Average Error: 24.2 → 8.8
Time: 7.0s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.3647818100246518 \cdot 10^{-283} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.3647818100246518 \cdot 10^{-283} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0\right):\\
\;\;\;\;x + \left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r673753 = x;
        double r673754 = y;
        double r673755 = z;
        double r673756 = r673754 - r673755;
        double r673757 = t;
        double r673758 = r673757 - r673753;
        double r673759 = r673756 * r673758;
        double r673760 = a;
        double r673761 = r673760 - r673755;
        double r673762 = r673759 / r673761;
        double r673763 = r673753 + r673762;
        return r673763;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r673764 = x;
        double r673765 = y;
        double r673766 = z;
        double r673767 = r673765 - r673766;
        double r673768 = t;
        double r673769 = r673768 - r673764;
        double r673770 = r673767 * r673769;
        double r673771 = a;
        double r673772 = r673771 - r673766;
        double r673773 = r673770 / r673772;
        double r673774 = r673764 + r673773;
        double r673775 = -3.364781810024652e-283;
        bool r673776 = r673774 <= r673775;
        double r673777 = 0.0;
        bool r673778 = r673774 <= r673777;
        double r673779 = !r673778;
        bool r673780 = r673776 || r673779;
        double r673781 = cbrt(r673767);
        double r673782 = r673781 * r673781;
        double r673783 = cbrt(r673772);
        double r673784 = r673782 / r673783;
        double r673785 = r673781 / r673783;
        double r673786 = cbrt(r673769);
        double r673787 = r673786 * r673786;
        double r673788 = r673783 * r673783;
        double r673789 = cbrt(r673788);
        double r673790 = r673787 / r673789;
        double r673791 = r673785 * r673790;
        double r673792 = r673784 * r673791;
        double r673793 = cbrt(r673783);
        double r673794 = r673786 / r673793;
        double r673795 = r673792 * r673794;
        double r673796 = r673764 + r673795;
        double r673797 = r673764 * r673765;
        double r673798 = r673797 / r673766;
        double r673799 = r673798 + r673768;
        double r673800 = r673768 * r673765;
        double r673801 = r673800 / r673766;
        double r673802 = r673799 - r673801;
        double r673803 = r673780 ? r673796 : r673802;
        return r673803;
}

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

Original24.2
Target12.3
Herbie8.8
\[\begin{array}{l} \mathbf{if}\;z \lt -1.25361310560950359 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y z) (- t x)) (- a z))) < -3.364781810024652e-283 or 0.0 < (+ x (/ (* (- y z) (- t x)) (- a z)))

    1. Initial program 20.9

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

    3. Applied add-cube-cbrt21.4

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

    4. Applied times-frac8.5

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt8.5

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

    7. Applied cbrt-prod8.6

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

    8. Applied add-cube-cbrt8.7

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

    9. Applied times-frac8.7

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

    10. Applied associate-*r*8.0

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

    12. Applied add-cube-cbrt8.0

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

    13. Applied times-frac8.0

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

    14. Applied associate-*l*7.8

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

    if -3.364781810024652e-283 < (+ x (/ (* (- y z) (- t x)) (- a z))) < 0.0

    1. Initial program 59.7

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

    2. Taylor expanded around inf 18.7

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification8.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.3647818100246518 \cdot 10^{-283} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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