Average Error: 23.5 → 7.8
Time: 26.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{y}{\frac{a - t}{z - t}} + \left(x - \frac{x}{\frac{a - t}{z - t}}\right)\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\frac{y}{\frac{a - t}{z - t}} + \left(x - \frac{x}{\frac{a - t}{z - t}}\right)
double f(double x, double y, double z, double t, double a) {
        double r44327900 = x;
        double r44327901 = y;
        double r44327902 = r44327901 - r44327900;
        double r44327903 = z;
        double r44327904 = t;
        double r44327905 = r44327903 - r44327904;
        double r44327906 = r44327902 * r44327905;
        double r44327907 = a;
        double r44327908 = r44327907 - r44327904;
        double r44327909 = r44327906 / r44327908;
        double r44327910 = r44327900 + r44327909;
        return r44327910;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r44327911 = y;
        double r44327912 = a;
        double r44327913 = t;
        double r44327914 = r44327912 - r44327913;
        double r44327915 = z;
        double r44327916 = r44327915 - r44327913;
        double r44327917 = r44327914 / r44327916;
        double r44327918 = r44327911 / r44327917;
        double r44327919 = x;
        double r44327920 = r44327919 / r44327917;
        double r44327921 = r44327919 - r44327920;
        double r44327922 = r44327918 + r44327921;
        return r44327922;
}

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

Original23.5
Target9.4
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 23.5

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

  3. Applied associate-/l*12.0

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

  5. Applied div-sub12.0

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

  6. Applied associate-+r-12.0

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

  8. Applied +-commutative12.0

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

  9. Applied associate--l+7.8

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

  10. Final simplification7.8

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

Reproduce

herbie shell --seed 2019158 
(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))))