Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r20432307 = x;
        double r20432308 = cosh(r20432307);
        double r20432309 = y;
        double r20432310 = sin(r20432309);
        double r20432311 = r20432310 / r20432309;
        double r20432312 = r20432308 * r20432311;
        return r20432312;
}
↓
double f(double x, double y) {
        double r20432313 = x;
        double r20432314 = cosh(r20432313);
        double r20432315 = y;
        double r20432316 = sin(r20432315);
        double r20432317 = r20432316 / r20432315;
        double r20432318 = r20432314 * r20432317;
        return r20432318;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]

  2. Final simplification0.1

    \[\leadsto \cosh x \cdot \frac{\sin y}{y}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))