Details

sample104.0ms

Algorithm

intervals

Results

67.0ms	178×	body	1280	valid
14.0ms	239×	body	80	valid
8.0ms	33×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify225.0ms

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: 31.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite36.0ms

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:

5.0ms	(- (exp x) 2.0)
29.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series75.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- (exp x) 2.0)
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.0b	(fma x x (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 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
6.0ms	(* 1/12 (pow x 4))

series230.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
60.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
37.0ms	(* 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

prune146.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- 2.0) 2.0 (exp (+ x x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
0.3b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
4.4b	(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:

0.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
16.0ms	(* (+ (exp x) 2.0) (exp x))
7.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series566.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
23.0ms	(* (+ (exp x) 2.0) (exp x))
406.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
96.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

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

prune230.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes39.0ms

Accuracy

87.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.2s	5660×	body	1280	valid
441.0ms	7756×	body	80	valid
297.0ms	1244×	body	640	valid
98.0ms	621×	body	320	valid
35.0ms	307×	body	160	valid