Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify6.0ms

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

localize6.0ms

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))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`times-frac`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `distribute-lft-out--`
5×	`add-log-exp`
4×	`associate-/r/` `difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `flip3--` `frac-add` `sum-log` `flip--`

Counts

3 → 87

Calls

3 calls:

27.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
6.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ x (+ x 1.0))

series191.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
28.0ms	(/ 1.0 (- x 1.0))
37.0ms	(/ x (+ x 1.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	379	534
1	1365	507
2	5001	502

prune175.0ms

Filtered

96 candidates to 70 candidates (72.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	1	97

Merged error: 0b

Counts

97 → 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))

rewrite44.0ms

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×	`frac-times` `associate-r/` `associate-r*`
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` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 128

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))
6.0ms	(/ 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:

171.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
37.0ms	(/ x (+ x 1.0))
48.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
49.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	776	1139
1	3935	1063
2	5002	1061

prune315.0ms

Filtered

140 candidates to 112 candidates (80.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	1	141

Merged error: 0b

Counts

141 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample262.0ms

Algorithm

intervals

Results

179.0ms

8000×

body

valid