Average Error: 10.2 → 0.5
Time: 18.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r24732934 = x;
        double r24732935 = y;
        double r24732936 = z;
        double r24732937 = t;
        double r24732938 = r24732936 - r24732937;
        double r24732939 = r24732935 * r24732938;
        double r24732940 = a;
        double r24732941 = r24732940 - r24732937;
        double r24732942 = r24732939 / r24732941;
        double r24732943 = r24732934 + r24732942;
        return r24732943;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24732944 = y;
        double r24732945 = a;
        double r24732946 = t;
        double r24732947 = r24732945 - r24732946;
        double r24732948 = cbrt(r24732947);
        double r24732949 = z;
        double r24732950 = r24732949 - r24732946;
        double r24732951 = cbrt(r24732950);
        double r24732952 = r24732948 / r24732951;
        double r24732953 = r24732952 * r24732952;
        double r24732954 = r24732944 / r24732953;
        double r24732955 = r24732954 / r24732952;
        double r24732956 = x;
        double r24732957 = r24732955 + r24732956;
        return r24732957;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

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Results

Enter valid numbers for all inputs

Target

Original10.2
Target1.1
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.2

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

  3. Applied associate-/l*1.1

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

  5. Applied add-cube-cbrt1.6

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

  6. Applied add-cube-cbrt1.5

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

  7. Applied times-frac1.5

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

  8. Applied associate-/r*0.5

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

  9. Simplified0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019163 
(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))))