Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	70×	body	1280	valid
6.0ms	57×	body	640	valid
2.0ms	28×	body	320	valid
2.0ms	87×	body	80	overflowed
2.0ms	87×	body	80	valid
1.0ms	14×	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: 41.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

19.0ms	(/ (exp x) (- (exp x) 1.0))
10.0ms	(- (exp x) 1.0)

series42.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
13.0ms	(- (exp x) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354

prune123.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `associate-l`
9×	`times-frac` `add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l` `add-log-exp`
2×	`flip3-+` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

27.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
34.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
7.0ms	(* x 1/6)

series114.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
57.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
17.0ms	(* x 1/6)

simplify58.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	401	620
1	1835	574
2	5001	572

prune193.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (exp x))
0.2b	(cbrt (exp x))
0.2b	(cbrt (exp x))
0.3b	(* x 1/6)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

2.0ms	(cbrt (exp x))
2.0ms	(cbrt (exp x))
2.0ms	(cbrt (exp x))
7.0ms	(* x 1/6)

series245.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (exp x))
76.0ms	(cbrt (exp x))
77.0ms	(cbrt (exp x))
13.0ms	(* x 1/6)

simplify39.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	93	216
1	296	198
2	1144	192
3	5002	177

prune175.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

12.0ms	(+ (* 1/12 x) (/ 1 x))
7.0ms	(* 1/12 x)

series53.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* 1/12 x) (/ 1 x))
16.0ms	(* 1/12 x)

simplify69.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	130	119
1	448	110
2	2305	109
3	5001	109

prune57.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.2b remaining)

Error of 1.1b against oracle of 0.9b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample946.0ms

Algorithm

intervals

Results

395.0ms	2253×	body	1280	valid
184.0ms	1676×	body	640	valid
58.0ms	829×	body	320	valid
55.0ms	2822×	body	80	valid
50.0ms	2556×	body	80	overflowed
19.0ms	422×	body	160	valid