Details

sample52.0ms

Algorithm

intervals

Results

24.0ms	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

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: 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))

rewrite28.0ms

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:

7.0ms	(- 1.0 (cos x))
20.0ms	(/ (- 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 (26.0ms)

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

prune123.0ms

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))

rewrite54.0ms

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:

20.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series105.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
40.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify56.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (44.0ms)

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

prune278.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
144×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
113×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 354

Calls

4 calls:

77.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
3.0ms	(pow (cos x) 3)
6.0ms	(+ 1.0 (cos x))
33.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series206.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
33.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify147.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	828	4951
1	3244	4033
2	5002	3940

prune454.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`add-exp-log` `prod-diff` `add-cbrt-cube`
6×	`fma-def`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `fma-neg` `associate-/r*`
2×	`cbrt-undiv` `+-commutative` `flip3--` `flip3-+` `associate-*r/` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/` `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 → 87

Calls

4 calls:

22.0ms	(/ (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) (- 1.0 (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
6.0ms	(+ 1.0 (cos x))
7.0ms	(+ 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series62.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (* (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)) (- 1.0 (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
10.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify44.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	316	855
1	1436	652
2	5001	484

prune214.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch74.0ms

Steps

Iters	Range		Point
11	1.661404138935296e-22	2.5556453819330236	0.032295631090667354
9	-0.04331797882383785	-2.2082264187638084e-10	-0.03408999554764363

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	38	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

730.0ms	1572×	body	2560	valid
280.0ms	1279×	body	1280	valid
231.0ms	1512×	body	640	valid
94.0ms	928×	body	320	valid
73.0ms	2237×	body	80	valid
34.0ms	472×	body	160	valid