Average Error: 0.5 → 0.3
Time: 9.8s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\left(x \cdot \frac{60}{z - t} - \frac{60 \cdot y}{z - t}\right) + a \cdot 120\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\left(x \cdot \frac{60}{z - t} - \frac{60 \cdot y}{z - t}\right) + a \cdot 120
double f(double x, double y, double z, double t, double a) {
        double r541735 = 60.0;
        double r541736 = x;
        double r541737 = y;
        double r541738 = r541736 - r541737;
        double r541739 = r541735 * r541738;
        double r541740 = z;
        double r541741 = t;
        double r541742 = r541740 - r541741;
        double r541743 = r541739 / r541742;
        double r541744 = a;
        double r541745 = 120.0;
        double r541746 = r541744 * r541745;
        double r541747 = r541743 + r541746;
        return r541747;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r541748 = x;
        double r541749 = 60.0;
        double r541750 = z;
        double r541751 = t;
        double r541752 = r541750 - r541751;
        double r541753 = r541749 / r541752;
        double r541754 = r541748 * r541753;
        double r541755 = y;
        double r541756 = r541749 * r541755;
        double r541757 = r541756 / r541752;
        double r541758 = r541754 - r541757;
        double r541759 = a;
        double r541760 = 120.0;
        double r541761 = r541759 * r541760;
        double r541762 = r541758 + r541761;
        return r541762;
}

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
Herbie0.3
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.5

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

  3. Applied sub-neg0.5

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

  4. Applied distribute-lft-in0.5

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

  5. Simplified0.5

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

  7. Applied distribute-rgt-neg-out0.5

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

  8. Applied unsub-neg0.5

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

  9. Applied div-sub0.5

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

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

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

  12. Applied times-frac0.3

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2020042 
(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)))