Average Error: 1.4 → 1.2
Time: 6.3s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\frac{y}{\frac{a - t}{z - t}} + x\]
x + y \cdot \frac{z - t}{a - t}
↓
\frac{y}{\frac{a - t}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r620148 = x;
        double r620149 = y;
        double r620150 = z;
        double r620151 = t;
        double r620152 = r620150 - r620151;
        double r620153 = a;
        double r620154 = r620153 - r620151;
        double r620155 = r620152 / r620154;
        double r620156 = r620149 * r620155;
        double r620157 = r620148 + r620156;
        return r620157;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r620158 = y;
        double r620159 = a;
        double r620160 = t;
        double r620161 = r620159 - r620160;
        double r620162 = z;
        double r620163 = r620162 - r620160;
        double r620164 = r620161 / r620163;
        double r620165 = r620158 / r620164;
        double r620166 = x;
        double r620167 = r620165 + r620166;
        return r620167;
}

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

Original1.4
Target0.4
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.4

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

  3. Applied clear-num1.4

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.4

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

  6. Applied associate-*l*1.4

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

  7. Simplified1.2

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

  8. Final simplification1.2

    \[\leadsto \frac{y}{\frac{a - t}{z - t}} + x\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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