Average Error: 0.5 → 0.1
Time: 5.2s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[a \cdot 120 + \frac{60}{\frac{z - t}{x - y}}\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
a \cdot 120 + \frac{60}{\frac{z - t}{x - y}}
double f(double x, double y, double z, double t, double a) {
        double r877363 = 60.0;
        double r877364 = x;
        double r877365 = y;
        double r877366 = r877364 - r877365;
        double r877367 = r877363 * r877366;
        double r877368 = z;
        double r877369 = t;
        double r877370 = r877368 - r877369;
        double r877371 = r877367 / r877370;
        double r877372 = a;
        double r877373 = 120.0;
        double r877374 = r877372 * r877373;
        double r877375 = r877371 + r877374;
        return r877375;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r877376 = a;
        double r877377 = 120.0;
        double r877378 = r877376 * r877377;
        double r877379 = 60.0;
        double r877380 = z;
        double r877381 = t;
        double r877382 = r877380 - r877381;
        double r877383 = x;
        double r877384 = y;
        double r877385 = r877383 - r877384;
        double r877386 = r877382 / r877385;
        double r877387 = r877379 / r877386;
        double r877388 = r877378 + r877387;
        return r877388;
}

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

Derivation

  1. Initial program 0.5

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

  3. Applied *-un-lft-identity0.5

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  7. Applied clear-num0.2

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

  9. Applied *-un-lft-identity0.2

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

  10. Applied associate-*l*0.2

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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)))