Average Error: 24.6 → 11.9
Time: 8.8s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.857258472878047342686922637475217130218 \cdot 10^{143} \lor \neg \left(t \le 8.281375759210086334394664376626091105613 \cdot 10^{228}\right):\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.857258472878047342686922637475217130218 \cdot 10^{143} \lor \neg \left(t \le 8.281375759210086334394664376626091105613 \cdot 10^{228}\right):\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r460046 = x;
        double r460047 = y;
        double r460048 = r460047 - r460046;
        double r460049 = z;
        double r460050 = t;
        double r460051 = r460049 - r460050;
        double r460052 = r460048 * r460051;
        double r460053 = a;
        double r460054 = r460053 - r460050;
        double r460055 = r460052 / r460054;
        double r460056 = r460046 + r460055;
        return r460056;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r460057 = t;
        double r460058 = -1.8572584728780473e+143;
        bool r460059 = r460057 <= r460058;
        double r460060 = 8.281375759210086e+228;
        bool r460061 = r460057 <= r460060;
        double r460062 = !r460061;
        bool r460063 = r460059 || r460062;
        double r460064 = y;
        double r460065 = x;
        double r460066 = z;
        double r460067 = r460065 * r460066;
        double r460068 = r460067 / r460057;
        double r460069 = r460064 + r460068;
        double r460070 = r460066 * r460064;
        double r460071 = r460070 / r460057;
        double r460072 = r460069 - r460071;
        double r460073 = r460064 - r460065;
        double r460074 = 1.0;
        double r460075 = a;
        double r460076 = r460075 - r460057;
        double r460077 = r460066 - r460057;
        double r460078 = r460076 / r460077;
        double r460079 = r460074 / r460078;
        double r460080 = r460073 * r460079;
        double r460081 = r460065 + r460080;
        double r460082 = r460063 ? r460072 : r460081;
        return r460082;
}

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

Original24.6
Target9.4
Herbie11.9
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.8572584728780473e+143 or 8.281375759210086e+228 < t

    1. Initial program 48.7

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

    2. Taylor expanded around inf 24.0

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

    if -1.8572584728780473e+143 < t < 8.281375759210086e+228

    1. Initial program 17.4

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

    3. Applied associate-/l*8.2

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

    5. Applied div-inv8.3

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.857258472878047342686922637475217130218 \cdot 10^{143} \lor \neg \left(t \le 8.281375759210086334394664376626091105613 \cdot 10^{228}\right):\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(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))))