Average Error: 6.6 → 1.0
Time: 2.8s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -8.5364205869367377 \cdot 10^{142}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 4.89281685888807661 \cdot 10^{-136}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.053801819903552 \cdot 10^{308}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\
\;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -8.5364205869367377 \cdot 10^{142}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 4.89281685888807661 \cdot 10^{-136}:\\
\;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.053801819903552 \cdot 10^{308}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\

\end{array}
double f(double x, double y, double z, double t) {
        double r491860 = x;
        double r491861 = y;
        double r491862 = r491861 - r491860;
        double r491863 = z;
        double r491864 = r491862 * r491863;
        double r491865 = t;
        double r491866 = r491864 / r491865;
        double r491867 = r491860 + r491866;
        return r491867;
}
↓
double f(double x, double y, double z, double t) {
        double r491868 = x;
        double r491869 = y;
        double r491870 = r491869 - r491868;
        double r491871 = z;
        double r491872 = r491870 * r491871;
        double r491873 = t;
        double r491874 = r491872 / r491873;
        double r491875 = r491868 + r491874;
        double r491876 = -inf.0;
        bool r491877 = r491875 <= r491876;
        double r491878 = r491873 / r491870;
        double r491879 = r491871 / r491878;
        double r491880 = r491879 + r491868;
        double r491881 = -8.536420586936738e+142;
        bool r491882 = r491875 <= r491881;
        double r491883 = 1.0;
        double r491884 = r491883 / r491873;
        double r491885 = r491872 * r491884;
        double r491886 = r491868 + r491885;
        double r491887 = 4.8928168588880766e-136;
        bool r491888 = r491875 <= r491887;
        double r491889 = 1.053801819903552e+308;
        bool r491890 = r491875 <= r491889;
        double r491891 = r491890 ? r491875 : r491880;
        double r491892 = r491888 ? r491880 : r491891;
        double r491893 = r491882 ? r491886 : r491892;
        double r491894 = r491877 ? r491880 : r491893;
        return r491894;
}

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

Original6.6
Target2.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0 or -8.536420586936738e+142 < (+ x (/ (* (- y x) z) t)) < 4.8928168588880766e-136 or 1.053801819903552e+308 < (+ x (/ (* (- y x) z) t))

    1. Initial program 14.3

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]

    2. Simplified1.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]
    3. Using strategy rm

    4. Applied clear-num2.1

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{t}{y - x}}}, z, x\right)\]
    5. Using strategy rm

    6. Applied fma-udef2.1

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

    7. Simplified1.8

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < -8.536420586936738e+142

    1. Initial program 0.1

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
    2. Using strategy rm

    3. Applied div-inv0.2

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}}\]

    if 4.8928168588880766e-136 < (+ x (/ (* (- y x) z) t)) < 1.053801819903552e+308

    1. Initial program 0.3

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -8.5364205869367377 \cdot 10^{142}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 4.89281685888807661 \cdot 10^{-136}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.053801819903552 \cdot 10^{308}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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