Average Error: 10.6 → 1.3
Time: 8.6s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{y - z}{a - z} \cdot t\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{y - z}{a - z} \cdot t
double f(double x, double y, double z, double t, double a) {
        double r469112 = x;
        double r469113 = y;
        double r469114 = z;
        double r469115 = r469113 - r469114;
        double r469116 = t;
        double r469117 = r469115 * r469116;
        double r469118 = a;
        double r469119 = r469118 - r469114;
        double r469120 = r469117 / r469119;
        double r469121 = r469112 + r469120;
        return r469121;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r469122 = x;
        double r469123 = y;
        double r469124 = z;
        double r469125 = r469123 - r469124;
        double r469126 = a;
        double r469127 = r469126 - r469124;
        double r469128 = r469125 / r469127;
        double r469129 = t;
        double r469130 = r469128 * r469129;
        double r469131 = r469122 + r469130;
        return r469131;
}

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

Original10.6
Target0.5
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.6

    \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
  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. Final simplification1.3

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

Reproduce

herbie shell --seed 2019298 
(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))))