Details

sample82.0ms

Algorithm

intervals

Results

24.0ms	56×	body	1280	valid
16.0ms	293×	body	80	valid
16.0ms	50×	body	640	valid
5.0ms	29×	body	320	valid
3.0ms	56×	body	80	overflowed
1.0ms	10×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (+ 1.0 eps) x)))
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

81×	`exp-neg` `frac-sub`
80×	`frac-times`
61×	`neg-sub0` `exp-diff`
40×	`associate-r/` `associate-l/`
31×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
20×	`un-div-inv`
18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `exp-prod` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `times-frac` `fma-neg` `diff-log` `prod-diff` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 178

Calls

4 calls:

3.0ms	(exp (- (* (+ 1.0 eps) x)))
30.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
37.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
29.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (- (* (+ 1.0 eps) x)))
46.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
52.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
328.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify146.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	1321	4118
1	4794	3811
2	5001	3793

prune486.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 1 expressions with local error:

5.6b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify29.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	42	89
1	136	78
2	722	78
3	5002	75

prune45.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

series40.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	49	82
1	132	67
2	534	67
3	3076	67
4	5001	67

prune38.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.4b	(expm1 (log1p (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
9.1b	(log1p (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`expm1-log1p-u`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `fma-udef` `expm1-udef`

Counts

3 → 32

Calls

3 calls:

0.0ms	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.0ms	(expm1 (log1p (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
0.0ms	(log1p (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series279.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
145.0ms	(expm1 (log1p (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
92.0ms	(log1p (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	256	339
1	839	298
2	3626	272
3	5002	268

prune107.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes50.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 17.0b

bsearch124.0ms

Steps

Iters	Range		Point
9	0.7889543571722019	588165898.4936482	439.217255613825

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	23
1	54	23
2	54	23

end0.0ms

sample2.2s

Algorithm

intervals

Results

734.0ms	1672×	body	1280	valid
576.0ms	10038×	body	80	valid
322.0ms	1253×	body	640	valid
120.0ms	1972×	body	80	overflowed
115.0ms	660×	body	320	valid
35.0ms	317×	body	160	valid