Average Error: 10.9 → 1.2
Time: 6.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r609196 = x;
        double r609197 = y;
        double r609198 = z;
        double r609199 = t;
        double r609200 = r609198 - r609199;
        double r609201 = r609197 * r609200;
        double r609202 = a;
        double r609203 = r609202 - r609199;
        double r609204 = r609201 / r609203;
        double r609205 = r609196 + r609204;
        return r609205;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r609206 = x;
        double r609207 = y;
        double r609208 = z;
        double r609209 = a;
        double r609210 = t;
        double r609211 = r609209 - r609210;
        double r609212 = r609208 / r609211;
        double r609213 = r609210 / r609211;
        double r609214 = r609212 - r609213;
        double r609215 = r609207 * r609214;
        double r609216 = r609206 + r609215;
        return r609216;
}

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

Original10.9
Target1.0
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied *-un-lft-identity10.9

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

  4. Applied times-frac1.2

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

  5. Simplified1.2

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

  7. Applied div-sub1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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