Details

Time bar (total: 12.5s)

sample143.0ms

Algorithm
intervals
Results
45.0ms249×body160nan
39.0ms523×body80nan
38.0ms256×body80valid

simplify138.0ms

Calls
1 calls:
Slowest
137.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize14.0ms

Local error

Found 2 expressions with local error:

28.0b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×sqrt-prod
14×*-un-lft-identity
10×difference-of-squares
5×difference-of-sqr-1
4×add-log-exp
3×pow1 swap-sqr *-commutative add-cube-cbrt unswap-sqr
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 distribute-lft-out--
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 associate-*l* flip-+ flip-- distribute-lft-out
Calls
2 calls:
Slowest
30.0ms
(sqrt (- (* x x) 1))
26.0ms
(+ x (sqrt (- (* x x) 1)))

series116.0ms

Calls
2 calls:
Slowest
65.0ms
(+ x (sqrt (- (* x x) 1)))
51.0ms
(sqrt (- (* x x) 1))

simplify2.5s

Calls
32 calls:
Slowest
464.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
226.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
222.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
214.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
214.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))

prune444.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 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))
0.0b
(sqrt (- x 1))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×sqrt-prod
24×*-un-lft-identity
16×sqrt-div
10×pow1 associate-*r* add-cube-cbrt
8×associate-*l*
6×add-cbrt-cube add-exp-log add-log-exp
5×flip3-+ flip-+
4×frac-times sqrt-pow1 flip3-- pow1/2 insert-posit16 flip-- distribute-lft-out difference-of-squares unswap-sqr
3×pow-prod-down
2×rem-sqrt-square difference-of-sqr-1 associate-*l/ associate-*r/ distribute-lft-out--
1×+-commutative sum-log sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
53.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
39.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
7.0ms
(sqrt (- x 1))
5.0ms
(sqrt (+ x 1))

series231.0ms

Calls
4 calls:
Slowest
92.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
80.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
31.0ms
(sqrt (- x 1))
27.0ms
(sqrt (+ x 1))

simplify3.5s

Calls
77 calls:
Slowest
363.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
268.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
254.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
192.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
183.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- x 1)))

prune891.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s16087×body80nan
1.4s7615×body160nan
709.0ms8000×body80valid