Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	53×	body	640	valid
5.0ms	20×	body	1280	valid
4.0ms	143×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	14×	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

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

localize8.0ms

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)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

1261×	`associate-/r*`
1123×	`*-un-lft-identity`
1080×	`frac-sub`
1012×	`frac-add`
966×	`associate-/l*`
867×	`add-sqr-sqrt`
663×	`add-cube-cbrt`
322×	`frac-2neg` `clear-num`
121×	`distribute-lft-out`
106×	`distribute-lft-out--`
100×	`difference-of-squares`
47×	`times-frac`
13×	`flip3--` `flip--`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `associate-/r/`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `flip3-+` `diff-log` `div-exp` `sum-log` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 1212

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
22.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
63.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(/ 1.0 (- x 1.0))
46.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
228.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify293.0ms

Algorithm

egg-herbie

Counts

1224 → 1224

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	28253

prune1.4s

Filtered

1224 candidates to 538 candidates (56.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1221	3	1224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1222	3	1225

Merged error: 0.0b

Counts

1225 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0))
0.0b	(/ (+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) 1)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) (/ (- x 1.0) 1.0)))
0.0b	(* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) (/ (- x 1.0) 1.0))
15.6b	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) 1))

rewrite4.1m

Algorithm

rewrite-expression-head

Rules

1629421×	`associate-*l/`
1344779×	`frac-times`
1177284×	`associate-/r*`
1165429×	`associate-/l*`
1076588×	`*-un-lft-identity`
803460×	`add-sqr-sqrt`
757988×	`frac-add`
746130×	`frac-sub`
689415×	`add-cube-cbrt`
682376×	`associate-/l/`
657319×	`associate-*r/`
368188×	`clear-num`
295297×	`frac-2neg`
292310×	`cbrt-prod`
146107×	`un-div-inv`
101444×	`distribute-lft-out`
97104×	`flip3-+` `flip-+`
59110×	`flip3--` `flip--`
58384×	`distribute-lft-out--`
54871×	`difference-of-squares`
15209×	`associate-l`
8109×	`times-frac`
2270×	`associate-/r/`
2232×	`*-commutative`
1866×	`unswap-sqr`
1587×	`associate-r`
149×	`div-inv`
139×	`add-cbrt-cube`
103×	`add-exp-log`
58×	`cbrt-undiv`
54×	`cbrt-unprod`
38×	`div-exp` `prod-exp`
28×	`swap-sqr`
11×	`pow1`
6×	`add-log-exp`
4×	`pow-prod-down`
1×	`+-commutative` `sum-log`

Counts

4 → 769640

Calls

4 calls:

231.0ms	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0))
32.9s	(/ (+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) 1)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) (/ (- x 1.0) 1.0)))
114.0ms	(* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) (/ (- x 1.0) 1.0))
9.9s	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) 1))

series12.0s

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0))
11.3s	(/ (+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) 1)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) (/ (- x 1.0) 1.0)))
204.0ms	(* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) (/ (- x 1.0) 1.0))
249.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ x 2.0)) (* (/ (+ x 1.0) (cbrt 1.0)) 1)) (/ (- x 1.0) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) (/ x 2.0)) 1))

simplify5.7m

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (28.4s)

Iter	Nodes	Cost
0	555244	28422382