Details

Time bar (total: 17.5s)

sample131.0ms

Algorithm
intervals
Results
80.0ms715×body80nan
31.0ms256×body80valid

simplify49.0ms

Calls
1 calls:
Slowest
49.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×div-inv
8×add-sqr-sqrt log-prod add-cube-cbrt
6×associate-/l* add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u fma-def distribute-rgt-out add-cbrt-cube insert-posit16 log1p-expm1-u 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
9.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
4.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
3.0ms
(/ (sqrt (- 1 (* x x))) x)
1.0ms
(- 1 (* x x))

series232.0ms

Calls
4 calls:
Slowest
114.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
57.0ms
(/ (sqrt (- 1 (* x x))) x)
41.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
20.0ms
(- 1 (* x x))

simplify4.0s

Calls
43 calls:
Slowest
449.0ms
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
372.0ms
(- (+ (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (log (- (sqrt -1)))) (/ 1 (* x (sqrt -1))))
343.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
313.0ms
(log (+ (pow (/ 1 x) 3) (pow (/ (sqrt (- 1 (* x x))) x) 3)))
312.0ms
(- (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))

prune810.0ms

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))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×frac-add
8×log-div sqrt-div
7×*-un-lft-identity
6×log-prod
5×add-sqr-sqrt flip3-- add-cube-cbrt flip-- add-log-exp
4×frac-times pow1 fma-def distribute-rgt-out associate-*l/ add-exp-log
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u div-inv
2×flip3-+ distribute-rgt1-in associate-*r/ un-div-inv flip-+
1×+-commutative sum-log sub-neg rem-log-exp log-pow
Calls
3 calls:
Slowest
12.0ms
(+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x)))
10.0ms
(log (+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x))))
1.0ms
(- 1 (* x x))

series166.0ms

Calls
3 calls:
Slowest
101.0ms
(log (+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x))))
46.0ms
(+ (/ 1 x) (* (sqrt (- 1 (* x x))) (/ 1 x)))
18.0ms
(- 1 (* x x))

simplify6.1s

Calls
44 calls:
Slowest
440.0ms
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
434.0ms
(+ (* 1 (sqrt (+ 1 (* x x)))) (* x (* (sqrt (- (* 1 1) (* (* x x) (* x x)))) (/ 1 x))))
429.0ms
(log (+ (* 1 (sqrt (+ 1 (* x x)))) (* x (* (sqrt (- (* 1 1) (* (* x x) (* x x)))) (/ 1 x)))))
415.0ms
(log (+ (* 1 (sqrt (+ (* 1 1) (+ (* (* x x) (* x x)) (* 1 (* x x)))))) (* x (* (sqrt (- (pow 1 3) (pow (* x x) 3))) (/ 1 x)))))
413.0ms
(log (+ (* 1 (* (sqrt (+ (* 1 1) (+ (* (* x x) (* x x)) (* 1 (* x x))))) x)) (* x (* (sqrt (- (pow 1 3) (pow (* x x) 3))) 1))))

prune639.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.8s24129×body80nan
1.0s8000×body80valid