Average Error: 10.4 → 1.2
Time: 13.4s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \left(\frac{y}{a - z} \cdot t - t \cdot \frac{z}{a - z}\right)\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \left(\frac{y}{a - z} \cdot t - t \cdot \frac{z}{a - z}\right)
double f(double x, double y, double z, double t, double a) {
        double r351807 = x;
        double r351808 = y;
        double r351809 = z;
        double r351810 = r351808 - r351809;
        double r351811 = t;
        double r351812 = r351810 * r351811;
        double r351813 = a;
        double r351814 = r351813 - r351809;
        double r351815 = r351812 / r351814;
        double r351816 = r351807 + r351815;
        return r351816;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r351817 = x;
        double r351818 = y;
        double r351819 = a;
        double r351820 = z;
        double r351821 = r351819 - r351820;
        double r351822 = r351818 / r351821;
        double r351823 = t;
        double r351824 = r351822 * r351823;
        double r351825 = r351820 / r351821;
        double r351826 = r351823 * r351825;
        double r351827 = r351824 - r351826;
        double r351828 = r351817 + r351827;
        return r351828;
}

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

Original10.4
Target0.5
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  2. Simplified2.9

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

  4. Applied *-un-lft-identity2.9

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

  5. Applied associate-*l*2.9

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

  6. Simplified3.0

    \[\leadsto 1 \cdot \color{blue}{\frac{y - z}{\frac{a - z}{t}}} + x\]
  7. Using strategy rm

  8. Applied div-sub3.0

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

  9. Simplified3.4

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

  10. Simplified1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2019179 
(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))))