Details

sample131.0ms

Algorithm

intervals

Results

76.0ms	657×	body	80	nan
33.0ms	256×	body	80	valid

simplify45.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
46×	`times-frac`
45×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
28×	`sqrt-prod`
13×	`fma-def`
12×	`difference-of-squares`
8×	`div-inv` `distribute-lft-out` `associate-/l*` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `distribute-rgt-out` `flip3--` `fma-neg` `prod-diff` `flip--`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-exp` `frac-add` `distribute-rgt1-in` `flip-+`

Counts

4 → 135

Calls

4 calls:

Slowest

16.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
14.0ms	(sqrt (- 1 (* x x)))
9.0ms	(- 1 (* x x))
9.0ms	(/ (sqrt (- 1 (* x x))) x)

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(/ (sqrt (- 1 (* x x))) x)
95.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
69.0ms	(sqrt (- 1 (* x x)))
45.0ms	(- 1 (* x x))

simplify1.3s

Counts: 147 → 147

prune1.7s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
149×	`*-un-lft-identity`
140×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
85×	`sqrt-prod`
38×	`associate-/r*`
34×	`difference-of-squares`
17×	`add-exp-log`
13×	`fma-def`
12×	`sqrt-div`
11×	`add-cbrt-cube` `associate-/r/` `div-inv`
8×	`div-exp`
7×	`distribute-lft-out`
6×	`pow1` `flip3--` `flip--` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `frac-add` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 254

Calls

4 calls:

Slowest

42.0ms	(+ (/ 1 x) (/ 1 (/ x (sqrt (- 1 (* x x))))))
11.0ms	(/ 1 (/ x (sqrt (- 1 (* x x)))))
9.0ms	(sqrt (- 1 (* x x)))
8.0ms	(/ x (sqrt (- 1 (* x x))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(/ 1 (/ x (sqrt (- 1 (* x x)))))
147.0ms	(/ x (sqrt (- 1 (* x x))))
116.0ms	(+ (/ 1 x) (/ 1 (/ x (sqrt (- 1 (* x x))))))
58.0ms	(sqrt (- 1 (* x x)))

simplify1.3s

Counts: 266 → 266

prune2.6s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.3s	23218×	body	80	nan
1.0s	8000×	body	80	valid