Details

Time bar (total: 1.0m)

sample98.0ms

Algorithm
intervals
Results
60.0ms723×body80nan
23.0ms256×body80valid

simplify52.0ms

Calls
1 calls:
Slowest
52.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
354×add-sqr-sqrt
281×*-un-lft-identity
258×associate-/l*
234×frac-add
219×sqrt-prod
150×difference-of-squares
119×add-cube-cbrt
108×associate-/r*
79×times-frac
36×clear-num frac-2neg distribute-lft-out--
30×swap-sqr *-commutative unswap-sqr
22×sqrt-div
20×associate-/l/
18×associate-*l*
14×distribute-lft-out
12×flip3-- flip--
8×add-log-exp
7×div-inv
6×add-cbrt-cube add-exp-log
5×pow1
4×insert-posit16
3×distribute-rgt-out
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
96.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
59.0ms
(/ (sqrt (- 1 (* x x))) x)
32.0ms
(sqrt (- 1 (* x x)))
21.0ms
(- 1 (* x x))

series384.0ms

Calls
4 calls:
Slowest
146.0ms
(/ (sqrt (- 1 (* x x))) x)
98.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
74.0ms
(- 1 (* x x))
66.0ms
(sqrt (- 1 (* x x)))

simplify44.9s

Calls
687 calls:
Slowest
1.2s
(+ (* (/ 1 (* (cbrt x) (cbrt x))) (cbrt x)) (* (cbrt x) (/ (sqrt (- 1 (* x x))) (* (cbrt x) (cbrt x)))))
483.0ms
(+ (* (/ 1 (sqrt x)) (/ x (sqrt (- 1 (sqrt (* x x)))))) (* (sqrt x) (sqrt (+ 1 (sqrt (* x x))))))
437.0ms
(+ (* (/ 1 (* (cbrt x) (cbrt x))) (/ x (sqrt (- 1 (* x x))))) (* (cbrt x) 1))
401.0ms
(+ (* (/ 1 (* (cbrt x) (cbrt x))) (/ x (sqrt (- 1 (* x x))))) (* (cbrt x) (sqrt 1)))
386.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))

prune3.9s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

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))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
63×add-sqr-sqrt
30×sqrt-prod
21×times-frac
20×distribute-lft-out difference-of-squares
17×add-cube-cbrt
14×distribute-lft-out--
8×add-log-exp
7×associate-*l* associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×swap-sqr *-commutative insert-posit16 unswap-sqr
3×associate-/r*
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
126.0ms
(/ (+ 1 (sqrt (- 1 (* x x)))) x)
57.0ms
(+ 1 (sqrt (- 1 (* x x))))
29.0ms
(sqrt (- 1 (* x x)))
20.0ms
(- 1 (* x x))

series292.0ms

Calls
4 calls:
Slowest
101.0ms
(/ (+ 1 (sqrt (- 1 (* x x)))) x)
78.0ms
(- 1 (* x x))
70.0ms
(sqrt (- 1 (* x x)))
43.0ms
(+ 1 (sqrt (- 1 (* x x))))

simplify4.9s

Calls
115 calls:
Slowest
359.0ms
(/ (* (* (+ 1 (sqrt (- 1 (* x x)))) (+ 1 (sqrt (- 1 (* x x))))) (+ 1 (sqrt (- 1 (* x x))))) (* (* x x) x))
332.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
322.0ms
(- (* 1 1) (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))))
320.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
294.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample5.0s

Algorithm
intervals
Results
3.5s23850×body80nan
1.1s8000×body80valid