Average Error: 24.0 → 10.7
Time: 5.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -3.1703164045461676 \cdot 10^{-144} \lor \neg \left(a \le 3.1595740263796063 \cdot 10^{-93}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -3.1703164045461676 \cdot 10^{-144} \lor \neg \left(a \le 3.1595740263796063 \cdot 10^{-93}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r706093 = x;
        double r706094 = y;
        double r706095 = r706094 - r706093;
        double r706096 = z;
        double r706097 = t;
        double r706098 = r706096 - r706097;
        double r706099 = r706095 * r706098;
        double r706100 = a;
        double r706101 = r706100 - r706097;
        double r706102 = r706099 / r706101;
        double r706103 = r706093 + r706102;
        return r706103;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r706104 = a;
        double r706105 = -3.1703164045461676e-144;
        bool r706106 = r706104 <= r706105;
        double r706107 = 3.1595740263796063e-93;
        bool r706108 = r706104 <= r706107;
        double r706109 = !r706108;
        bool r706110 = r706106 || r706109;
        double r706111 = x;
        double r706112 = y;
        double r706113 = r706112 - r706111;
        double r706114 = z;
        double r706115 = t;
        double r706116 = r706114 - r706115;
        double r706117 = 1.0;
        double r706118 = r706104 - r706115;
        double r706119 = r706117 / r706118;
        double r706120 = r706116 * r706119;
        double r706121 = r706113 * r706120;
        double r706122 = r706111 + r706121;
        double r706123 = r706111 * r706114;
        double r706124 = r706123 / r706115;
        double r706125 = r706112 + r706124;
        double r706126 = r706114 * r706112;
        double r706127 = r706126 / r706115;
        double r706128 = r706125 - r706127;
        double r706129 = r706110 ? r706122 : r706128;
        return r706129;
}

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
Target9.2
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.1703164045461676e-144 or 3.1595740263796063e-93 < a

    1. Initial program 22.2

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

    3. Applied *-un-lft-identity22.2

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

    4. Applied times-frac8.8

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

    5. Simplified8.8

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

    7. Applied div-inv8.8

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

    if -3.1703164045461676e-144 < a < 3.1595740263796063e-93

    1. Initial program 28.9

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

    2. Taylor expanded around inf 15.6

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.1703164045461676 \cdot 10^{-144} \lor \neg \left(a \le 3.1595740263796063 \cdot 10^{-93}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(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 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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