Average Error: 0.5 → 0.1
Time: 21.1s
Precision: 64
\[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]
↓
\[\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]
\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0
↓
\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0
double f(double x, double y, double z, double t, double a) {
        double r39045870 = 60.0;
        double r39045871 = x;
        double r39045872 = y;
        double r39045873 = r39045871 - r39045872;
        double r39045874 = r39045870 * r39045873;
        double r39045875 = z;
        double r39045876 = t;
        double r39045877 = r39045875 - r39045876;
        double r39045878 = r39045874 / r39045877;
        double r39045879 = a;
        double r39045880 = 120.0;
        double r39045881 = r39045879 * r39045880;
        double r39045882 = r39045878 + r39045881;
        return r39045882;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r39045883 = 60.0;
        double r39045884 = z;
        double r39045885 = t;
        double r39045886 = r39045884 - r39045885;
        double r39045887 = x;
        double r39045888 = y;
        double r39045889 = r39045887 - r39045888;
        double r39045890 = r39045886 / r39045889;
        double r39045891 = r39045883 / r39045890;
        double r39045892 = a;
        double r39045893 = 120.0;
        double r39045894 = r39045892 * r39045893;
        double r39045895 = r39045891 + r39045894;
        return r39045895;
}

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

Original0.5
Target0.1
Herbie0.1
\[\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]

Derivation

  1. Initial program 0.5

    \[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{60.0}{z - t}, x - y, a \cdot 120.0\right)}\]
  3. Using strategy rm

  4. Applied div-inv0.2

    \[\leadsto \mathsf{fma}\left(\color{blue}{60.0 \cdot \frac{1}{z - t}}, x - y, a \cdot 120.0\right)\]
  5. Using strategy rm

  6. Applied fma-udef0.2

    \[\leadsto \color{blue}{\left(60.0 \cdot \frac{1}{z - t}\right) \cdot \left(x - y\right) + a \cdot 120.0}\]

  7. Simplified0.2

    \[\leadsto \color{blue}{\frac{x - y}{z - t} \cdot 60.0} + a \cdot 120.0\]
  8. Using strategy rm

  9. Applied clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{x - y}}} \cdot 60.0 + a \cdot 120.0\]
  10. Using strategy rm

  11. Applied associate-*l/0.1

    \[\leadsto \color{blue}{\frac{1 \cdot 60.0}{\frac{z - t}{x - y}}} + a \cdot 120.0\]

  12. Simplified0.1

    \[\leadsto \frac{\color{blue}{60.0}}{\frac{z - t}{x - y}} + a \cdot 120.0\]

  13. Final simplification0.1

    \[\leadsto \frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))