Average Error: 10.9 → 2.1
Time: 2.8s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{1} \cdot \left(\frac{\sqrt[3]{y - z}}{a - z} \cdot t\right)\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{1} \cdot \left(\frac{\sqrt[3]{y - z}}{a - z} \cdot t\right)
double f(double x, double y, double z, double t, double a) {
        double r593040 = x;
        double r593041 = y;
        double r593042 = z;
        double r593043 = r593041 - r593042;
        double r593044 = t;
        double r593045 = r593043 * r593044;
        double r593046 = a;
        double r593047 = r593046 - r593042;
        double r593048 = r593045 / r593047;
        double r593049 = r593040 + r593048;
        return r593049;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r593050 = x;
        double r593051 = y;
        double r593052 = z;
        double r593053 = r593051 - r593052;
        double r593054 = cbrt(r593053);
        double r593055 = r593054 * r593054;
        double r593056 = 1.0;
        double r593057 = r593055 / r593056;
        double r593058 = a;
        double r593059 = r593058 - r593052;
        double r593060 = r593054 / r593059;
        double r593061 = t;
        double r593062 = r593060 * r593061;
        double r593063 = r593057 * r593062;
        double r593064 = r593050 + r593063;
        return r593064;
}

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

Original10.9
Target0.5
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*3.0

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

  5. Applied associate-/r/1.3

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

  7. Applied *-un-lft-identity1.3

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

  8. Applied add-cube-cbrt1.8

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

  9. Applied times-frac1.8

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

  10. Applied associate-*l*2.1

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

  11. Final simplification2.1

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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