Average Error: 0.1 → 0.1
Time: 32.6s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)
double f(double x, double y, double z) {
        double r11810401 = x;
        double r11810402 = y;
        double r11810403 = 0.5;
        double r11810404 = r11810402 + r11810403;
        double r11810405 = log(r11810402);
        double r11810406 = r11810404 * r11810405;
        double r11810407 = r11810401 - r11810406;
        double r11810408 = r11810407 + r11810402;
        double r11810409 = z;
        double r11810410 = r11810408 - r11810409;
        return r11810410;
}
↓
double f(double x, double y, double z) {
        double r11810411 = x;
        double r11810412 = y;
        double r11810413 = log(r11810412);
        double r11810414 = 0.5;
        double r11810415 = r11810412 + r11810414;
        double r11810416 = z;
        double r11810417 = r11810416 - r11810412;
        double r11810418 = fma(r11810413, r11810415, r11810417);
        double r11810419 = r11810411 - r11810418;
        return r11810419;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x - \mathsf{fma}\left(\log y, 0.5 + y, z - y\right)}\]

  3. Final simplification0.1

    \[\leadsto x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))