Details

sample82.0ms

Algorithm

intervals

Results

58.0ms	188×	body	1280	valid
5.0ms	233×	body	80	valid
5.0ms	35×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify217.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.9b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite15.0ms

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:

4.0ms	(- (exp x) 2.0)
9.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series69.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune142.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

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

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

Counts

2 → 37

Calls

2 calls:

1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))

series158.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
38.0ms	(* 1/12 (pow x 4))

simplify88.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	123	177
1	469	163
2	2175	160
3	5002	160

prune84.0ms

Filtered

43 candidates to 29 candidates (67.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 0.0b

Counts

47 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

4.0ms	(+ (exp x) 2.0)
8.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
8.0ms	(* (+ (exp x) 2.0) (exp x))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 2.0)
213.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
26.0ms	(* (+ (exp x) 2.0) (exp x))
90.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	312	834
1	1220	713
2	5001	710

prune201.0ms

Filtered

87 candidates to 70 candidates (80.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0.0b

Counts

91 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
0.0b	(pow (exp (- x)) 3)
0.0b	(pow (- (exp x) 2.0) 3)
3.8b	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
21×	`unpow-prod-down` `cube-prod`
18×	`prod-diff`
16×	`fma-def`
14×	`distribute-lft-out--`
13×	`pow1`
12×	`cube-div` `pow-pow`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`exp-prod`
9×	`flip3--` `flip--` `distribute-lft-out`
8×	`add-cbrt-cube` `difference-of-squares`
7×	`add-exp-log` `swap-sqr`
6×	`pow-unpow` `add-log-exp`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `frac-add` `log1p-expm1-u`
3×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `cube-mult` `distribute-rgt-neg-in` `exp-diff` `unpow3` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `associate-r/` `associate-l/` `pow-exp` `rem-cube-cbrt`
1×	`+-commutative` `pow2` `neg-mul-1` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `sum-log` `pow-sqr` `sum-cubes` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 176

Calls

4 calls:

12.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
5.0ms	(pow (exp (- x)) 3)
5.0ms	(pow (- (exp x) 2.0) 3)
18.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

series259.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
26.0ms	(pow (exp (- x)) 3)
46.0ms	(pow (- (exp x) 2.0) 3)
153.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

simplify125.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	643	1322
1	3714	1084
2	5001	1083

prune402.0ms

Filtered

188 candidates to 103 candidates (54.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	188	4	192

Merged error: 0b

Counts

192 → 4

regimes20.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	5719×	body	1280	valid
196.0ms	7994×	body	80	valid
193.0ms	1222×	body	640	valid
61.0ms	605×	body	320	valid
19.0ms	306×	body	160	valid