Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	65×	body	1280	valid
9.0ms	83×	body	10240	exit
6.0ms	57×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	94×	body	80	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
4.3b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series41.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify190.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (182.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune155.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))

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 1/12 x (/ 1 x))

series48.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

(fma 1/12 x (/ 1 x))

simplify62.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	43
1	49	38
2	150	38
3	482	38
4	2338	38
5	5002	38

prune25.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.3b	(- 1 (/ 1.0 (exp x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

17.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
3.0ms	(/ 1.0 (exp x))
16.0ms	(- 1 (/ 1.0 (exp x)))

series103.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
19.0ms	(/ 1.0 (exp x))
35.0ms	(- 1 (/ 1.0 (exp x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	552	1839
1	2298	1281
2	5001	1188

prune183.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma 1/12 x (/ 1 x)))
0.1b	(fma 1/12 x (/ 1 x))
0.1b	(fma 1/12 x (/ 1 x))
0.1b	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (fma 1/12 x (/ 1 x)))
0.0ms	(fma 1/12 x (/ 1 x))
0.0ms	(fma 1/12 x (/ 1 x))
7.0ms	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (fma 1/12 x (/ 1 x)))
42.0ms	(fma 1/12 x (/ 1 x))
50.0ms	(fma 1/12 x (/ 1 x))
44.0ms	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

simplify180.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	154	418
1	595	364
2	3980	345
3	5001	345

prune165.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

96.6% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample1.1s

Algorithm

intervals

Results

373.0ms	2213×	body	1280	valid
288.0ms	2659×	body	10240	exit
190.0ms	1707×	body	640	valid
59.0ms	815×	body	320	valid
55.0ms	2857×	body	80	valid
18.0ms	410×	body	160	valid