Details

Time bar (total: 27.4s)

sample113.0ms

Algorithm
intervals
Results
40.0ms270×body160nan
32.0ms533×body80nan
20.0ms256×body80valid

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
115.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize12.0ms

Local error

Found 2 expressions with local error:

29.7b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite20.0ms

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
12.0ms
(+ x (sqrt (- (* x x) 1)))
8.0ms
(sqrt (- (* x x) 1))

series132.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(+ x (sqrt (- (* x x) 1)))
50.0ms
(sqrt (- (* x x) 1))

simplify2.4s

Counts
18 → 38
Calls
18 calls:
Slowest
418.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
245.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
223.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
203.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
203.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune353.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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
Counts
3 → 76
Calls
3 calls:
Slowest
23.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
7.0ms
(sqrt (- x 1))
4.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series218.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
93.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
82.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
43.0ms
(sqrt (- x 1))

simplify3.5s

Counts
64 → 85
Calls
64 calls:
Slowest
337.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
322.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
245.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
219.0ms
(* (exp x) (exp (* (sqrt (+ x 1)) (sqrt (- x 1)))))
216.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune860.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1)))
0.2b
(* (* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1))) (sqrt (- (sqrt x) 1)))
0.1b
(sqrt (+ (sqrt x) 1))
0.1b
(sqrt (- (sqrt x) 1))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
70×sqrt-div
50×sqrt-prod
42×add-sqr-sqrt
32×frac-times
30×*-un-lft-identity
25×flip3-+ flip-+
22×associate-*r*
18×pow1
16×associate-*l/
12×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×flip3-- pow-prod-down associate-*r/ flip--
8×associate-*l* difference-of-squares
7×sqrt-pow1 pow1/2
5×distribute-lft-out
4×difference-of-sqr-1 prod-exp cbrt-unprod insert-posit16 distribute-lft-out-- add-log-exp unswap-sqr
3×sqrt-unprod
2×rem-sqrt-square *-commutative
Counts
4 → 143
Calls
4 calls:
Slowest
74.0ms
(* (* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1))) (sqrt (- (sqrt x) 1)))
54.0ms
(* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1)))
6.0ms
(sqrt (- (sqrt x) 1))
6.0ms
(sqrt (+ (sqrt x) 1))

series606.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(* (* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1))) (sqrt (- (sqrt x) 1)))
127.0ms
(* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1)))
115.0ms
(sqrt (- (sqrt x) 1))
105.0ms
(sqrt (+ (sqrt x) 1))

simplify12.8s

Counts
144 → 155
Calls
144 calls:
Slowest
707.0ms
(* (* (* (* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1))) (* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1)))) (* (sqrt (+ x 1)) (sqrt (+ (sqrt x) 1)))) (* (* (sqrt (- (sqrt x) 1)) (sqrt (- (sqrt x) 1))) (sqrt (- (sqrt x) 1))))
527.0ms
(* (* (sqrt (- (* x x) (* 1 1))) (sqrt (- (* (sqrt x) (sqrt x)) (* 1 1)))) (sqrt (- (pow (sqrt x) 3) (pow 1 3))))
525.0ms
(* (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (sqrt (- (sqrt x) 1))) (sqrt (+ (sqrt x) 1)))
432.0ms
(* (* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow (sqrt x) 3) (pow 1 3)))) (sqrt (- (pow (sqrt x) 3) (pow 1 3))))
429.0ms
(* (* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ (pow (sqrt x) 3) (pow 1 3)))) (sqrt (- (* (sqrt x) (sqrt x)) (* 1 1))))

prune2.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.3s7663×body160nan
1.2s16125×body80nan
1.1s8000×body80valid