Details

sample80.0ms

Algorithm

intervals

Results

55.0ms	178×	body	1280	valid
7.0ms	43×	body	640	valid
6.0ms	249×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify225.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite32.0ms

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

series74.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
61.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune162.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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))

series215.0ms

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)))
41.0ms	(* 1/12 (pow x 4))

simplify100.0ms

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

prune147.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (+ (exp x) 2.0) (exp (+ x x)))
0.0b	(pow (exp x) 3)
0.0b	(pow (exp x) 3)
4.5b	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-pow`
6×	`pow1` `unpow-prod-down` `pow-unpow` `exp-prod` `cube-prod` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma 2.0 (+ (exp x) 2.0) (exp (+ x x)))
2.0ms	(pow (exp x) 3)
2.0ms	(pow (exp x) 3)
0.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma 2.0 (+ (exp x) 2.0) (exp (+ x x)))
24.0ms	(pow (exp x) 3)
24.0ms	(pow (exp x) 3)
128.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

simplify37.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	215	416
1	844	378
2	5001	366

prune285.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (- (pow (exp x) 3) (pow 2.0 3)))
0.0b	(pow (exp x) 3)
0.0b	(pow (exp x) 3)
4.6b	(+ (* (exp x) (- (pow (exp x) 3) (pow 2.0 3))) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

576×	`prod-diff`
328×	`add-sqr-sqrt`
312×	`*-un-lft-identity`
306×	`unpow-prod-down` `cube-prod`
302×	`add-cube-cbrt`
292×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
106×	`sqr-pow`
98×	`cube-mult` `unpow3`
25×	`associate-r`
16×	`difference-of-squares`
8×	`pow1` `pow-pow` `add-cbrt-cube`
6×	`pow-unpow` `exp-prod` `add-log-exp`
5×	`add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`associate-l`
2×	`pow-to-exp` `associate-*r/` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `associate-+r+` `flip3--` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 699

Calls

4 calls:

85.0ms	(* (exp x) (- (pow (exp x) 3) (pow 2.0 3)))
2.0ms	(pow (exp x) 3)
2.0ms	(pow (exp x) 3)
59.0ms	(+ (* (exp x) (- (pow (exp x) 3) (pow 2.0 3))) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

series213.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (exp x) (- (pow (exp x) 3) (pow 2.0 3)))
26.0ms	(pow (exp x) 3)
23.0ms	(pow (exp x) 3)
116.0ms	(+ (* (exp x) (- (pow (exp x) 3) (pow 2.0 3))) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

simplify222.0ms

Algorithm

egg-herbie

Counts

711 → 711

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	932	9404
1	3815	7399
2	5001	7395

prune1.4s

Filtered

711 candidates to 248 candidates (34.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes17.0ms

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

sample2.3s

Algorithm

intervals

Results

1.7s	5703×	body	1280	valid
184.0ms	7946×	body	80	valid
181.0ms	1152×	body	640	valid
64.0ms	649×	body	320	valid
20.0ms	323×	body	160	valid