Average Error: 23.1 → 8.5
Time: 20.7s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} = -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z} + x\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.0404769334557312 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\ \end{array}\]
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} = -\infty:\\
\;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z} + x\\

\mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.0404769334557312 \cdot 10^{-273}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\

\mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0:\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r28686783 = x;
        double r28686784 = y;
        double r28686785 = z;
        double r28686786 = r28686784 - r28686785;
        double r28686787 = t;
        double r28686788 = r28686787 - r28686783;
        double r28686789 = r28686786 * r28686788;
        double r28686790 = a;
        double r28686791 = r28686790 - r28686785;
        double r28686792 = r28686789 / r28686791;
        double r28686793 = r28686783 + r28686792;
        return r28686793;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28686794 = x;
        double r28686795 = y;
        double r28686796 = z;
        double r28686797 = r28686795 - r28686796;
        double r28686798 = t;
        double r28686799 = r28686798 - r28686794;
        double r28686800 = r28686797 * r28686799;
        double r28686801 = a;
        double r28686802 = r28686801 - r28686796;
        double r28686803 = r28686800 / r28686802;
        double r28686804 = r28686794 + r28686803;
        double r28686805 = -inf.0;
        bool r28686806 = r28686804 <= r28686805;
        double r28686807 = r28686799 / r28686802;
        double r28686808 = r28686797 * r28686807;
        double r28686809 = r28686808 + r28686794;
        double r28686810 = -3.0404769334557312e-273;
        bool r28686811 = r28686804 <= r28686810;
        double r28686812 = 0.0;
        bool r28686813 = r28686804 <= r28686812;
        double r28686814 = r28686794 / r28686796;
        double r28686815 = r28686798 / r28686796;
        double r28686816 = r28686814 - r28686815;
        double r28686817 = r28686795 * r28686816;
        double r28686818 = r28686798 + r28686817;
        double r28686819 = cbrt(r28686797);
        double r28686820 = cbrt(r28686802);
        double r28686821 = r28686819 / r28686820;
        double r28686822 = r28686799 / r28686820;
        double r28686823 = r28686821 * r28686822;
        double r28686824 = r28686819 * r28686819;
        double r28686825 = r28686824 / r28686820;
        double r28686826 = r28686823 * r28686825;
        double r28686827 = r28686794 + r28686826;
        double r28686828 = r28686813 ? r28686818 : r28686827;
        double r28686829 = r28686811 ? r28686804 : r28686828;
        double r28686830 = r28686806 ? r28686809 : r28686829;
        return r28686830;
}

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

Original23.1
Target11.7
Herbie8.5
\[\begin{array}{l} \mathbf{if}\;z \lt -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (+ x (/ (* (- y z) (- t x)) (- a z))) < -inf.0

    1. Initial program 60.9

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

    3. Applied *-un-lft-identity60.9

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

    4. Applied times-frac17.4

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

    5. Simplified17.4

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

    if -inf.0 < (+ x (/ (* (- y z) (- t x)) (- a z))) < -3.0404769334557312e-273

    1. Initial program 1.9

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

    if -3.0404769334557312e-273 < (+ x (/ (* (- y z) (- t x)) (- a z))) < 0.0

    1. Initial program 58.2

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

    3. Applied add-cube-cbrt58.1

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

    4. Applied times-frac58.0

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

    6. Applied *-un-lft-identity58.0

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

    7. Applied cbrt-prod58.0

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

    8. Applied add-cube-cbrt57.9

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

    9. Applied times-frac57.9

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

    10. Applied associate-*r*57.7

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

    11. Simplified57.9

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

    12. Taylor expanded around inf 21.1

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

    13. Simplified23.3

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

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

    1. Initial program 19.5

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

    3. Applied add-cube-cbrt20.0

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

    4. Applied times-frac8.0

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

    6. Applied add-cube-cbrt7.9

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

    7. Applied times-frac7.9

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

    8. Applied associate-*l*7.5

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

    10. Applied *-commutative7.5

      \[\leadsto x + \color{blue}{\left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification8.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} = -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z} + x\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.0404769334557312 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"

  :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))))