Average Error: 0.0 → 0.0
Time: 42.5s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[e^{\log 2 - \log \left(e^{x} + e^{-x}\right)}\]
\frac{2}{e^{x} + e^{-x}}
↓
e^{\log 2 - \log \left(e^{x} + e^{-x}\right)}
double f(double x) {
        double r14917314 = 2.0;
        double r14917315 = x;
        double r14917316 = exp(r14917315);
        double r14917317 = -r14917315;
        double r14917318 = exp(r14917317);
        double r14917319 = r14917316 + r14917318;
        double r14917320 = r14917314 / r14917319;
        return r14917320;
}
↓
double f(double x) {
        double r14917321 = 2.0;
        double r14917322 = log(r14917321);
        double r14917323 = x;
        double r14917324 = exp(r14917323);
        double r14917325 = -r14917323;
        double r14917326 = exp(r14917325);
        double r14917327 = r14917324 + r14917326;
        double r14917328 = log(r14917327);
        double r14917329 = r14917322 - r14917328;
        double r14917330 = exp(r14917329);
        return r14917330;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-exp-log0.0

    \[\leadsto \frac{2}{\color{blue}{e^{\log \left(e^{x} + e^{-x}\right)}}}\]

  4. Applied add-exp-log0.0

    \[\leadsto \frac{\color{blue}{e^{\log 2}}}{e^{\log \left(e^{x} + e^{-x}\right)}}\]

  5. Applied div-exp0.0

    \[\leadsto \color{blue}{e^{\log 2 - \log \left(e^{x} + e^{-x}\right)}}\]

  6. Final simplification0.0

    \[\leadsto e^{\log 2 - \log \left(e^{x} + e^{-x}\right)}\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))