Details

sample192.0ms

Algorithm

intervals

Results

130.0ms	837×	body	80	nan
35.0ms	256×	body	80	valid

simplify43.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
35×	`times-frac`
28×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
16×	`distribute-lft-out`
15×	`log-prod`
13×	`fma-def` `div-inv`
11×	`sqrt-prod`
6×	`distribute-rgt-out`
5×	`pow1` `add-log-exp`
4×	`add-exp-log`
3×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `sqrt-div` `frac-add` `distribute-rgt1-in` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 90

Calls

3 calls:

Slowest

34.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
12.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
11.0ms	(sqrt (- 1 (* x x)))

series370.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

199.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
108.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
63.0ms	(sqrt (- 1 (* x x)))

simplify1.5s

Counts: 99 → 99

prune848.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

31×	`sqrt-prod`
29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
9×	`pow1`
7×	`rem-sqrt-square` `sqrt-pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`div-inv` `pow-flip` `inv-pow` `difference-of-squares`
1×	`flip3--` `fma-udef` `flip--`

Counts

4 → 93

Calls

4 calls:

Slowest

7.0ms	(sqrt (/ 1 x))
5.0ms	(sqrt (- 1 (* x x)))
3.0ms	(sqrt (/ 1 x))
1.0ms	(fma (sqrt (/ 1 x)) (sqrt (/ 1 x)) (/ (sqrt (- 1 (* x x))) x))

series320.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

174.0ms	(fma (sqrt (/ 1 x)) (sqrt (/ 1 x)) (/ (sqrt (- 1 (* x x))) x))
86.0ms	(sqrt (- 1 (* x x)))
33.0ms	(sqrt (/ 1 x))
27.0ms	(sqrt (/ 1 x))

simplify828.0ms

Counts: 105 → 105

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.7s	24071×	body	80	nan
1.2s	8000×	body	80	valid