Average Error: 15.1 → 2.7
Time: 12.4s
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 r42459549 = x;
        double r42459550 = y;
        double r42459551 = z;
        double r42459552 = r42459550 / r42459551;
        double r42459553 = t;
        double r42459554 = r42459552 * r42459553;
        double r42459555 = r42459554 / r42459553;
        double r42459556 = r42459549 * r42459555;
        return r42459556;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r42459557 = y;
        double r42459558 = z;
        double r42459559 = r42459557 / r42459558;
        double r42459560 = -2.311589734371419e-251;
        bool r42459561 = r42459559 <= r42459560;
        double r42459562 = x;
        double r42459563 = r42459558 / r42459557;
        double r42459564 = r42459562 / r42459563;
        double r42459565 = 2.4604469162894e-321;
        bool r42459566 = r42459559 <= r42459565;
        double r42459567 = r42459562 / r42459558;
        double r42459568 = r42459567 * r42459557;
        double r42459569 = 2.6763432300690605e+68;
        bool r42459570 = r42459559 <= r42459569;
        double r42459571 = r42459570 ? r42459564 : r42459568;
        double r42459572 = r42459566 ? r42459568 : r42459571;
        double r42459573 = r42459561 ? r42459564 : r42459572;
        return r42459573;
}

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 
(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)))