Average Error: 11.3 → 1.3
Time: 47.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{z - t}{a - t} \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{z - t}{a - t} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r26294964 = x;
        double r26294965 = y;
        double r26294966 = z;
        double r26294967 = t;
        double r26294968 = r26294966 - r26294967;
        double r26294969 = r26294965 * r26294968;
        double r26294970 = a;
        double r26294971 = r26294970 - r26294967;
        double r26294972 = r26294969 / r26294971;
        double r26294973 = r26294964 + r26294972;
        return r26294973;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26294974 = z;
        double r26294975 = t;
        double r26294976 = r26294974 - r26294975;
        double r26294977 = a;
        double r26294978 = r26294977 - r26294975;
        double r26294979 = r26294976 / r26294978;
        double r26294980 = y;
        double r26294981 = r26294979 * r26294980;
        double r26294982 = x;
        double r26294983 = r26294981 + r26294982;
        return r26294983;
}

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

Original11.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.3

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

  2. Simplified2.8

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

  4. Applied clear-num3.1

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right)\]
  5. Using strategy rm

  6. Applied *-un-lft-identity3.1

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

  7. Applied add-cube-cbrt3.5

    \[\leadsto \mathsf{fma}\left(\frac{1}{\frac{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}{1 \cdot y}}, z - t, x\right)\]

  8. Applied times-frac3.5

    \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{y}}}, z - t, x\right)\]

  9. Applied associate-/r*3.3

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{1}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1}}}{\frac{\sqrt[3]{a - t}}{y}}}, z - t, x\right)\]

  10. Simplified3.3

    \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{1}{\sqrt[3]{a - t}} \cdot \frac{1}{\sqrt[3]{a - t}}}}{\frac{\sqrt[3]{a - t}}{y}}, z - t, x\right)\]
  11. Using strategy rm

  12. Applied fma-udef3.3

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{a - t}} \cdot \frac{1}{\sqrt[3]{a - t}}}{\frac{\sqrt[3]{a - t}}{y}} \cdot \left(z - t\right) + x}\]

  13. Simplified1.3

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

  14. Final simplification1.3

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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