Details

sample103.0ms

Algorithm

intervals

Results

66.0ms	713×	body	80	nan
20.0ms	256×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	20
3	20
2	18
1	14
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.0b	(/ (sqrt (- 1 (* x x))) x)
0.0b	(sqrt (- 1 (* x x)))
0.0b	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
59×	`times-frac`
50×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
31×	`sqrt-prod`
16×	`distribute-lft-out`
15×	`log-prod`
14×	`div-inv`
13×	`fma-def`
10×	`difference-of-squares`
8×	`associate-/l*`
7×	`add-exp-log`
6×	`pow1` `distribute-rgt-out` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`log-div` `associate-/r*`
2×	`flip3-+` `flip3--` `frac-add` `distribute-rgt1-in` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `log-pow`

Counts

4 → 142

Calls

4 calls:

13.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
17.0ms	(/ (sqrt (- 1 (* x x))) x)
11.0ms	(sqrt (- 1 (* x x)))
47.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series592.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
149.0ms	(/ (sqrt (- 1 (* x x))) x)
81.0ms	(sqrt (- 1 (* x x)))
101.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify2.2s

Counts

154 → 154

Iterations

Iter	Nodes
3	4352
2	1352
1	520
0	247

prune1.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1 (* x x)))
0.1b	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) x))
0.3b	(/ 1 (sqrt x))
0.3b	(/ 1 (sqrt x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `times-frac`
35×	`add-cube-cbrt`
29×	`sqrt-prod`
12×	`associate-/r*` `add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-div` `1-exp` `div-inv` `inv-pow` `difference-of-squares`
1×	`rem-sqrt-square` `flip3--` `fma-udef` `flip--`

Counts

4 → 127

Calls

4 calls:

5.0ms	(sqrt (- 1 (* x x)))
0.0ms	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) x))
5.0ms	(/ 1 (sqrt x))
5.0ms	(/ 1 (sqrt x))

series318.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (- 1 (* x x)))
188.0ms	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) x))
37.0ms	(/ 1 (sqrt x))
33.0ms	(/ 1 (sqrt x))

simplify1.3s

Counts

139 → 139

Iterations

Iter	Nodes
3	2161
2	802
1	358
0	175

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	10

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.3s	24407×	body	80	nan
1.1s	8000×	body	80	valid