Details

sample39.0ms

Algorithm

intervals

Results

13.0ms	82×	body	1280	valid
8.0ms	73×	body	10240	exit
4.0ms	41×	body	640	valid
3.0ms	39×	body	320	valid
2.0ms	85×	body	80	valid
1.0ms	9×	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: 42.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
2.5b	(- (exp x) 1.0)

rewrite14.0ms

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:

7.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series40.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify188.0ms

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

prune137.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

3.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
1.0ms	(fma 1/12 x (/ 1 x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
46.0ms	(fma 1/12 x (/ 1 x))

simplify36.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	90	126
1	306	119
2	1283	117
3	5001	116

prune58.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
2.5b	(- 1 (/ 1.0 (exp x)))

rewrite31.0ms

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:

4.0ms	(/ 1.0 (exp x))
12.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
8.0ms	(- 1 (/ 1.0 (exp x)))

series97.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1.0 (exp x))
50.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
34.0ms	(- 1 (/ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (46.0ms)

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

prune172.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(log1p (/ 1 (- 1 (/ 1.0 (exp x)))))
0.1b	(expm1 (log1p (/ 1 (- 1 (/ 1.0 (exp x))))))
2.5b	(- 1 (/ 1.0 (exp x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

9.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
1.0ms	(log1p (/ 1 (- 1 (/ 1.0 (exp x)))))
1.0ms	(expm1 (log1p (/ 1 (- 1 (/ 1.0 (exp x))))))
11.0ms	(- 1 (/ 1.0 (exp x)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
116.0ms	(log1p (/ 1 (- 1 (/ 1.0 (exp x)))))
154.0ms	(expm1 (log1p (/ 1 (- 1 (/ 1.0 (exp x))))))
34.0ms	(- 1 (/ 1.0 (exp x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	614	1899
1	2431	1318
2	5002	1221

prune192.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 21.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

387.0ms	2222×	body	1280	valid
291.0ms	2609×	body	10240	exit
187.0ms	1692×	body	640	valid
57.0ms	819×	body	320	valid
56.0ms	2879×	body	80	valid
18.0ms	390×	body	160	valid