Details

sample11.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
110×	`frac-add`
107×	`add-sqr-sqrt`
103×	`associate-/r*`
73×	`add-cube-cbrt`
69×	`associate-/l*`
50×	`times-frac`
23×	`frac-2neg` `clear-num`
22×	`distribute-lft-out`
21×	`fma-def`
19×	`distribute-lft-out--`
17×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `flip--` `flip-+`
1×	`+-commutative` `sum-log`

Counts

3 → 223

Calls

3 calls:

28.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ x (+ x 1.0))

series187.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
27.0ms	(/ 1.0 (- x 1.0))
33.0ms	(/ x (+ x 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1271	2062
1	5002	1979

prune388.0ms

Filtered

232 candidates to 147 candidates (63.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	1	233

Merged error: 0b

Counts

233 → 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))

rewrite678.0ms

Algorithm

rewrite-expression-head

Rules

2592×	`add-sqr-sqrt`
1602×	`associate-/r*`
1255×	`*-un-lft-identity`
1190×	`frac-add`
1075×	`difference-of-squares`
858×	`frac-times`
516×	`swap-sqr`
462×	`associate-/l*`
442×	`flip3-+` `flip-+`
434×	`unswap-sqr`
432×	`add-cube-cbrt` `*-commutative`
429×	`associate-*l/`
401×	`associate-l`
331×	`times-frac`
223×	`distribute-lft-out--`
154×	`frac-2neg` `clear-num`
142×	`distribute-lft-out`
116×	`fma-def`
22×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-/r/`
6×	`pow1` `add-log-exp`
5×	`+-commutative`
4×	`distribute-rgt-in` `expm1-log1p-u` `associate-+l+` `distribute-lft-in` `log1p-expm1-u` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `sum-log`

Counts

4 → 1770

Calls

4 calls:

165.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ x (+ x 1.0))
21.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
47.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

series294.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
34.0ms	(/ x (+ x 1.0))
50.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
45.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

simplify359.0ms

Algorithm

egg-herbie

Counts

1782 → 1782

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	32193

prune1.7s

Filtered

1782 candidates to 504 candidates (28.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	1782	0	1782
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1782	1	1783

Merged error: 0b

Counts

1783 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample276.0ms

Algorithm

intervals

Results

185.0ms

8000×

body

valid