Average Error: 14.6 → 6.2
Time: 7.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[x \cdot \frac{y}{z}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
x \cdot \frac{y}{z}
double f(double x, double y, double z, double t) {
        double r418917 = x;
        double r418918 = y;
        double r418919 = z;
        double r418920 = r418918 / r418919;
        double r418921 = t;
        double r418922 = r418920 * r418921;
        double r418923 = r418922 / r418921;
        double r418924 = r418917 * r418923;
        return r418924;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r418925 = x;
        double r418926 = y;
        double r418927 = z;
        double r418928 = r418926 / r418927;
        double r418929 = r418925 * r418928;
        return r418929;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target1.6
Herbie6.2
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < -9.977313556681295e+137 or -8.025550655899652e-304 < (/ y z)

    1. Initial program 17.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified9.1

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied associate-*r/4.9

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]

    if -9.977313556681295e+137 < (/ y z) < -8.025550655899652e-304

    1. Initial program 8.5

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified0.2

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.2

    \[\leadsto x \cdot \frac{y}{z}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045005e245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.90752223693390633e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.65895442315341522e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))