Average Error: 24.0 → 8.7
Time: 22.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -8.143669236760688 \cdot 10^{-278}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -8.143669236760688 \cdot 10^{-278}:\\
\;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\

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

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r32373127 = x;
        double r32373128 = y;
        double r32373129 = r32373128 - r32373127;
        double r32373130 = z;
        double r32373131 = t;
        double r32373132 = r32373130 - r32373131;
        double r32373133 = r32373129 * r32373132;
        double r32373134 = a;
        double r32373135 = r32373134 - r32373131;
        double r32373136 = r32373133 / r32373135;
        double r32373137 = r32373127 + r32373136;
        return r32373137;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32373138 = x;
        double r32373139 = y;
        double r32373140 = r32373139 - r32373138;
        double r32373141 = z;
        double r32373142 = t;
        double r32373143 = r32373141 - r32373142;
        double r32373144 = r32373140 * r32373143;
        double r32373145 = a;
        double r32373146 = r32373145 - r32373142;
        double r32373147 = r32373144 / r32373146;
        double r32373148 = r32373138 + r32373147;
        double r32373149 = -8.143669236760688e-278;
        bool r32373150 = r32373148 <= r32373149;
        double r32373151 = r32373143 / r32373146;
        double r32373152 = r32373140 * r32373151;
        double r32373153 = r32373152 + r32373138;
        double r32373154 = 0.0;
        bool r32373155 = r32373148 <= r32373154;
        double r32373156 = r32373141 * r32373138;
        double r32373157 = r32373156 / r32373142;
        double r32373158 = r32373157 + r32373139;
        double r32373159 = r32373141 * r32373139;
        double r32373160 = r32373159 / r32373142;
        double r32373161 = r32373158 - r32373160;
        double r32373162 = r32373155 ? r32373161 : r32373153;
        double r32373163 = r32373150 ? r32373153 : r32373162;
        return r32373163;
}

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

Original24.0
Target9.5
Herbie8.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -8.143669236760688e-278 or 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

    1. Initial program 20.5

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

    3. Applied *-un-lft-identity20.5

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

    4. Applied times-frac7.4

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

    5. Simplified7.4

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

    if -8.143669236760688e-278 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

    1. Initial program 58.7

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

    2. Taylor expanded around inf 21.4

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

  4. Final simplification8.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -8.143669236760688 \cdot 10^{-278}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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))))