Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 2.1 → 2.1

Time: 27.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r104179827 = x;
        double r104179828 = y;
        double r104179829 = r104179828 - r104179827;
        double r104179830 = z;
        double r104179831 = t;
        double r104179832 = r104179830 / r104179831;
        double r104179833 = r104179829 * r104179832;
        double r104179834 = r104179827 + r104179833;
        return r104179834;
}

↓

double f(double x, double y, double z, double t) {
        double r104179835 = x;
        double r104179836 = y;
        double r104179837 = r104179836 - r104179835;
        double r104179838 = z;
        double r104179839 = t;
        double r104179840 = r104179838 / r104179839;
        double r104179841 = r104179837 * r104179840;
        double r104179842 = r104179835 + r104179841;
        return r104179842;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.3
Herbie	2.1

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 2.1

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

2. Final simplification 2.1

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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