Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}
double f(double x) {
        double r5004401 = 2.0;
        double r5004402 = x;
        double r5004403 = exp(r5004402);
        double r5004404 = -r5004402;
        double r5004405 = exp(r5004404);
        double r5004406 = r5004403 + r5004405;
        double r5004407 = r5004401 / r5004406;
        return r5004407;
}
↓
double f(double x) {
        double r5004408 = 2.0;
        double r5004409 = x;
        double r5004410 = exp(r5004409);
        double r5004411 = -r5004409;
        double r5004412 = exp(r5004411);
        double r5004413 = r5004410 + r5004412;
        double r5004414 = r5004408 / r5004413;
        double r5004415 = sqrt(r5004414);
        double r5004416 = r5004415 * r5004415;
        return r5004416;
}

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-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))