Details

Time bar (total: 16.2s)

sample92.0ms

Algorithm
intervals
Results
56.0ms715×body80nan
23.0ms256×body80valid

simplify56.0ms

Calls
1 calls:
Slowest
55.0ms
(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
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0b
(/ (sqrt (- 1 (* x x))) x)
0.0b
(- 1 (* x x))
0.0b
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
11×div-inv
8×log-prod
7×add-sqr-sqrt add-cube-cbrt
6×associate-/l* add-log-exp
5×pow1 add-exp-log
4×distribute-rgt-out add-cbrt-cube insert-posit16 distribute-lft-out
3×log-div sqrt-prod
2×flip3-+ flip3-- sqrt-div frac-add distribute-rgt1-in flip-+ flip-- associate-/l/
1×+-commutative clear-num sum-log sub-neg frac-2neg rem-log-exp log-pow
Calls
4 calls:
Slowest
7.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
6.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
4.0ms
(/ (sqrt (- 1 (* x x))) x)
1.0ms
(- 1 (* x x))

series220.0ms

Calls
4 calls:
Slowest
91.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
58.0ms
(/ (sqrt (- 1 (* x x))) x)
42.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
28.0ms
(- 1 (* x x))

simplify3.7s

Calls
41 calls:
Slowest
411.0ms
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
395.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
331.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* (/ (sqrt (- 1 (* x x))) x) (/ (sqrt (- 1 (* x x))) x))))
317.0ms
(- (+ (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (log (- (sqrt -1)))) (/ 1 (* x (sqrt -1))))
305.0ms
(log (+ (pow (/ 1 x) 3) (pow (/ (sqrt (- 1 (* x x))) x) 3)))

prune695.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×frac-add
8×log-div sqrt-div
6×log-prod *-un-lft-identity
5×flip3-- flip-- add-log-exp
4×add-sqr-sqrt frac-times pow1 distribute-rgt-out associate-*l/ add-exp-log add-cube-cbrt
3×add-cbrt-cube insert-posit16
2×flip3-+ distribute-rgt1-in associate-*r/ un-div-inv flip-+ div-inv
1×+-commutative sum-log sub-neg rem-log-exp log-pow
Calls
3 calls:
Slowest
8.0ms
(+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x)))
5.0ms
(log (+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x))))
1.0ms
(- 1 (* x x))

series171.0ms

Calls
3 calls:
Slowest
110.0ms
(log (+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x))))
32.0ms
(+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x)))
29.0ms
(- 1 (* x x))

simplify5.7s

Calls
42 calls:
Slowest
566.0ms
(log (+ (pow (/ 1 x) 3) (pow (* (sqrt (- 1 (* x x))) (/ 1 x)) 3)))
439.0ms
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
439.0ms
(log (+ (* 1 (sqrt (+ 1 (* x x)))) (* x (* (sqrt (- (* 1 1) (* (* x x) (* x x)))) (/ 1 x)))))
382.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
366.0ms
(+ (* 1 (sqrt (+ (* 1 1) (+ (* (* x x) (* x x)) (* 1 (* x x)))))) (* x (* (sqrt (- (pow 1 3) (pow (* x x) 3))) (/ 1 x))))

prune617.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.9s

Algorithm
intervals
Results
3.1s24129×body80nan
995.0ms8000×body80valid