Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	75×	body	1280	valid
6.0ms	180×	body	80	valid
5.0ms	56×	body	640	valid
1.0ms	22×	body	320	valid
1.0ms	17×	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: 40.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.1b	(- (exp x) 1.0)

rewrite40.0ms

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:

26.0ms	(/ (- (exp x) 1.0) x)
12.0ms	(- (exp x) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (exp x) 1.0) x)
18.0ms	(- (exp x) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

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

prune138.0ms

Pruning

4 alts after pruning (4 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))

series22.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify26.0ms

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

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/6 (pow x 3) x)
2.4b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
8.8b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma 1/6 (pow x 3) x)
5.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series161.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma 1/6 (pow x 3) x)
47.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
41.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify86.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	140	391
1	510	356
2	2915	356
3	5002	356

prune144.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
0.0b	(+ (exp x) 1.0)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
4.1b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite61.0ms

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:

30.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
9.0ms	(+ (exp x) 1.0)
15.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
8.0ms	(+ (exp x) 1.0)
66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (42.0ms)

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

prune379.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch31.0ms

Steps

Iters	Range		Point
9	-0.04331797882383785	-1.989428328455626e-07	-0.00013831627271264325

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample893.0ms

Algorithm

intervals

Results

370.0ms	2235×	body	1280	valid
174.0ms	1724×	body	640	valid
96.0ms	5401×	body	80	valid
57.0ms	810×	body	320	valid
17.0ms	411×	body	160	valid