Average Error: 24.5 → 10.6
Time: 14.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le \frac{-7837677536452411}{1.151721931403058273999497857967611355871 \cdot 10^{164}} \lor \neg \left(a \le \frac{2186591066829205}{1.296723615275310299535127457403487859691 \cdot 10^{179}}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le \frac{-7837677536452411}{1.151721931403058273999497857967611355871 \cdot 10^{164}} \lor \neg \left(a \le \frac{2186591066829205}{1.296723615275310299535127457403487859691 \cdot 10^{179}}\right):\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

\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 r403032 = x;
        double r403033 = y;
        double r403034 = r403033 - r403032;
        double r403035 = z;
        double r403036 = t;
        double r403037 = r403035 - r403036;
        double r403038 = r403034 * r403037;
        double r403039 = a;
        double r403040 = r403039 - r403036;
        double r403041 = r403038 / r403040;
        double r403042 = r403032 + r403041;
        return r403042;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r403043 = a;
        double r403044 = -7837677536452411.0;
        double r403045 = 1.1517219314030583e+164;
        double r403046 = r403044 / r403045;
        bool r403047 = r403043 <= r403046;
        double r403048 = 2186591066829205.0;
        double r403049 = 1.2967236152753103e+179;
        double r403050 = r403048 / r403049;
        bool r403051 = r403043 <= r403050;
        double r403052 = !r403051;
        bool r403053 = r403047 || r403052;
        double r403054 = x;
        double r403055 = y;
        double r403056 = r403055 - r403054;
        double r403057 = t;
        double r403058 = r403043 - r403057;
        double r403059 = 1.0;
        double r403060 = z;
        double r403061 = r403060 - r403057;
        double r403062 = r403059 / r403061;
        double r403063 = r403058 * r403062;
        double r403064 = r403056 / r403063;
        double r403065 = r403054 + r403064;
        double r403066 = r403054 * r403060;
        double r403067 = r403066 / r403057;
        double r403068 = r403055 + r403067;
        double r403069 = r403060 * r403055;
        double r403070 = r403069 / r403057;
        double r403071 = r403068 - r403070;
        double r403072 = r403053 ? r403065 : r403071;
        return r403072;
}

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 2 regimes

  2. if a < -6.805182156168845e-149 or 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*9.7

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

    5. Applied div-inv9.7

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

    if -6.805182156168845e-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

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

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le \frac{-7837677536452411}{1.151721931403058273999497857967611355871 \cdot 10^{164}} \lor \neg \left(a \le \frac{2186591066829205}{1.296723615275310299535127457403487859691 \cdot 10^{179}}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

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))))