Average Error: 0.0 → 0.0
Time: 3.2s
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. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))

Details

Time bar (total: 1.1s)Debug log

start38.0ms

Algorithm
intervals

setup27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 18
Calls

1 calls. Slowest were:

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

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

34.0ms
(/ 2 (+ (exp x) (exp (- x))))

simplify277.0ms

Counts
9 → 21
Calls

9 calls. Slowest were:

193.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
49.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
10.0ms
(/ 2 (+ (exp (* -1 x)) (exp x)))

prune191.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 1 expressions with local error:

12.4b
(fma 5/24 (pow x 4) (fma (* x x) -1/2 1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma 5/24 (pow x 4) (fma (* x x) -1/2 1))

series31.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

31.0ms
(fma 5/24 (pow x 4) (fma (* x x) -1/2 1))

simplify181.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

70.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
59.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
50.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))

prune182.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms