Average Error: 0.1 → 0.1
Time: 31.8s
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 r16334566 = x;
        double r16334567 = y;
        double r16334568 = 0.5;
        double r16334569 = r16334567 + r16334568;
        double r16334570 = log(r16334567);
        double r16334571 = r16334569 * r16334570;
        double r16334572 = r16334566 - r16334571;
        double r16334573 = r16334572 + r16334567;
        double r16334574 = z;
        double r16334575 = r16334573 - r16334574;
        return r16334575;
}
↓
double f(double x, double y, double z) {
        double r16334576 = x;
        double r16334577 = y;
        double r16334578 = log(r16334577);
        double r16334579 = 0.5;
        double r16334580 = r16334577 + r16334579;
        double r16334581 = z;
        double r16334582 = r16334581 - r16334577;
        double r16334583 = fma(r16334578, r16334580, r16334582);
        double r16334584 = r16334576 - r16334583;
        return r16334584;
}

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))