Average Error: 23.5 → 10.9
Time: 19.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.95393039354896 \cdot 10^{-270}:\\ \;\;\;\;\left(\frac{y}{\frac{a - t}{z - t}} + x\right) - \left(\frac{\sqrt[3]{x}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{a - t}}{z - t}}\\ \mathbf{elif}\;a \le 1.7492318001765757 \cdot 10^{-157}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\frac{a - t}{z - t}} + x\right) - \frac{x}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.95393039354896 \cdot 10^{-270}:\\
\;\;\;\;\left(\frac{y}{\frac{a - t}{z - t}} + x\right) - \left(\frac{\sqrt[3]{x}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{a - t}}{z - t}}\\

\mathbf{elif}\;a \le 1.7492318001765757 \cdot 10^{-157}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{y}{\frac{a - t}{z - t}} + x\right) - \frac{x}{\frac{a - t}{z - t}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r31324665 = x;
        double r31324666 = y;
        double r31324667 = r31324666 - r31324665;
        double r31324668 = z;
        double r31324669 = t;
        double r31324670 = r31324668 - r31324669;
        double r31324671 = r31324667 * r31324670;
        double r31324672 = a;
        double r31324673 = r31324672 - r31324669;
        double r31324674 = r31324671 / r31324673;
        double r31324675 = r31324665 + r31324674;
        return r31324675;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31324676 = a;
        double r31324677 = -4.95393039354896e-270;
        bool r31324678 = r31324676 <= r31324677;
        double r31324679 = y;
        double r31324680 = t;
        double r31324681 = r31324676 - r31324680;
        double r31324682 = z;
        double r31324683 = r31324682 - r31324680;
        double r31324684 = r31324681 / r31324683;
        double r31324685 = r31324679 / r31324684;
        double r31324686 = x;
        double r31324687 = r31324685 + r31324686;
        double r31324688 = cbrt(r31324686);
        double r31324689 = cbrt(r31324681);
        double r31324690 = r31324688 / r31324689;
        double r31324691 = r31324690 * r31324690;
        double r31324692 = r31324689 / r31324683;
        double r31324693 = r31324688 / r31324692;
        double r31324694 = r31324691 * r31324693;
        double r31324695 = r31324687 - r31324694;
        double r31324696 = 1.7492318001765757e-157;
        bool r31324697 = r31324676 <= r31324696;
        double r31324698 = r31324686 * r31324682;
        double r31324699 = r31324698 / r31324680;
        double r31324700 = r31324679 + r31324699;
        double r31324701 = r31324682 * r31324679;
        double r31324702 = r31324701 / r31324680;
        double r31324703 = r31324700 - r31324702;
        double r31324704 = r31324686 / r31324684;
        double r31324705 = r31324687 - r31324704;
        double r31324706 = r31324697 ? r31324703 : r31324705;
        double r31324707 = r31324678 ? r31324695 : r31324706;
        return r31324707;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original23.5
Target9.4
Herbie10.9
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -4.95393039354896e-270

    1. Initial program 23.4

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

    3. Applied associate-/l*11.4

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-sub11.5

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

    6. Applied associate-+r-11.5

      \[\leadsto \color{blue}{\left(x + \frac{y}{\frac{a - t}{z - t}}\right) - \frac{x}{\frac{a - t}{z - t}}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity11.5

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

    9. Applied add-cube-cbrt11.6

      \[\leadsto \left(x + \frac{y}{\frac{a - t}{z - t}}\right) - \frac{x}{\frac{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}{1 \cdot \left(z - t\right)}}\]

    10. Applied times-frac11.6

      \[\leadsto \left(x + \frac{y}{\frac{a - t}{z - t}}\right) - \frac{x}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{z - t}}}\]

    11. Applied add-cube-cbrt11.6

      \[\leadsto \left(x + \frac{y}{\frac{a - t}{z - t}}\right) - \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{z - t}}\]

    12. Applied times-frac11.7

      \[\leadsto \left(x + \frac{y}{\frac{a - t}{z - t}}\right) - \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{a - t}}{z - t}}}\]

    13. Simplified11.7

      \[\leadsto \left(x + \frac{y}{\frac{a - t}{z - t}}\right) - \color{blue}{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{a - t}}\right)} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{a - t}}{z - t}}\]

    if -4.95393039354896e-270 < a < 1.7492318001765757e-157

    1. Initial program 28.5

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

    2. Taylor expanded around inf 11.3

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

    if 1.7492318001765757e-157 < a

    1. Initial program 21.9

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

    3. Applied associate-/l*9.8

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-sub9.8

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

    6. Applied associate-+r-9.8

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

  4. Final simplification10.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.95393039354896 \cdot 10^{-270}:\\ \;\;\;\;\left(\frac{y}{\frac{a - t}{z - t}} + x\right) - \left(\frac{\sqrt[3]{x}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{a - t}}{z - t}}\\ \mathbf{elif}\;a \le 1.7492318001765757 \cdot 10^{-157}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\frac{a - t}{z - t}} + x\right) - \frac{x}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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