Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	65×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	32×	body	320	valid
2.0ms	18×	body	1280	valid
0.0ms	7×	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: 10.8b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite233.0ms

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))
37.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
182.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
45.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
25.0ms	(/ 1.0 (+ x 1.0))
214.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (41.0ms)

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

prune255.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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)) (- x 1.0))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
15.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

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)))
16.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
22.0ms	(* (* (+ x 1.0) x) (- x 1.0))
10.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series229.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
38.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
100.0ms	(* (* (+ 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))

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1037	2507
1	5001	2360

prune499.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite51.0ms

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:

9.0ms	(* (+ x 1.0) x)
19.0ms	(* (* (+ x 1.0) x) (- x 1.0))
20.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series231.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (+ x 1.0) x)
95.0ms	(* (* (+ x 1.0) x) (- x 1.0))
88.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (55.0ms)

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

prune164.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (- x 1.0))
0.0b	(* (+ x 1.0) x)
0.1b	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
0.6b	(/ 1 (* (+ x 1.0) x))

rewrite72.0ms

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:

5.0ms	(/ 2.0 (- x 1.0))
9.0ms	(* (+ x 1.0) x)
44.0ms	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
8.0ms	(/ 1 (* (+ x 1.0) x))

series205.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 2.0 (- x 1.0))
42.0ms	(* (+ x 1.0) x)
92.0ms	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
36.0ms	(/ 1 (* (+ x 1.0) x))

simplify88.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (76.0ms)

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

prune254.0ms

Pruning

5 alts after pruning (3 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

sample572.0ms

Algorithm

intervals

Results

195.0ms	1894×	body	640	valid
113.0ms	4186×	body	80	valid
77.0ms	903×	body	320	valid
76.0ms	547×	body	1280	valid
24.0ms	470×	body	160	valid