Details

sample129.0ms

Algorithm

intervals

Results

75.0ms	723×	body	80	nan
35.0ms	256×	body	80	valid

simplify72.0ms

Calls

1 calls:

Slowest

72.0ms

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

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

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

398×	`add-sqr-sqrt`
319×	`*-un-lft-identity`
258×	`associate-/l*`
234×	`frac-add`
219×	`sqrt-prod`
157×	`add-cube-cbrt`
150×	`difference-of-squares`
108×	`associate-/r*`
88×	`times-frac`
45×	`prod-diff`
39×	`swap-sqr`
36×	`clear-num` `frac-2neg` `distribute-lft-out--`
33×	`*-commutative` `unswap-sqr`
27×	`associate-l`
22×	`sqrt-div`
20×	`associate-/l/`
14×	`distribute-lft-out`
13×	`fma-def`
12×	`flip3--` `flip--`
9×	`associate-r`
8×	`div-inv` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-out` `fma-neg`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-exp` `distribute-rgt1-in` `flip-+`

Calls

4 calls:

Slowest

69.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
59.0ms	(/ (sqrt (- 1 (* x x))) x)
29.0ms	(sqrt (- 1 (* x x)))
13.0ms	(- 1 (* x x))

series389.0ms

Calls

4 calls:

Slowest

115.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
114.0ms	(/ (sqrt (- 1 (* x x))) x)
87.0ms	(sqrt (- 1 (* x x)))
73.0ms	(- 1 (* x x))

simplify56.4s

Calls

790 calls:

Slowest

1.1s	(+ (* (/ 1 (* (cbrt x) (cbrt x))) (cbrt x)) (* (cbrt x) (/ (sqrt (- 1 (* x x))) (* (cbrt x) (cbrt x)))))
482.0ms	(fma (- (* x x)) (* 1 1) (* (* x x) (* 1 1)))
432.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
403.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
395.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))

prune4.8s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
101×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
45×	`prod-diff`
30×	`sqrt-prod`
21×	`times-frac`
20×	`distribute-lft-out` `difference-of-squares`
16×	`associate-l`
14×	`distribute-lft-out--`
13×	`swap-sqr`
9×	`associate-r`
8×	`add-log-exp`
7×	`-commutative` `associate-/l` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `fma-neg`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `div-inv`

Calls

4 calls:

Slowest

148.0ms	(/ (+ 1 (sqrt (- 1 (* x x)))) x)
46.0ms	(sqrt (- 1 (* x x)))
29.0ms	(+ 1 (sqrt (- 1 (* x x))))
24.0ms	(- 1 (* x x))

series241.0ms

Calls

4 calls:

Slowest

89.0ms	(/ (+ 1 (sqrt (- 1 (* x x)))) x)
58.0ms	(sqrt (- 1 (* x x)))
47.0ms	(- 1 (* x x))
46.0ms	(+ 1 (sqrt (- 1 (* x x))))

simplify12.2s

Calls

209 calls:

Slowest

420.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
402.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
383.0ms	(/ (* (* (+ 1 (sqrt (- 1 (* x x)))) (+ 1 (sqrt (- 1 (* x x))))) (+ 1 (sqrt (- 1 (* x x))))) (* (* x x) x))
357.0ms	(fma 1 1 (- (* (* (cbrt x) (cbrt x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))))
322.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))

prune1.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.4s	23850×	body	80	nan
1.0s	8000×	body	80	valid