Details

sample101.0ms

Algorithm

intervals

Results

67.0ms	173×	body	1280	valid
10.0ms	45×	body	640	valid
10.0ms	242×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify213.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

7.0ms	(- (exp x) 2.0)
25.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series66.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
54.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune149.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))

series209.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
119.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))

simplify97.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	143	265
1	544	240
2	2626	237
3	5001	237

prune128.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(fma (- 2.0) 2.0 (exp (+ x x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
3.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

8.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
15.0ms	(* (+ (exp x) 2.0) (exp x))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series359.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
39.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
22.0ms	(* (+ (exp x) 2.0) (exp x))
90.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	309	842
1	1272	718
2	5002	714

prune208.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.2s	5711×	body	1280	valid
330.0ms	8016×	body	80	valid
281.0ms	1207×	body	640	valid
95.0ms	625×	body	320	valid
29.0ms	298×	body	160	valid