Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
Internal Precision: 128
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{e^{x} + e^{-x}}\]

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

    \[\frac{2}{e^{x} + e^{-x}}\]

  2. Final simplification0.0

    \[\leadsto \frac{2}{e^{x} + e^{-x}}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))

Details

Time bar (total: 3.3s)Debug log

sample35.0ms

Algorithm
intervals

simplify8.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

8.0ms
(/ 2 (+ (exp x) (exp (- x))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ 2 (+ (exp x) (exp (- x))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

5.0ms
(/ 2 (+ (exp x) (exp (- x))))

series54.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

54.0ms
(/ 2 (+ (exp x) (exp (- x))))

simplify317.0ms

Counts
9 → 19
Calls

9 calls. Slowest were:

195.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
54.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
16.0ms
(/ 2 (+ (exp (* -1 x)) (exp x)))

prune179.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (exp (/ 2 (+ (exp x) (exp (- x))))))
0.0b
(exp (/ 2 (+ (exp x) (exp (- x)))))
0.0b
(/ 2 (+ (exp x) (exp (- x))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
3 → 48
Calls

3 calls. Slowest were:

3.0ms
(log (exp (/ 2 (+ (exp x) (exp (- x))))))
3.0ms
(/ 2 (+ (exp x) (exp (- x))))
2.0ms
(exp (/ 2 (+ (exp x) (exp (- x)))))

series169.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

94.0ms
(exp (/ 2 (+ (exp x) (exp (- x)))))
42.0ms
(/ 2 (+ (exp x) (exp (- x))))
32.0ms
(log (exp (/ 2 (+ (exp x) (exp (- x))))))

simplify1.1s

Counts
31 → 57
Calls

31 calls. Slowest were:

247.0ms
(exp (/ 2 (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))))
178.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
163.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))

prune501.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample810.0ms

Algorithm
intervals