Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	65×	body	1280	valid
9.0ms	62×	body	640	valid
6.0ms	97×	body	80	valid
3.0ms	80×	body	80	overflowed
2.0ms	20×	body	320	valid
1.0ms	12×	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: 40.4b

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.5b	(- (exp x) 1.0)

rewrite16.0ms

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)

series41.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify198.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (185.0ms)

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

prune160.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.1b	(fma 1/6 (pow x 3) x)
9.3b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

3.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series142.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
76.0ms	(fma 1/6 (pow x 3) x)
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify100.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	178	458
1	614	416
2	3125	414
3	5002	414

prune174.0ms

Pruning

6 alts after pruning (5 fresh and 1 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)
0.0ms	(fma 1/12 x (/ 1 x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
43.0ms	(fma 1/12 x (/ 1 x))

simplify42.0ms

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

prune69.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))
0.6b	(cbrt (fma 1/12 x (/ 1 x)))
0.6b	(cbrt (fma 1/12 x (/ 1 x)))
0.6b	(cbrt (fma 1/12 x (/ 1 x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))
107.0ms	(cbrt (fma 1/12 x (/ 1 x)))
102.0ms	(cbrt (fma 1/12 x (/ 1 x)))
102.0ms	(cbrt (fma 1/12 x (/ 1 x)))

simplify127.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	277	823
1	911	765
2	4122	688
3	5001	652

prune236.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes81.0ms

Accuracy

96.9% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

463.0ms	2207×	body	1280	valid
243.0ms	1658×	body	640	valid
102.0ms	2876×	body	80	valid
95.0ms	2535×	body	80	overflowed
80.0ms	818×	body	320	valid
33.0ms	442×	body	160	valid