Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \left(\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}}\]

  4. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \left(\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)\]

Reproduce

herbie shell --seed 2018365 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))

Details

Time bar (total: 13.5s)Debug log

start58.0ms

Algorithm
intervals

setup24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- x 1))
0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
0.0b
(/ x (+ x 1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

9.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
2.0ms
(/ 1 (- x 1))
1.0ms
(/ x (+ x 1))

series69.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

46.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
12.0ms
(/ 1 (- x 1))
11.0ms
(/ x (+ x 1))

simplify690.0ms

Counts
25 → 56
Calls

25 calls. Slowest were:

120.0ms
(- (+ x (+ (pow x 2) 1)))
105.0ms
(+ (* 1 (+ x 1)) (* (- x 1) x))
94.0ms
(- (+ (* 2 (pow x 2)) (+ (* 2 (pow x 4)) 1)))

prune471.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (- x 1))
0.0b
(* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 101
Calls

4 calls. Slowest were:

16.0ms
(* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
2.0ms
(/ 1 (- x 1))
2.0ms
(/ 1 (- x 1))

series236.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

208.0ms
(* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
11.0ms
(/ 1 (- x 1))
10.0ms
(/ 1 (- x 1))
7.0ms
(/ 1 (- x 1))

simplify7.8s

Counts
78 → 113
Calls

78 calls. Slowest were:

542.0ms
(* (cbrt (+ (pow (/ 1 (- x 1)) 3) (pow (/ x (+ x 1)) 3))) (cbrt (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ x (+ x 1)) (/ x (+ x 1))))))
529.0ms
(* (cbrt (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ x (+ x 1)) (/ x (+ x 1))))) (cbrt (+ (pow (/ 1 (- x 1)) 3) (pow (/ x (+ x 1)) 3))))
414.0ms
(* (cbrt (+ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ 1 (- x 1)) (/ x (+ x 1)))))) (cbrt (- (/ 1 (- x 1)) (/ x (+ x 1)))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x 1))
0.0b
(log (exp (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
0.0b
(exp (+ (/ 1 (- x 1)) (/ x (+ x 1))))
0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

25.0ms
(exp (+ (/ 1 (- x 1)) (/ x (+ x 1))))
19.0ms
(log (exp (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
9.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

series179.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

90.0ms
(exp (+ (/ 1 (- x 1)) (/ x (+ x 1))))
39.0ms
(log (exp (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
38.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
11.0ms
(/ 1 (- x 1))

simplify1.6s

Counts
41 → 77
Calls

41 calls. Slowest were:

457.0ms
(- (+ (* 2/3 (* (pow x 6) (exp -1))) (exp -1)) (* 2 (* (pow x 2) (exp -1))))
137.0ms
(+ (* 1 (+ x 1)) (* (- x 1) x))
128.0ms
(- (+ (* 2 (pow x 2)) (+ (* 2 (pow x 4)) 1)))

prune838.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms