Average Error: 25.4 → 11.5
Time: 18.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -3.452239314087017250091497734735345175539 \cdot 10^{-77} \lor \neg \left(a \le 2.35264995122292980564493356798464128914 \cdot 10^{-79}\right):\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -3.452239314087017250091497734735345175539 \cdot 10^{-77} \lor \neg \left(a \le 2.35264995122292980564493356798464128914 \cdot 10^{-79}\right):\\
\;\;\;\;x + \frac{z - t}{a - t} \cdot \left(y - x\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 r449082 = x;
        double r449083 = y;
        double r449084 = r449083 - r449082;
        double r449085 = z;
        double r449086 = t;
        double r449087 = r449085 - r449086;
        double r449088 = r449084 * r449087;
        double r449089 = a;
        double r449090 = r449089 - r449086;
        double r449091 = r449088 / r449090;
        double r449092 = r449082 + r449091;
        return r449092;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r449093 = a;
        double r449094 = -3.4522393140870173e-77;
        bool r449095 = r449093 <= r449094;
        double r449096 = 2.3526499512229298e-79;
        bool r449097 = r449093 <= r449096;
        double r449098 = !r449097;
        bool r449099 = r449095 || r449098;
        double r449100 = x;
        double r449101 = z;
        double r449102 = t;
        double r449103 = r449101 - r449102;
        double r449104 = r449093 - r449102;
        double r449105 = r449103 / r449104;
        double r449106 = y;
        double r449107 = r449106 - r449100;
        double r449108 = r449105 * r449107;
        double r449109 = r449100 + r449108;
        double r449110 = r449100 * r449101;
        double r449111 = r449110 / r449102;
        double r449112 = r449106 + r449111;
        double r449113 = r449101 * r449106;
        double r449114 = r449113 / r449102;
        double r449115 = r449112 - r449114;
        double r449116 = r449099 ? r449109 : r449115;
        return r449116;
}

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

Original25.4
Target9.8
Herbie11.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.4522393140870173e-77 or 2.3526499512229298e-79 < 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 *-un-lft-identity23.1

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

    4. Applied times-frac8.5

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

    5. Simplified8.5

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

    7. Applied div-inv8.6

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

    9. Applied *-un-lft-identity8.6

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

    10. Applied associate-*l*8.6

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

    11. Simplified8.5

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

    if -3.4522393140870173e-77 < a < 2.3526499512229298e-79

    1. Initial program 29.9

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

    2. Taylor expanded around inf 17.3

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

  4. Final simplification11.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.452239314087017250091497734735345175539 \cdot 10^{-77} \lor \neg \left(a \le 2.35264995122292980564493356798464128914 \cdot 10^{-79}\right):\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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))))