Average Error: 10.4 → 1.1
Time: 15.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r363075 = x;
        double r363076 = y;
        double r363077 = z;
        double r363078 = t;
        double r363079 = r363077 - r363078;
        double r363080 = r363076 * r363079;
        double r363081 = a;
        double r363082 = r363081 - r363078;
        double r363083 = r363080 / r363082;
        double r363084 = r363075 + r363083;
        return r363084;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r363085 = x;
        double r363086 = y;
        double r363087 = cbrt(r363086);
        double r363088 = r363087 * r363087;
        double r363089 = a;
        double r363090 = t;
        double r363091 = r363089 - r363090;
        double r363092 = cbrt(r363091);
        double r363093 = r363092 * r363092;
        double r363094 = r363088 / r363093;
        double r363095 = z;
        double r363096 = r363095 - r363090;
        double r363097 = r363092 / r363096;
        double r363098 = r363087 / r363097;
        double r363099 = r363094 * r363098;
        double r363100 = r363085 + r363099;
        return r363100;
}

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

Original10.4
Target1.2
Herbie1.1
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.2

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

  5. Applied *-un-lft-identity1.2

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

  6. Applied add-cube-cbrt1.7

    \[\leadsto x + \frac{y}{\frac{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}{1 \cdot \left(z - t\right)}}\]

  7. Applied times-frac1.7

    \[\leadsto x + \frac{y}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{z - t}}}\]

  8. Applied add-cube-cbrt1.8

    \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{z - t}}\]

  9. Applied times-frac1.1

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}}\]

  10. Simplified1.1

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

  11. Final simplification1.1

    \[\leadsto x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{a - t}}{z - t}}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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