Details

Time bar (total: 11.9s)

sample146.0ms

Algorithm
intervals
Results
51.0ms263×body160nan
44.0ms533×body80nan
26.0ms256×body80valid

simplify113.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
113.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize13.0ms

Local error

Found 2 expressions with local error:

29.4b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite37.0ms

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
Counts
2 → 32
Calls
2 calls:
Slowest
23.0ms
(+ x (sqrt (- (* x x) 1)))
13.0ms
(sqrt (- (* x x) 1))

series113.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
58.0ms
(sqrt (- (* x x) 1))
56.0ms
(+ x (sqrt (- (* x x) 1)))

simplify2.5s

Counts
18 → 38
Calls
18 calls:
Slowest
467.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
243.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
243.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
227.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
193.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))

prune642.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 2 expressions with local error:

0.5b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
10×associate-*r*
7×associate-*l*
6×pow1 add-cube-cbrt
4×frac-times flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp unswap-sqr
3×flip3-- pow-prod-down flip--
2×sqrt-pow1 pow1/2 associate-*l/ associate-*r/ insert-posit16 difference-of-squares
1×+-commutative sum-log sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 56
Calls
2 calls:
Slowest
49.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
5.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series176.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
94.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
82.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify3.2s

Counts
50 → 62
Calls
50 calls:
Slowest
327.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
321.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
239.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
225.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
222.0ms
(* (exp x) (exp (* (sqrt (+ x 1)) (sqrt (- x 1)))))

prune634.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.8s7715×body160nan
1.3s16362×body80nan
739.0ms8000×body80valid