Average Error: 23.9 → 11.6
Time: 21.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \left(y - x\right) \cdot \frac{z - t}{a - t}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
x + \left(y - x\right) \cdot \frac{z - t}{a - t}
double f(double x, double y, double z, double t, double a) {
        double r491924 = x;
        double r491925 = y;
        double r491926 = r491925 - r491924;
        double r491927 = z;
        double r491928 = t;
        double r491929 = r491927 - r491928;
        double r491930 = r491926 * r491929;
        double r491931 = a;
        double r491932 = r491931 - r491928;
        double r491933 = r491930 / r491932;
        double r491934 = r491924 + r491933;
        return r491934;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r491935 = x;
        double r491936 = y;
        double r491937 = r491936 - r491935;
        double r491938 = z;
        double r491939 = t;
        double r491940 = r491938 - r491939;
        double r491941 = a;
        double r491942 = r491941 - r491939;
        double r491943 = r491940 / r491942;
        double r491944 = r491937 * r491943;
        double r491945 = r491935 + r491944;
        return r491945;
}

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

Original23.9
Target9.0
Herbie11.6
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 23.9

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

  3. Applied *-un-lft-identity23.9

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

  4. Applied times-frac11.6

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

  5. Simplified11.6

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

  6. Final simplification11.6

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

Reproduce

herbie shell --seed 2019198 
(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) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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