Average Error: 1.3 → 0.5
Time: 6.1s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r567121 = x;
        double r567122 = y;
        double r567123 = z;
        double r567124 = t;
        double r567125 = r567123 - r567124;
        double r567126 = a;
        double r567127 = r567123 - r567126;
        double r567128 = r567125 / r567127;
        double r567129 = r567122 * r567128;
        double r567130 = r567121 + r567129;
        return r567130;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r567131 = x;
        double r567132 = y;
        double r567133 = z;
        double r567134 = a;
        double r567135 = r567133 - r567134;
        double r567136 = cbrt(r567135);
        double r567137 = r567136 * r567136;
        double r567138 = t;
        double r567139 = r567133 - r567138;
        double r567140 = cbrt(r567139);
        double r567141 = r567140 * r567140;
        double r567142 = r567137 / r567141;
        double r567143 = r567132 / r567142;
        double r567144 = 1.0;
        double r567145 = r567136 / r567140;
        double r567146 = r567144 / r567145;
        double r567147 = r567143 * r567146;
        double r567148 = r567131 + r567147;
        return r567148;
}

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
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied clear-num1.4

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

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

  8. Applied *-un-lft-identity1.7

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

  9. Applied times-frac1.7

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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