Average Error: 15.3 → 6.9
Time: 9.0s
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 r69872 = x;
        double r69873 = y;
        double r69874 = z;
        double r69875 = r69873 / r69874;
        double r69876 = t;
        double r69877 = r69875 * r69876;
        double r69878 = r69877 / r69876;
        double r69879 = r69872 * r69878;
        return r69879;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r69880 = x;
        double r69881 = y;
        double r69882 = z;
        double r69883 = r69881 / r69882;
        double r69884 = r69880 * r69883;
        return r69884;
}

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 4 regimes

  2. if (/ y z) < -1.2673089964731026e+219

    1. Initial program 44.2

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

    2. Simplified29.9

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

    4. Applied associate-*r/1.2

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

    6. Applied clear-num1.3

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    7. Using strategy rm

    8. Applied associate-/r*1.1

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]

    if -1.2673089964731026e+219 < (/ y z) < -6.788877789726705e-200

    1. Initial program 8.3

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

    2. Simplified0.2

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

    4. Applied associate-*r/9.9

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

    6. Applied associate-/l*0.3

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

    if -6.788877789726705e-200 < (/ y z) < 1.8144342740217e-313 or 3.400558014790777e+303 < (/ y z)

    1. Initial program 25.8

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

    2. Simplified21.8

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

    4. Applied associate-*r/0.5

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

    if 1.8144342740217e-313 < (/ y z) < 3.400558014790777e+303

    1. Initial program 10.8

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

    2. Simplified0.2

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification6.9

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

Reproduce

herbie shell --seed 2019297 
(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)))