Average Error: 14.6 → 6.2
Time: 7.2s
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 r61089 = x;
        double r61090 = y;
        double r61091 = z;
        double r61092 = r61090 / r61091;
        double r61093 = t;
        double r61094 = r61092 * r61093;
        double r61095 = r61094 / r61093;
        double r61096 = r61089 * r61095;
        return r61096;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r61097 = x;
        double r61098 = y;
        double r61099 = z;
        double r61100 = r61098 / r61099;
        double r61101 = r61097 * r61100;
        return r61101;
}

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

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"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))