Details

sample123.0ms

Algorithm

intervals

Results

35.0ms	302×	body	80	valid
34.0ms	50×	body	1280	valid
17.0ms	37×	body	640	valid
9.0ms	51×	body	80	overflowed
9.0ms	27×	body	320	valid
3.0ms	12×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

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

localize17.0ms

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)
3.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite119.0ms

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:

30.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
39.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms	(* (- 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:

49.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
32.0ms	(* (- 1.0 eps) x)
326.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1372	4120
1	5001	3814

prune501.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 1 expressions with local error:

6.4b	(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))))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(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

prune40.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (- (* x eps) (* 1.0 x))) eps)
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
4.1b	(- (fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (* 1.0 (exp (- (* x eps) (* 1.0 x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`times-frac`
12×	`exp-sum`
10×	`associate-l` `add-cbrt-cube`
8×	`pow1` `add-exp-log`
7×	`prod-diff`
6×	`associate-r` `associate-/l*` `add-log-exp`
5×	`sub-neg`
4×	`exp-neg` `expm1-log1p-u` `frac-times` `flip3--` `exp-diff` `associate-*l/` `flip--` `log1p-expm1-u`
3×	`neg-sub0` `fma-neg` `associate-/r*`
2×	`associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-exp` `associate--l+` `clear-num` `un-div-inv` `flip-+` `fma-udef` `div-inv` `associate-/l/` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 118

Calls

4 calls:

12.0ms	(/ (exp (- (* x eps) (* 1.0 x))) eps)
39.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
12.0ms	(* (+ 1.0 eps) x)
5.0ms	(- (fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (* 1.0 (exp (- (* x eps) (* 1.0 x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (exp (- (* x eps) (* 1.0 x))) eps)
50.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
31.0ms	(* (+ 1.0 eps) x)
177.0ms	(- (fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (* 1.0 (exp (- (* x eps) (* 1.0 x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	535	1424
1	2049	1302
2	5001	1270

prune436.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.5b

regimes44.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.7b

bsearch195.0ms

Steps

Iters	Range		Point
10	6.5383237107547055e-09	649.3281407255394	347.89305073499355

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	49	26
2	49	26

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	1706×	body	1280	valid
1.2s	9989×	body	80	valid
580.0ms	1231×	body	640	valid
222.0ms	1928×	body	80	overflowed
210.0ms	641×	body	320	valid
67.0ms	305×	body	160	valid