Average Error: 9.7 → 0.5
Time: 18.8s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\frac{\frac{\frac{t}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{y - z}}}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{y - z}}}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{y - z}}} + x\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\frac{\frac{\frac{t}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{y - z}}}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{y - z}}}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{y - z}}} + x
double f(double x, double y, double z, double t, double a) {
        double r21811135 = x;
        double r21811136 = y;
        double r21811137 = z;
        double r21811138 = r21811136 - r21811137;
        double r21811139 = t;
        double r21811140 = r21811138 * r21811139;
        double r21811141 = a;
        double r21811142 = r21811141 - r21811137;
        double r21811143 = r21811140 / r21811142;
        double r21811144 = r21811135 + r21811143;
        return r21811144;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r21811145 = t;
        double r21811146 = a;
        double r21811147 = z;
        double r21811148 = r21811146 - r21811147;
        double r21811149 = cbrt(r21811148);
        double r21811150 = y;
        double r21811151 = r21811150 - r21811147;
        double r21811152 = cbrt(r21811151);
        double r21811153 = r21811149 / r21811152;
        double r21811154 = r21811145 / r21811153;
        double r21811155 = r21811154 / r21811153;
        double r21811156 = r21811155 / r21811153;
        double r21811157 = x;
        double r21811158 = r21811156 + r21811157;
        return r21811158;
}

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

Original9.7
Target0.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 9.7

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

  3. Applied *-commutative9.7

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

  4. Applied associate-/l*1.2

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied add-cube-cbrt1.6

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

  8. Applied times-frac1.6

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

  9. Applied associate-/r*0.6

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

  10. Simplified0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :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))))