Details

sample58.0ms

Algorithm

intervals

Results

30.0ms	59×	body	2560	valid
8.0ms	59×	body	640	valid
8.0ms	38×	body	1280	valid
2.0ms	70×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	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: 33.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b	(- 1.0 (cos x))
18.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

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))

series64.0ms

Counts

2 → 6

Calls

2 calls:

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

prune124.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
13.4b	(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))
45.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify105.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (101.0ms)

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

prune105.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
1.3b	(- 1.0 (cos x))
1.3b	(- 1.0 (cos x))

rewrite29.0ms

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:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
9.0ms	(/ (sqrt (- 1.0 (cos x))) x)
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (sqrt (- 1.0 (cos x))) x)
87.0ms	(/ (sqrt (- 1.0 (cos x))) x)
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify182.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 3 (164.0ms)

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

prune349.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.1b	(- (pow 1.0 3) (pow (cos x) 3))
1.3b	(- 1.0 (cos x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

153×	`prod-diff`
115×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
89×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
17×	`difference-of-squares`
15×	`fma-neg`
10×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `pow-to-exp` `sqr-cos` `associate-+l+` `distribute-rgt-out` `pow-pow` `fma-def` `flip3-+` `pow-exp` `sum-log` `flip-+` `rem-cube-cbrt`

Counts

4 → 261

Calls

4 calls:

3.0ms	(pow (cos x) 3)
6.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))
4.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
44.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
45.0ms	(- (pow 1.0 3) (pow (cos x) 3))
18.0ms	(- 1.0 (cos x))

simplify143.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	673	2909
1	2709	1980
2	5002	1955

prune385.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes93.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch87.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	0.031419704770434244
8	-1.0806682141483241	-0.0004106978961831668	-0.032095584675305884

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

743.0ms	1585×	body	2560	valid
276.0ms	1257×	body	1280	valid
228.0ms	1538×	body	640	valid
97.0ms	905×	body	320	valid
69.0ms	2254×	body	80	valid
34.0ms	461×	body	160	valid