Details

sample109.0ms

Algorithm

intervals

Results

30.0ms	69×	body	1280	valid
30.0ms	66×	body	10240	exit
18.0ms	323×	body	80	valid
9.0ms	38×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	7×	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: 31.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 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))))
1.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite113.0ms

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:

10.0ms	(* (- 1.0 eps) x)
28.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
40.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
25.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
48.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
48.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
193.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1372	4120
1	5001	3814

prune484.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

4.6b	(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))))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify30.0ms

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

prune39.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
0.0b	(/ (exp (- (* x eps) (* 1.0 x))) eps)
0.0b	(/ 1 (exp (fma x eps (* 1.0 x))))
1.2b	(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`exp-sum`
13×	`associate-/l*`
10×	`associate-/r*` `add-cbrt-cube`
7×	`add-exp-log`
5×	`pow1` `fma-udef`
4×	`expm1-log1p-u` `sub-neg` `distribute-neg-in` `pow-flip` `div-exp` `prod-diff` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `exp-prod` `frac-2neg` `clear-num` `div-inv` `associate-/l/`
2×	`exp-diff`
1×	`neg-sub0` `exp-neg` `rec-exp` `1-exp` `inv-pow`

Counts

4 → 127

Calls

4 calls:

20.0ms	(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
12.0ms	(/ (exp (- (* x eps) (* 1.0 x))) eps)
3.0ms	(/ 1 (exp (fma x eps (* 1.0 x))))
0.0ms	(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
29.0ms	(/ (exp (- (* x eps) (* 1.0 x))) eps)
25.0ms	(/ 1 (exp (fma x eps (* 1.0 x))))
176.0ms	(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

simplify54.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	418	1386
1	1414	1237
2	5001	1188

prune495.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

95.8% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.9b

bsearch147.0ms

Steps

Iters	Range		Point
10	3.9524390088012255e-07	7103758.057079569	130.4040333957902

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	31
1	59	31
2	59	31

end0.0ms

sample2.9s

Algorithm

intervals

Results

773.0ms	1902×	body	10240	exit
760.0ms	1689×	body	1280	valid
565.0ms	10213×	body	80	valid
327.0ms	1265×	body	640	valid
103.0ms	617×	body	320	valid
35.0ms	326×	body	160	valid