Details

sample38.0ms

Algorithm

intervals

Results

14.0ms	77×	body	1280	valid
8.0ms	78×	body	10240	exit
5.0ms	47×	body	640	valid
2.0ms	99×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	8×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
2.7b	(- (exp x) 1.0)

rewrite15.0ms

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)

series45.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify186.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (181.0ms)

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

prune143.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

3 alts after pruning (3 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))

rewrite4.0ms

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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
48.0ms	(fma 1/12 x (/ 1 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (35.0ms)

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

prune64.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
2.6b	(- 1 (/ 1.0 (exp x)))

rewrite36.0ms

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))
10.0ms	(- 1 (/ 1.0 (exp x)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
12.0ms	(/ 1.0 (exp x))
39.0ms	(- 1 (/ 1.0 (exp x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (47.0ms)

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

prune184.0ms

Filtered

154 candidates to 73 candidates (47.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ 1 (- 1 (/ 1.0 (exp x)))))
2.6b	(- 1 (/ 1.0 (exp x)))
2.6b	(- 1 (/ 1.0 (exp x)))
2.6b	(- 1 (/ 1.0 (exp x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
121×	`add-cube-cbrt`
117×	`times-frac` `prod-diff`
30×	`cbrt-prod`
24×	`difference-of-squares`
10×	`div-inv` `add-log-exp`
9×	`fma-neg`
6×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3`

Counts

4 → 224

Calls

4 calls:

10.0ms	(cbrt (/ 1 (- 1 (/ 1.0 (exp x)))))
10.0ms	(- 1 (/ 1.0 (exp x)))
14.0ms	(- 1 (/ 1.0 (exp x)))
10.0ms	(- 1 (/ 1.0 (exp x)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (/ 1 (- 1 (/ 1.0 (exp x)))))
35.0ms	(- 1 (/ 1.0 (exp x)))
36.0ms	(- 1 (/ 1.0 (exp x)))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	567	4224
1	2108	2729
2	5001	2447

prune282.0ms

Filtered

236 candidates to 82 candidates (34.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

97.1% (0.6b remaining)

Error of 0.6b 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	23	13
1	23	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

378.0ms	2261×	body	1280	valid
276.0ms	2564×	body	10240	exit
169.0ms	1606×	body	640	valid
58.0ms	837×	body	320	valid
54.0ms	2893×	body	80	valid
17.0ms	404×	body	160	valid