Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	75×	body	1280	valid
10.0ms	94×	body	10240	exit
5.0ms	56×	body	640	valid
2.0ms	86×	body	80	valid
1.0ms	22×	body	320	valid
1.0ms	17×	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: 42.2b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
4.1b	(- (exp x) 1.0)

rewrite34.0ms

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:

21.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series42.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify184.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (178.0ms)

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

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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))

rewrite7.0ms

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:

6.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms	(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))

simplify35.0ms

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

prune61.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
4.1b	(- 1 (/ 1.0 (exp x)))

rewrite64.0ms

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:

6.0ms	(/ 1.0 (exp x))
31.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
21.0ms	(- 1 (/ 1.0 (exp x)))

series102.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1.0 (exp x))
46.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
38.0ms	(- 1 (/ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (47.0ms)

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

prune173.0ms

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	(pow (- 1 (/ 1.0 (exp x))) 3)
0.0b	(/ 1 (pow (- 1 (/ 1.0 (exp x))) 3))
0.0b	(cbrt (/ 1 (pow (- 1 (/ 1.0 (exp x))) 3)))
4.1b	(- 1 (/ 1.0 (exp x)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

245×	`add-sqr-sqrt`
193×	`times-frac`
177×	`*-un-lft-identity`
109×	`add-cube-cbrt`
72×	`cbrt-prod`
68×	`difference-of-squares`
64×	`unpow-prod-down` `cube-prod`
39×	`prod-diff`
22×	`associate-/r*`
17×	`distribute-lft-out--`
14×	`add-exp-log`
8×	`cube-mult` `unpow3` `sqr-pow`
7×	`add-cbrt-cube`
6×	`cube-div` `div-exp` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `pow-to-exp` `flip3--` `pow-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`rec-exp` `pow-unpow` `fma-neg` `1-exp` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `cbrt-div` `pow-flip` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `inv-pow` `rem-cube-cbrt`

Counts

4 → 298

Calls

4 calls:

28.0ms	(pow (- 1 (/ 1.0 (exp x))) 3)
63.0ms	(/ 1 (pow (- 1 (/ 1.0 (exp x))) 3))
35.0ms	(cbrt (/ 1 (pow (- 1 (/ 1.0 (exp x))) 3)))
18.0ms	(- 1 (/ 1.0 (exp x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (- 1 (/ 1.0 (exp x))) 3)
83.0ms	(/ 1 (pow (- 1 (/ 1.0 (exp x))) 3))
53.0ms	(cbrt (/ 1 (pow (- 1 (/ 1.0 (exp x))) 3)))
35.0ms	(- 1 (/ 1.0 (exp x)))

simplify104.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	815	3868
1	3620	2939
2	5003	2813

prune289.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

96.8% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	21	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

376.0ms	2218×	body	1280	valid
259.0ms	2501×	body	10240	exit
180.0ms	1716×	body	640	valid
56.0ms	2863×	body	80	valid
54.0ms	795×	body	320	valid
21.0ms	410×	body	160	valid