Details

sample51.0ms

Algorithm

intervals

Results

24.0ms	79×	body	1280	valid
10.0ms	57×	body	640	valid
4.0ms	144×	body	80	valid
3.0ms	27×	body	320	valid
1.0ms	13×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.6b	(- (exp x) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

12.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377

prune145.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))

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:

0.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify27.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52

prune37.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
3.6b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log` `fma-udef` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
14.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
100.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	531	2009
1	1917	1909
2	5001	1904

prune403.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (- 1.0 (exp x)) (exp (* 2 x)))
0.0b	(pow (exp x) 3)
3.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.6b	(- 1.0 (exp x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `fma-neg` `cube-prod`
2×	`fma-udef`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma 1.0 (- 1.0 (exp x)) (exp (* 2 x)))
2.0ms	(pow (exp x) 3)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0ms	(- 1.0 (exp x))

series115.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma 1.0 (- 1.0 (exp x)) (exp (* 2 x)))
24.0ms	(pow (exp x) 3)
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
13.0ms	(- 1.0 (exp x))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	289	428
1	1161	366
2	5001	362

prune284.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch34.0ms

Steps

Iters	Range		Point
8	-0.05879146692607421	-6.246474786567043e-06	-0.00014211215699186535

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	19
1	32	19

end0.0ms

sample902.0ms

Algorithm

intervals

Results

404.0ms	2280×	body	1280	valid
172.0ms	1575×	body	640	valid
103.0ms	5402×	body	80	valid
69.0ms	889×	body	320	valid
20.0ms	433×	body	160	valid