Average Error: 24.5 → 10.6
Time: 28.4s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -6.186660797876992217305744119765362832497 \cdot 10^{-149}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 1.686242959618626939016913009565689776441 \cdot 10^{-164}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -6.186660797876992217305744119765362832497 \cdot 10^{-149}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;a \le 1.686242959618626939016913009565689776441 \cdot 10^{-164}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r466764 = x;
        double r466765 = y;
        double r466766 = r466765 - r466764;
        double r466767 = z;
        double r466768 = t;
        double r466769 = r466767 - r466768;
        double r466770 = r466766 * r466769;
        double r466771 = a;
        double r466772 = r466771 - r466768;
        double r466773 = r466770 / r466772;
        double r466774 = r466764 + r466773;
        return r466774;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r466775 = a;
        double r466776 = -6.186660797876992e-149;
        bool r466777 = r466775 <= r466776;
        double r466778 = x;
        double r466779 = y;
        double r466780 = r466779 - r466778;
        double r466781 = z;
        double r466782 = t;
        double r466783 = r466781 - r466782;
        double r466784 = r466775 - r466782;
        double r466785 = r466783 / r466784;
        double r466786 = r466780 * r466785;
        double r466787 = r466778 + r466786;
        double r466788 = 1.686242959618627e-164;
        bool r466789 = r466775 <= r466788;
        double r466790 = r466778 * r466781;
        double r466791 = r466790 / r466782;
        double r466792 = r466779 + r466791;
        double r466793 = r466781 * r466779;
        double r466794 = r466793 / r466782;
        double r466795 = r466792 - r466794;
        double r466796 = 1.0;
        double r466797 = r466796 / r466783;
        double r466798 = r466784 * r466797;
        double r466799 = r466780 / r466798;
        double r466800 = r466778 + r466799;
        double r466801 = r466789 ? r466795 : r466800;
        double r466802 = r466777 ? r466787 : r466801;
        return r466802;
}

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

Original24.5
Target9.6
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -6.186660797876992e-149

    1. Initial program 23.0

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

    3. Applied *-un-lft-identity23.0

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

    4. Applied times-frac10.0

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

    5. Simplified10.0

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

    if -6.186660797876992e-149 < a < 1.686242959618627e-164

    1. Initial program 29.7

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

    2. Taylor expanded around inf 13.8

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

    if 1.686242959618627e-164 < a

    1. Initial program 23.1

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

    3. Applied associate-/l*9.4

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

    5. Applied div-inv9.5

      \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -6.186660797876992217305744119765362832497 \cdot 10^{-149}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 1.686242959618626939016913009565689776441 \cdot 10^{-164}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.7744031700831742e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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