Average Error: 0.1 → 0.1
Time: 21.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r8326570 = x;
        double r8326571 = y;
        double r8326572 = sin(r8326571);
        double r8326573 = r8326570 * r8326572;
        double r8326574 = z;
        double r8326575 = cos(r8326571);
        double r8326576 = r8326574 * r8326575;
        double r8326577 = r8326573 + r8326576;
        return r8326577;
}
↓
double f(double x, double y, double z) {
        double r8326578 = y;
        double r8326579 = cos(r8326578);
        double r8326580 = z;
        double r8326581 = x;
        double r8326582 = sin(r8326578);
        double r8326583 = r8326581 * r8326582;
        double r8326584 = fma(r8326579, r8326580, r8326583);
        return r8326584;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))