Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	53×	body	640	valid
4.0ms	143×	body	80	valid
3.0ms	20×	body	1280	valid
2.0ms	26×	body	320	valid
1.0ms	14×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 8.7b

Counts

2 → 1

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))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

1765×	`*-un-lft-identity`
1348×	`add-sqr-sqrt`
1261×	`associate-/r*`
1132×	`add-cube-cbrt`
1080×	`frac-sub`
1012×	`frac-add`
966×	`associate-/l*`
703×	`times-frac`
468×	`prod-diff`
322×	`frac-2neg` `clear-num`
236×	`associate-+l+`
203×	`distribute-lft-out`
109×	`distribute-lft-out--`
104×	`difference-of-squares`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
13×	`flip3--` `flip--`
11×	`add-log-exp`
10×	`fma-def`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `sum-log`
1×	`+-commutative` `associate-+l-`

Counts

4 → 1716

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
32.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
94.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(/ 1.0 (- x 1.0))
48.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
237.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify392.0ms

Algorithm

egg-herbie

Counts

1728 → 1728

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5001	37459

prune2.8s

Filtered

1728 candidates to 918 candidates (46.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1725	3	1728
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1726	3	1729

Merged error: 0.1b

Counts

1729 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.3b	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.7b	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
15.2b	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite9.9m

Algorithm

rewrite-expression-head

Calls

4 calls:

26.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
292.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
58.5s	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
2.4m	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))