Details

sample110.0ms

Algorithm

intervals

Results

30.0ms	69×	body	1280	valid
26.0ms	66×	body	10240	exit
22.0ms	323×	body	80	valid
9.0ms	38×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify38.0ms

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: 31.8b

localize17.0ms

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)))))

rewrite65.0ms

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:

7.0ms	(* (- 1.0 eps) x)
13.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
17.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
18.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (- 1.0 eps) x)
45.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
52.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
198.0ms	(- (* (+ 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 (27.0ms)

Iter	Nodes	Cost
0	1372	4120
1	5001	3814

prune628.0ms

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:

1.0ms

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

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(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

prune39.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(/ 1 (exp (fma x eps (* 1.0 x))))
2.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* 1.0 (- (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps) (/ 1 (exp (fma x eps (* 1.0 x)))))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

792×	`times-frac`
539×	`add-sqr-sqrt` `*-un-lft-identity`
537×	`add-cube-cbrt`
516×	`associate--r+`
513×	`prod-diff`
258×	`distribute-rgt-in` `distribute-lft-in`
200×	`exp-sum`
100×	`distribute-neg-in` `fma-udef`
66×	`div-inv`
36×	`frac-sub`
35×	`associate-*r/`
17×	`exp-neg`
16×	`frac-times`
13×	`neg-sub0` `exp-diff`
12×	`flip3-+` `flip-+`
10×	`flip3--` `add-cbrt-cube` `flip--`
8×	`associate-*l/`
7×	`pow1` `add-exp-log` `associate-/r` `associate-/l`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-flip` `associate-l` `un-div-inv` `log1p-expm1-u`
3×	`sub-neg` `exp-prod` `div-exp` `associate-r`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`rec-exp` `fma-neg` `diff-log` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 664

Calls

4 calls:

13.0ms	(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
5.0ms	(/ 1 (exp (fma x eps (* 1.0 x))))
64.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* 1.0 (- (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps) (/ 1 (exp (fma x eps (* 1.0 x)))))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
49.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
22.0ms	(/ 1 (exp (fma x eps (* 1.0 x))))
256.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* 1.0 (- (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps) (/ 1 (exp (fma x eps (* 1.0 x)))))))

simplify224.0ms

Algorithm

egg-herbie

Counts

676 → 676

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	4117	21660
1	5001	21604

prune4.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes58.0ms

Accuracy

95.8% (0.7b remaining)

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

bsearch148.0ms

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	54	27
1	67	27
2	67	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

778.0ms	1902×	body	10240	exit
749.0ms	1689×	body	1280	valid
563.0ms	10213×	body	80	valid
329.0ms	1265×	body	640	valid
112.0ms	617×	body	320	valid
37.0ms	326×	body	160	valid