Average Error: 0.5 → 0.1
Time: 17.8s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\left(\frac{x}{\frac{z - t}{60}} - \frac{y}{\frac{z - t}{60}}\right) + a \cdot 120\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\left(\frac{x}{\frac{z - t}{60}} - \frac{y}{\frac{z - t}{60}}\right) + a \cdot 120
double f(double x, double y, double z, double t, double a) {
        double r513052 = 60.0;
        double r513053 = x;
        double r513054 = y;
        double r513055 = r513053 - r513054;
        double r513056 = r513052 * r513055;
        double r513057 = z;
        double r513058 = t;
        double r513059 = r513057 - r513058;
        double r513060 = r513056 / r513059;
        double r513061 = a;
        double r513062 = 120.0;
        double r513063 = r513061 * r513062;
        double r513064 = r513060 + r513063;
        return r513064;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r513065 = x;
        double r513066 = z;
        double r513067 = t;
        double r513068 = r513066 - r513067;
        double r513069 = 60.0;
        double r513070 = r513068 / r513069;
        double r513071 = r513065 / r513070;
        double r513072 = y;
        double r513073 = r513072 / r513070;
        double r513074 = r513071 - r513073;
        double r513075 = a;
        double r513076 = 120.0;
        double r513077 = r513075 * r513076;
        double r513078 = r513074 + r513077;
        return r513078;
}

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
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.5

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120\]
  4. Using strategy rm

  5. Applied clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z - t}{x - y}}{60}}} + a \cdot 120\]
  6. Using strategy rm

  7. Applied div-inv0.2

    \[\leadsto \frac{1}{\color{blue}{\frac{z - t}{x - y} \cdot \frac{1}{60}}} + a \cdot 120\]

  8. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{z - t}{x - y}}}{\frac{1}{60}}} + a \cdot 120\]

  9. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{x - y}{z - t}}}{\frac{1}{60}} + a \cdot 120\]
  10. Using strategy rm

  11. Applied div-sub0.2

    \[\leadsto \frac{\color{blue}{\frac{x}{z - t} - \frac{y}{z - t}}}{\frac{1}{60}} + a \cdot 120\]

  12. Applied div-sub0.2

    \[\leadsto \color{blue}{\left(\frac{\frac{x}{z - t}}{\frac{1}{60}} - \frac{\frac{y}{z - t}}{\frac{1}{60}}\right)} + a \cdot 120\]

  13. Simplified0.1

    \[\leadsto \left(\color{blue}{\frac{x}{\frac{z - t}{60}}} - \frac{\frac{y}{z - t}}{\frac{1}{60}}\right) + a \cdot 120\]

  14. Simplified0.1

    \[\leadsto \left(\frac{x}{\frac{z - t}{60}} - \color{blue}{\frac{y}{\frac{z - t}{60}}}\right) + a \cdot 120\]

  15. Final simplification0.1

    \[\leadsto \left(\frac{x}{\frac{z - t}{60}} - \frac{y}{\frac{z - t}{60}}\right) + a \cdot 120\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))