Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
50×	`times-frac`
45×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
21×	`fma-def`
11×	`distribute-lft-out`
9×	`associate-/r*` `distribute-lft-out--`
7×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/r/` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+`
1×	`+-commutative` `frac-add` `sum-log`

Counts

3 → 114

Calls

3 calls:

26.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ x (+ x 1.0))

series192.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
29.0ms	(/ 1.0 (- x 1.0))
38.0ms	(/ x (+ x 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	400	551
1	1470	525
2	5001	521

prune230.0ms

Filtered

123 candidates to 94 candidates (76.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	1	124

Merged error: 0b

Counts

124 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ x (+ x 1.0))
0.6b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
11.7b	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
37×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
18×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`difference-of-squares`
6×	`pow1` `flip3-+` `associate-/r/` `flip-+` `associate-/l*` `add-log-exp`
5×	`frac-add` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-r*` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`distribute-rgt-in` `associate-+l+` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*l/` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 137

Calls

4 calls:

15.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ x (+ x 1.0))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
12.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

series306.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
38.0ms	(/ x (+ x 1.0))
48.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
50.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	817	1171
1	4190	1086
2	5001	1081

prune331.0ms

Filtered

149 candidates to 121 candidates (81.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	1	150

Merged error: 0b

Counts

150 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample283.0ms

Algorithm

intervals

Results

194.0ms

8000×

body

valid