/ (/ (- 1.0 (cos x)) x) x)
18.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series95.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
17.0ms	(- 1.0 (cos x))

simplify55.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (37.0ms)

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

prune278.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

74.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
25.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series200.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
25.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify96.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5001	2810

prune408.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (- 1.0 (cos x))) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.4b	(+ (cos x) 1.0)
0.4b	(+ (cos x) 1.0)
1.1b	(- 1.0 (cos x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

52.0ms	(/ (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (- 1.0 (cos x))) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
6.0ms	(+ (cos x) 1.0)
6.0ms	(+ (cos x) 1.0)
6.0ms	(- 1.0 (cos x))

series56.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (- 1.0 (cos x))) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
9.0ms	(+ (cos x) 1.0)
9.0ms	(+ (cos x) 1.0)
17.0ms	(- 1.0 (cos x))

simplify52.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	378	886
1	1856	759
2	5001	577

prune195.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.7b

bsearch78.0ms

Steps

Iters	Range		Point
11	1.661404138935296e-22	2.5556453819330236	0.031210463015068444
9	-0.04331797882383785	-2.2082264187638084e-10	-0.03408999554764363

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample1.5s

Algorithm

intervals

Results

711.0ms	1572×	body	2560	valid
280.0ms	1279×	body	1280	valid
211.0ms	1512×	body	640	valid
89.0ms	928×	body	320	valid
72.0ms	2237×	body	80	valid
33.0ms	472×	body	160	valid