Average Error: 0.0 → 0.1
Time: 18.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\sqrt{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \left(\sqrt{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r103380 = x;
        double r103381 = sin(r103380);
        double r103382 = y;
        double r103383 = sinh(r103382);
        double r103384 = r103383 / r103382;
        double r103385 = r103381 * r103384;
        return r103385;
}
↓
double f(double x, double y) {
        double r103386 = x;
        double r103387 = sin(r103386);
        double r103388 = y;
        double r103389 = sinh(r103388);
        double r103390 = r103389 / r103388;
        double r103391 = sqrt(r103390);
        double r103392 = sqrt(r103391);
        double r103393 = r103392 * r103392;
        double r103394 = r103387 * r103393;
        double r103395 = r103394 * r103391;
        return r103395;
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

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Derivation

  1. Initial program 0.0

    \[\sin x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \sin x \cdot \color{blue}{\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)}\]

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{\left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)} \cdot \sqrt{\frac{\sinh y}{y}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.0

    \[\leadsto \left(\sqrt{\color{blue}{\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}}} \cdot \sin x\right) \cdot \sqrt{\frac{\sinh y}{y}}\]

  8. Applied sqrt-prod0.1

    \[\leadsto \left(\color{blue}{\left(\sqrt{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right)} \cdot \sin x\right) \cdot \sqrt{\frac{\sinh y}{y}}\]

  9. Final simplification0.1

    \[\leadsto \left(\sin x \cdot \left(\sqrt{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))