Average Error: 10.5 → 1.0
Time: 18.9s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{t}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right) + x\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{t}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right) + x
double f(double x, double y, double z, double t, double a) {
        double r25990063 = x;
        double r25990064 = y;
        double r25990065 = z;
        double r25990066 = r25990064 - r25990065;
        double r25990067 = t;
        double r25990068 = r25990066 * r25990067;
        double r25990069 = a;
        double r25990070 = r25990069 - r25990065;
        double r25990071 = r25990068 / r25990070;
        double r25990072 = r25990063 + r25990071;
        return r25990072;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25990073 = y;
        double r25990074 = z;
        double r25990075 = r25990073 - r25990074;
        double r25990076 = cbrt(r25990075);
        double r25990077 = r25990076 * r25990076;
        double r25990078 = a;
        double r25990079 = r25990078 - r25990074;
        double r25990080 = cbrt(r25990079);
        double r25990081 = r25990077 / r25990080;
        double r25990082 = t;
        double r25990083 = r25990082 / r25990080;
        double r25990084 = r25990076 / r25990080;
        double r25990085 = r25990083 * r25990084;
        double r25990086 = r25990081 * r25990085;
        double r25990087 = x;
        double r25990088 = r25990086 + r25990087;
        return r25990088;
}

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

Original10.5
Target0.6
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  3. Applied add-cube-cbrt10.9

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

  4. Applied times-frac1.9

    \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.8

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

  7. Applied times-frac1.8

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

  8. Applied associate-*l*1.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2019169 
(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))))