Average Error: 14.5 → 1.4
Time: 12.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.96646549046934189 \cdot 10^{230}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2270242891442878 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.933654612229097 \cdot 10^{80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.96646549046934189 \cdot 10^{230}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le -3.2270242891442878 \cdot 10^{-105}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le -0.0:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 6.933654612229097 \cdot 10^{80}:\\
\;\;\;\;\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 r421445 = x;
        double r421446 = y;
        double r421447 = z;
        double r421448 = r421446 / r421447;
        double r421449 = t;
        double r421450 = r421448 * r421449;
        double r421451 = r421450 / r421449;
        double r421452 = r421445 * r421451;
        return r421452;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r421453 = y;
        double r421454 = z;
        double r421455 = r421453 / r421454;
        double r421456 = -1.966465490469342e+230;
        bool r421457 = r421455 <= r421456;
        double r421458 = x;
        double r421459 = r421454 / r421458;
        double r421460 = r421453 / r421459;
        double r421461 = -3.2270242891442878e-105;
        bool r421462 = r421455 <= r421461;
        double r421463 = r421455 * r421458;
        double r421464 = -0.0;
        bool r421465 = r421455 <= r421464;
        double r421466 = r421453 * r421458;
        double r421467 = r421466 / r421454;
        double r421468 = 6.933654612229097e+80;
        bool r421469 = r421455 <= r421468;
        double r421470 = r421469 ? r421463 : r421460;
        double r421471 = r421465 ? r421467 : r421470;
        double r421472 = r421462 ? r421463 : r421471;
        double r421473 = r421457 ? r421460 : r421472;
        return r421473;
}

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

Original14.5
Target1.5
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.966465490469342e+230 or 6.933654612229097e+80 < (/ y z)

    1. Initial program 32.0

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

    2. Simplified3.2

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

    4. Applied associate-/l*4.4

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

    if -1.966465490469342e+230 < (/ y z) < -3.2270242891442878e-105 or -0.0 < (/ y z) < 6.933654612229097e+80

    1. Initial program 9.0

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

    2. Simplified8.3

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

    4. Applied associate-/l*8.7

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

    6. Applied associate-/r/2.5

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

    if -3.2270242891442878e-105 < (/ y z) < -0.0

    1. Initial program 15.3

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

    2. Simplified1.8

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.96646549046934189 \cdot 10^{230}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2270242891442878 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.933654612229097 \cdot 10^{80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(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)))