Average Error: 0.5 → 0.1
Time: 4.7s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right) + a \cdot 120\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right) + a \cdot 120
double f(double x, double y, double z, double t, double a) {
        double r803570 = 60.0;
        double r803571 = x;
        double r803572 = y;
        double r803573 = r803571 - r803572;
        double r803574 = r803570 * r803573;
        double r803575 = z;
        double r803576 = t;
        double r803577 = r803575 - r803576;
        double r803578 = r803574 / r803577;
        double r803579 = a;
        double r803580 = 120.0;
        double r803581 = r803579 * r803580;
        double r803582 = r803578 + r803581;
        return r803582;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r803583 = 60.0;
        double r803584 = x;
        double r803585 = z;
        double r803586 = t;
        double r803587 = r803585 - r803586;
        double r803588 = r803584 / r803587;
        double r803589 = y;
        double r803590 = r803589 / r803587;
        double r803591 = r803588 - r803590;
        double r803592 = r803583 * r803591;
        double r803593 = a;
        double r803594 = 120.0;
        double r803595 = r803593 * r803594;
        double r803596 = r803592 + r803595;
        return r803596;
}

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 *-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 div-sub0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))