Average Error: 15.1 → 1.0
Time: 13.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.3161828153264955 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.4642773403213894 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.802087804866568 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.7035288058957 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.3161828153264955 \cdot 10^{+221}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -4.4642773403213894 \cdot 10^{-101}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 9.802087804866568 \cdot 10^{-279}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.7035288058957 \cdot 10^{+120}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r23448093 = x;
        double r23448094 = y;
        double r23448095 = z;
        double r23448096 = r23448094 / r23448095;
        double r23448097 = t;
        double r23448098 = r23448096 * r23448097;
        double r23448099 = r23448098 / r23448097;
        double r23448100 = r23448093 * r23448099;
        return r23448100;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r23448101 = y;
        double r23448102 = z;
        double r23448103 = r23448101 / r23448102;
        double r23448104 = -2.3161828153264955e+221;
        bool r23448105 = r23448103 <= r23448104;
        double r23448106 = x;
        double r23448107 = r23448106 / r23448102;
        double r23448108 = r23448101 * r23448107;
        double r23448109 = -4.4642773403213894e-101;
        bool r23448110 = r23448103 <= r23448109;
        double r23448111 = r23448103 * r23448106;
        double r23448112 = 9.802087804866568e-279;
        bool r23448113 = r23448103 <= r23448112;
        double r23448114 = 1.7035288058957e+120;
        bool r23448115 = r23448103 <= r23448114;
        double r23448116 = r23448102 / r23448106;
        double r23448117 = r23448101 / r23448116;
        double r23448118 = r23448115 ? r23448111 : r23448117;
        double r23448119 = r23448113 ? r23448108 : r23448118;
        double r23448120 = r23448110 ? r23448111 : r23448119;
        double r23448121 = r23448105 ? r23448108 : r23448120;
        return r23448121;
}

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

Original15.1
Target1.5
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -2.3161828153264955e+221 or -4.4642773403213894e-101 < (/ y z) < 9.802087804866568e-279

    1. Initial program 21.4

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

    2. Simplified1.6

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

    if -2.3161828153264955e+221 < (/ y z) < -4.4642773403213894e-101 or 9.802087804866568e-279 < (/ y z) < 1.7035288058957e+120

    1. Initial program 7.6

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

    2. Simplified9.6

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

    4. Applied associate-*r/9.7

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

    6. Applied clear-num10.1

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

    8. Applied associate-/r*0.8

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

    9. Applied associate-/r/0.3

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

    10. Simplified0.2

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

    if 1.7035288058957e+120 < (/ y z)

    1. Initial program 31.1

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

    2. Simplified2.6

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

    4. Applied clear-num3.0

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

    5. Applied un-div-inv2.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.3161828153264955 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.4642773403213894 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.802087804866568 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.7035288058957 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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