Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	83×	body	1280	valid
10.0ms	95×	body	10240	exit
6.0ms	55×	body	640	valid
2.0ms	29×	body	320	valid
2.0ms	82×	body	80	valid
0.0ms	8×	body	160	valid

simplify6.0ms

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: 43.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
2.3b	(- (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)

series45.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify192.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (186.0ms)

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

prune145.0ms

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))

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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
44.0ms	(fma 1/12 x (/ 1 x))

simplify37.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (34.0ms)

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

prune62.0ms

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))))
2.3b	(- 1 (/ 1.0 (exp x)))

rewrite28.0ms

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))
9.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
9.0ms	(- 1 (/ 1.0 (exp x)))

series99.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1.0 (exp x))
47.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (47.0ms)

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

prune177.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.7b	(* (/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0))
0.7b	(/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x))))
2.3b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube`
9×	`add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `fma-udef`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
10.0ms	(* (/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0))
4.0ms	(/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x))))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (exp x) 1.0)
81.0ms	(* (/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0))
71.0ms	(/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x))))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	436	984
1	1853	887
2	5003	871

prune266.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

96.2% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 21.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

384.0ms	2255×	body	1280	valid
267.0ms	2500×	body	10240	exit
172.0ms	1660×	body	640	valid
59.0ms	2865×	body	80	valid
53.0ms	793×	body	320	valid
18.0ms	429×	body	160	valid