Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	54×	body	640	valid
7.0ms	131×	body	80	valid
5.0ms	21×	body	1280	valid
5.0ms	31×	body	320	valid
2.0ms	19×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
37.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
179.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))
4.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816

prune707.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 1.0 (/ 1 (- x 1.0))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
35×	`times-frac`
23×	`add-cube-cbrt`
11×	`add-log-exp`
10×	`add-exp-log`
9×	`associate-/r*`
8×	`add-cbrt-cube` `difference-of-squares`
7×	`distribute-lft-out--`
6×	`frac-add` `associate-/l*`
5×	`pow1` `distribute-lft-out`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-*r/` `div-exp` `un-div-inv` `frac-sub`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `clear-num` `sum-log` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `rec-exp` `pow-flip` `1-exp` `inv-pow`

Counts

4 → 115

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
6.0ms	(/ 1 (- x 1.0))
37.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
165.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 1.0 (/ 1 (- x 1.0))))

series20.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (+ x 1.0))
2.0ms	(/ 1 (- x 1.0))
4.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 1.0 (/ 1 (- x 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	539	918
1	2122	862
2	5002	835

prune660.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
18.7b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

2.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
37.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
19.0ms	(* (* (+ x 1.0) x) (- x 1.0))
11.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series16.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
6.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
6.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.5b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

19.0ms	(* (* (+ x 1.0) x) (- x 1.0))
16.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* (* (+ x 1.0) x) (- x 1.0))
6.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	398	514
1	1892	442
2	5002	441

prune318.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample1.0s

Algorithm

intervals

Results

372.0ms	1898×	body	640	valid
214.0ms	4039×	body	80	valid
146.0ms	975×	body	320	valid
145.0ms	589×	body	1280	valid
49.0ms	500×	body	160	valid