Average Error: 1.3 → 3.3
Time: 15.8s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\left(x + \frac{z}{\frac{a - t}{y}}\right) - \frac{t}{\frac{a - t}{y}}\]
x + y \cdot \frac{z - t}{a - t}
↓
\left(x + \frac{z}{\frac{a - t}{y}}\right) - \frac{t}{\frac{a - t}{y}}
double f(double x, double y, double z, double t, double a) {
        double r379094 = x;
        double r379095 = y;
        double r379096 = z;
        double r379097 = t;
        double r379098 = r379096 - r379097;
        double r379099 = a;
        double r379100 = r379099 - r379097;
        double r379101 = r379098 / r379100;
        double r379102 = r379095 * r379101;
        double r379103 = r379094 + r379102;
        return r379103;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r379104 = x;
        double r379105 = z;
        double r379106 = a;
        double r379107 = t;
        double r379108 = r379106 - r379107;
        double r379109 = y;
        double r379110 = r379108 / r379109;
        double r379111 = r379105 / r379110;
        double r379112 = r379104 + r379111;
        double r379113 = r379107 / r379110;
        double r379114 = r379112 - r379113;
        return r379114;
}

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

Original1.3
Target0.5
Herbie3.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.3

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

  3. Applied add-cube-cbrt1.9

    \[\leadsto x + y \cdot \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}\]

  4. Applied add-cube-cbrt1.7

    \[\leadsto x + y \cdot \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}\]

  5. Applied times-frac1.7

    \[\leadsto x + y \cdot \color{blue}{\left(\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\right)}\]

  6. Applied associate-*r*0.5

    \[\leadsto x + \color{blue}{\left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}}\]

  7. Final simplification3.3

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

Reproduce

herbie shell --seed 2019298 
(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 -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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