Details

sample80.0ms

Algorithm

intervals

Results

51.0ms	181×	body	1280	valid
9.0ms	38×	body	640	valid
6.0ms	267×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

10.0ms	(- (exp x) 2.0)
49.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series65.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(- (exp x) 2.0)
50.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune91.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

24.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
10.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
12.0ms	(* 1/360 (pow x 6))
12.0ms	(* 1/12 (pow x 4))

series260.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
121.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
52.0ms	(* 1/360 (pow x 6))
34.0ms	(* 1/12 (pow x 4))

simplify52.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune399.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (exp x) (- (exp x) 2.0))
0.0b	(* (+ (exp x) 2.0) (exp x))
3.3b	(+ (* (exp x) (- (exp x) 2.0)) 1)

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube`
16×	`add-exp-log`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`flip3-+` `flip-+`
8×	`pow1` `add-cube-cbrt` `associate-r` `associate-/l/`
7×	`associate-l`
6×	`associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `distribute-lft-in` `associate-*r/` `div-exp`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `times-frac` `clear-num` `associate-/r` `sum-log` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

59.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
36.0ms	(* (exp x) (- (exp x) 2.0))
37.0ms	(* (+ (exp x) 2.0) (exp x))
20.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

series193.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
34.0ms	(* (exp x) (- (exp x) 2.0))
19.0ms	(* (+ (exp x) 2.0) (exp x))
52.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

simplify97.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	527	1022
1	3419	776
2	5001	765

prune200.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 2.0) (* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))
3.3b	(+ (* (exp x) (- (exp x) 2.0)) 1)
3.3b	(+ (* (exp x) (- (exp x) 2.0)) 1)

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-div`
36×	`flip3-+` `flip-+`
32×	`frac-times`
27×	`add-cbrt-cube`
26×	`associate-/l/`
24×	`add-exp-log` `add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
16×	`associate-*r/`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
8×	`associate-+l+` `sqrt-pow1` `pow1/2` `swap-sqr` `add-log-exp`
6×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
5×	`pow-prod-up`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 140

Calls

4 calls:

186.0ms	(/ (* (+ (exp x) 2.0) (* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))) (* (+ (exp x) 2.0) (exp x)))
136.0ms	(* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))
20.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)
20.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

series247.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (* (+ (exp x) 2.0) (* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))) (* (+ (exp x) 2.0) (exp x)))
53.0ms	(* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))
54.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)
50.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

simplify117.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	622	2206
1	3438	1718
2	5003	1674

prune351.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.6s	5686×	body	1280	valid
189.0ms	8425×	body	80	valid
189.0ms	1243×	body	640	valid
59.0ms	613×	body	320	valid
17.0ms	300×	body	160	valid