Average Error: 15.1 → 2.7
Time: 13.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.311589734371419027279238960116033835921 \cdot 10^{-251}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 2.460446916289407789999312588483742434378 \cdot 10^{-321}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 2.676343230069060529690221971470663563109 \cdot 10^{68}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.311589734371419027279238960116033835921 \cdot 10^{-251}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 2.460446916289407789999312588483742434378 \cdot 10^{-321}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 2.676343230069060529690221971470663563109 \cdot 10^{68}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r38776017 = x;
        double r38776018 = y;
        double r38776019 = z;
        double r38776020 = r38776018 / r38776019;
        double r38776021 = t;
        double r38776022 = r38776020 * r38776021;
        double r38776023 = r38776022 / r38776021;
        double r38776024 = r38776017 * r38776023;
        return r38776024;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r38776025 = y;
        double r38776026 = z;
        double r38776027 = r38776025 / r38776026;
        double r38776028 = -2.311589734371419e-251;
        bool r38776029 = r38776027 <= r38776028;
        double r38776030 = x;
        double r38776031 = r38776026 / r38776025;
        double r38776032 = r38776030 / r38776031;
        double r38776033 = 2.4604469162894e-321;
        bool r38776034 = r38776027 <= r38776033;
        double r38776035 = r38776030 / r38776026;
        double r38776036 = r38776035 * r38776025;
        double r38776037 = 2.6763432300690605e+68;
        bool r38776038 = r38776027 <= r38776037;
        double r38776039 = r38776038 ? r38776032 : r38776036;
        double r38776040 = r38776034 ? r38776036 : r38776039;
        double r38776041 = r38776029 ? r38776032 : r38776040;
        return r38776041;
}

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
Target1.8
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < -2.311589734371419e-251 or 2.4604469162894e-321 < (/ y z) < 2.6763432300690605e+68

    1. Initial program 12.0

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

    2. Simplified8.0

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

    4. Applied associate-/l*2.8

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

    if -2.311589734371419e-251 < (/ y z) < 2.4604469162894e-321 or 2.6763432300690605e+68 < (/ y z)

    1. Initial program 21.9

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

    2. Simplified2.4

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

    4. Applied associate-/l*13.6

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

    6. Applied associate-/r/2.5

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.311589734371419027279238960116033835921 \cdot 10^{-251}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 2.460446916289407789999312588483742434378 \cdot 10^{-321}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 2.676343230069060529690221971470663563109 \cdot 10^{68}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))