Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	64×	body	640	valid
3.0ms	43×	body	320	valid
3.0ms	121×	body	80	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: 7.6b

localize11.0ms

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))
3.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite360.0ms

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:

10.0ms	(/ 1.0 (+ x 1.0))
12.0ms	(/ 1.0 (- x 1.0))
60.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
274.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (+ x 1.0))
28.0ms	(/ 1.0 (- x 1.0))
46.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
223.0ms	(+ (- (/ 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 (37.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5001	816

prune244.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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))
3.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- (- x 1.0))))

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

241×	`*-un-lft-identity`
196×	`times-frac`
147×	`add-sqr-sqrt`
114×	`distribute-rgt-neg-in`
100×	`distribute-lft-neg-in`
91×	`add-cube-cbrt`
42×	`distribute-lft-out--`
26×	`neg-mul-1` `difference-of-squares`
25×	`distribute-lft-out`
18×	`associate-/r*`
13×	`associate-/l*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `associate-/r/`
3×	`flip3--` `distribute-frac-neg` `frac-add` `flip--`
2×	`cbrt-undiv` `neg-sub0` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv` `distribute-neg-frac`
1×	`+-commutative` `associate-+l-` `associate-+r-` `unsub-neg`

Counts

4 → 268

Calls

4 calls:

11.0ms	(/ 1.0 (+ x 1.0))
23.0ms	(/ (- 1.0) (- (- x 1.0)))
58.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
344.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- (- x 1.0))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(/ (- 1.0) (- (- x 1.0)))
44.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
225.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- (- x 1.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	873	2340
1	3222	2266
2	5002	2265

prune551.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

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))
21.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite181.0ms

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:

94.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
45.0ms	(* (* (+ x 1.0) x) (- x 1.0))
28.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series241.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
41.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
104.0ms	(* (* (+ x 1.0) x) (- x 1.0))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune450.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

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))
0.3b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite105.0ms

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:

21.0ms	(* (+ x 1.0) x)
42.0ms	(* (* (+ x 1.0) x) (- x 1.0))
38.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series243.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (+ x 1.0) x)
104.0ms	(* (* (+ x 1.0) x) (- x 1.0))
93.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (51.0ms)

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

prune156.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.0b 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

sample578.0ms

Algorithm

intervals

Results

182.0ms	1872×	body	640	valid
116.0ms	4149×	body	80	valid
74.0ms	964×	body	320	valid
67.0ms	550×	body	1280	valid
23.0ms	468×	body	160	valid