Details

sample107.0ms

Algorithm

intervals

Results

33.0ms	76×	body	10240	exit
23.0ms	53×	body	1280	valid
18.0ms	324×	body	80	valid
10.0ms	41×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (38.0ms)

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: 29.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out`

Counts

4 → 183

Calls

4 calls:

33.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
41.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms	(* (- 1.0 eps) x)
31.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
34.0ms	(* (- 1.0 eps) x)
194.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1372	4120
1	5001	3814

prune477.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

7.0b	(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))))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(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 (26.0ms)

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

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize7.0ms

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)

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify105.0ms

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

prune29.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
2.9b	(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (- (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`associate-*l/`
4×	`exp-neg` `expm1-log1p-u` `frac-times` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`neg-sub0` `exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`associate-*r/` `distribute-lft-out--`
1×	`flip3-+` `times-frac` `un-div-inv` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 89

Calls

4 calls:

10.0ms	(* (+ 1.0 eps) x)
41.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms	(* (- 1.0 eps) x)
0.0ms	(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (- (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ 1.0 eps) x)
53.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
29.0ms	(* (- 1.0 eps) x)
184.0ms	(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (- (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	420	763
1	1716	677
2	5002	672

prune319.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes57.0ms

Accuracy

96.9% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 17.1b

bsearch146.0ms

Steps

Iters	Range		Point
10	7.241082556785e-09	30809428.134158503	434.1645604525621

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	21
1	56	21
2	56	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

776.0ms	1912×	body	10240	exit
747.0ms	1700×	body	1280	valid
570.0ms	10216×	body	80	valid
324.0ms	1281×	body	640	valid
107.0ms	633×	body	320	valid
33.0ms	307×	body	160	valid