Average Error: 10.6 → 1.6
Time: 15.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\frac{\sqrt[3]{y}}{a - t} \cdot \left(z - t\right)\right)\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\frac{\sqrt[3]{y}}{a - t} \cdot \left(z - t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r440675 = x;
        double r440676 = y;
        double r440677 = z;
        double r440678 = t;
        double r440679 = r440677 - r440678;
        double r440680 = r440676 * r440679;
        double r440681 = a;
        double r440682 = r440681 - r440678;
        double r440683 = r440680 / r440682;
        double r440684 = r440675 + r440683;
        return r440684;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r440685 = x;
        double r440686 = y;
        double r440687 = cbrt(r440686);
        double r440688 = r440687 * r440687;
        double r440689 = a;
        double r440690 = t;
        double r440691 = r440689 - r440690;
        double r440692 = r440687 / r440691;
        double r440693 = z;
        double r440694 = r440693 - r440690;
        double r440695 = r440692 * r440694;
        double r440696 = r440688 * r440695;
        double r440697 = r440685 + r440696;
        return r440697;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target1.2
Herbie1.6
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  2. Simplified10.6

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

  4. Applied associate-/l*1.2

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

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

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

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

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

  8. Applied times-frac1.2

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

  9. Applied add-cube-cbrt1.7

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

  10. Applied times-frac1.7

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

  11. Simplified1.7

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

  12. Simplified1.6

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

  13. Final simplification1.6

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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