Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	65×	body	1280	valid
6.0ms	63×	body	640	valid
3.0ms	153×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	12×	body	160	valid

simplify7.0ms

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: 40.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (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:

13.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

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

prune140.0ms

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))

series21.0ms

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

prune36.0ms

Pruning

3 alts after pruning (2 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)
3.5b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
9.5b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite4.0ms

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)
2.0ms	(/ (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))

series150.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(fma 1/6 (pow x 3) x)
48.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify89.0ms

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

prune151.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/6 (pow x 3) x)
3.6b	(* (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (/ 1 x))
9.5b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`add-exp-log` `*-un-lft-identity`
11×	`add-cube-cbrt` `times-frac`
8×	`add-cbrt-cube`
5×	`pow1`
4×	`prod-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`div-exp` `cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 1/6 (pow x 3) x)
9.0ms	(* (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (/ 1 x))
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series149.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(fma 1/6 (pow x 3) x)
47.0ms	(* (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (/ 1 x))
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	232	451
1	1174	390
2	5003	374

prune160.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes18.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 21.4b

bsearch23.0ms

Steps

Iters	Range		Point
7	-0.00043085380315138777	-1.8212635929712337e-06	-0.00019141971874233585

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample862.0ms

Algorithm

intervals

Results

389.0ms	2326×	body	1280	valid
172.0ms	1605×	body	640	valid
99.0ms	5570×	body	80	valid
54.0ms	816×	body	320	valid
18.0ms	421×	body	160	valid