Details

sample46.0ms

Algorithm

intervals

Results

17.0ms	66×	body	1280	valid
10.0ms	53×	body	640	valid
6.0ms	181×	body	80	valid
5.0ms	39×	body	320	valid
1.0ms	11×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 40.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.0b	(- (exp x) 1.0)

rewrite20.0ms

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)

series60.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (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

prune143.0ms

Pruning

3 alts after pruning (3 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 (4.0ms)

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

prune39.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.1b	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
6.4b	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
1.0ms	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
1.0ms	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

series74.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
34.0ms	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
20.0ms	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

simplify262.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	163	366
1	636	347
2	4979	341
3	5001	341

prune139.0ms

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	(exp (fma 1/6 (pow x 2) (fma 1/2 x 1)))
0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.5b	(log (exp (fma 1/6 (pow x 2) (fma 1/2 x 1))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity`
4×	`pow1` `log-prod` `log-pow` `add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

3 → 42

Calls

3 calls:

1.0ms	(exp (fma 1/6 (pow x 2) (fma 1/2 x 1)))
0.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
1.0ms	(log (exp (fma 1/6 (pow x 2) (fma 1/2 x 1))))

series59.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(exp (fma 1/6 (pow x 2) (fma 1/2 x 1)))
20.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
21.0ms	(log (exp (fma 1/6 (pow x 2) (fma 1/2 x 1))))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	97	260
1	269	232
2	1105	231
3	5001	230

prune132.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch32.0ms

Steps

Iters	Range		Point
8	-1.3862719480695398	-4.2961337728369966e-05	-0.00013840294310751077

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

625.0ms	2380×	body	1280	valid
289.0ms	1623×	body	640	valid
188.0ms	5461×	body	80	valid
103.0ms	848×	body	320	valid
32.0ms	404×	body	160	valid