Details

Time bar (total: 11.9s)

sample74.0ms

Algorithm
intervals
Results
24.0ms514×body80nan
23.0ms234×body160nan
14.0ms256×body80valid

simplify124.0ms

Calls
1 calls:
Slowest
124.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize31.0ms

Local error

Found 2 expressions with local error:

30.4b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity sqrt-prod
5×add-sqr-sqrt
4×add-log-exp
3×pow1 add-cube-cbrt
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 difference-of-sqr-1 flip-+ flip-- distribute-lft-out
Calls
2 calls:
Slowest
23.0ms
(+ x (sqrt (- (* x x) 1)))
16.0ms
(sqrt (- (* x x) 1))

series158.0ms

Calls
2 calls:
Slowest
89.0ms
(+ x (sqrt (- (* x x) 1)))
69.0ms
(sqrt (- (* x x) 1))

simplify2.4s

Calls
18 calls:
Slowest
413.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
308.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
245.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))
212.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
202.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune297.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b
(sqrt (- x 1))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
5×add-cbrt-cube add-exp-log add-log-exp
4×frac-times flip3-+ flip3-- flip-+ flip-- difference-of-squares unswap-sqr
3×sqrt-pow1 pow1/2 pow-prod-down insert-posit16
2×difference-of-sqr-1 associate-*l/ associate-*r/ distribute-lft-out--
1×+-commutative rem-sqrt-square sum-log sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out
Calls
3 calls:
Slowest
42.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
5.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
4.0ms
(sqrt (- x 1))

series224.0ms

Calls
3 calls:
Slowest
103.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
78.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
44.0ms
(sqrt (- x 1))

simplify3.3s

Calls
64 calls:
Slowest
343.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
252.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
224.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
221.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
199.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))))

prune728.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.0s7557×body160nan
1.2s16003×body80nan
851.0ms8000×body80valid