Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	59×	body	640	valid
3.0ms	133×	body	80	valid
3.0ms	36×	body	320	valid
2.0ms	15×	body	1280	valid
1.0ms	13×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
35×	`times-frac`
33×	`add-sqr-sqrt`
14×	`distribute-lft-out--`
13×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`distribute-lft-out`
8×	`difference-of-squares`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `flip3--` `frac-add` `flip--` `associate-/l*`
2×	`sub-neg` `associate-+l+` `diff-log` `sum-log` `associate-/r/` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

3 → 81

Calls

3 calls:

10.0ms	(/ 1.0 (- x 1.0))
57.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
261.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ 1.0 (- x 1.0))
38.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
196.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	421	692
1	1417	662
2	5002	653

prune166.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
19.3b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite178.0ms

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:

90.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
7.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
42.0ms	(* (* (+ x 1.0) x) (- x 1.0))
29.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series202.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
34.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
86.0ms	(* (* (+ 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))

simplify44.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune411.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.1b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

20.0ms	(* (+ x 1.0) x)
43.0ms	(* (* (+ x 1.0) x) (- x 1.0))
33.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (+ x 1.0) x)
89.0ms	(* (* (+ x 1.0) x) (- x 1.0))
83.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	430	600
1	2219	516
2	5002	515

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ 2.0 (- x 1.0))
0.0b	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
0.2b	(/ 1 (* (+ x 1.0) x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
50×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-cbrt-cube`
29×	`add-cube-cbrt`
24×	`associate-r` `prod-exp`
20×	`div-exp`
13×	`associate-l`
11×	`pow1`
10×	`cbrt-undiv` `cbrt-unprod`
8×	`associate-/r/`
7×	`associate-*l/` `distribute-lft-out--` `difference-of-squares`
6×	`rec-exp` `1-exp` `associate-/r` `associate-/l`
4×	`div-inv` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `unswap-sqr`
2×	`flip3--` `pow-flip` `frac-2neg` `clear-num` `*-commutative` `flip--`
1×	`frac-times` `associate-*r/` `distribute-lft-out` `inv-pow`

Counts

4 → 152

Calls

4 calls:

20.0ms	(* (+ x 1.0) x)
10.0ms	(/ 2.0 (- x 1.0))
80.0ms	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
17.0ms	(/ 1 (* (+ x 1.0) x))

series181.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (+ x 1.0) x)
30.0ms	(/ 2.0 (- x 1.0))
83.0ms	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
29.0ms	(/ 1 (* (+ x 1.0) x))

simplify86.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	646	1005
1	3429	855
2	5002	847

prune249.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes16.0ms

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	15	6
1	15	6

end0.0ms

sample589.0ms

Algorithm

intervals

Results

187.0ms	1840×	body	640	valid
111.0ms	4166×	body	80	valid
75.0ms	927×	body	320	valid
75.0ms	600×	body	1280	valid
23.0ms	468×	body	160	valid