Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	62×	body	1280	valid
8.0ms	78×	body	10240	exit
5.0ms	46×	body	640	valid
2.0ms	108×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	13×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 37.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.8b	(- (exp x) 1.0)

rewrite30.0ms

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:

17.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify189.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (183.0ms)

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

prune144.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

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))

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

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

simplify60.0ms

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

prune31.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
3.8b	(- 1 (/ 1.0 (exp x)))

rewrite63.0ms

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:

33.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
6.0ms	(/ 1.0 (exp x))
18.0ms	(- 1 (/ 1.0 (exp x)))

series101.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
13.0ms	(/ 1.0 (exp x))
35.0ms	(- 1 (/ 1.0 (exp x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (46.0ms)

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

prune177.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1 (expm1 (log1p (/ 1.0 (exp x))))))
0.0b	(/ 1.0 (exp x))
0.2b	(log1p (/ 1.0 (exp x)))
35.8b	(- 1 (expm1 (log1p (/ 1.0 (exp x)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
27×	`times-frac`
10×	`difference-of-squares`
9×	`add-exp-log` `prod-diff` `associate-/r*`
8×	`add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `expm1-log1p-u` `distribute-lft-out--`
4×	`log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `log1p-udef` `pow-flip` `diff-log` `1-exp` `log1p-expm1` `inv-pow` `expm1-udef` `associate--r-`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/ 1 (- 1 (expm1 (log1p (/ 1.0 (exp x))))))
6.0ms	(/ 1.0 (exp x))
0.0ms	(log1p (/ 1.0 (exp x)))
10.0ms	(- 1 (expm1 (log1p (/ 1.0 (exp x)))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ 1 (- 1 (expm1 (log1p (/ 1.0 (exp x))))))
13.0ms	(/ 1.0 (exp x))
80.0ms	(log1p (/ 1.0 (exp x)))
207.0ms	(- 1 (expm1 (log1p (/ 1.0 (exp x)))))

simplify195.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	461	1181
1	1970	806
2	5002	776

prune218.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

97.3% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

372.0ms	2283×	body	1280	valid
250.0ms	2513×	body	10240	exit
172.0ms	1665×	body	640	valid
53.0ms	2915×	body	80	valid
52.0ms	761×	body	320	valid
15.0ms	379×	body	160	valid