Average Error: 0.5 → 0.1
Time: 19.5s
Precision: 64
\[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]
↓
\[\left(x - y\right) \cdot \frac{60.0}{z - t} + a \cdot 120.0\]
\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0
↓
\left(x - y\right) \cdot \frac{60.0}{z - t} + a \cdot 120.0
double f(double x, double y, double z, double t, double a) {
        double r39197740 = 60.0;
        double r39197741 = x;
        double r39197742 = y;
        double r39197743 = r39197741 - r39197742;
        double r39197744 = r39197740 * r39197743;
        double r39197745 = z;
        double r39197746 = t;
        double r39197747 = r39197745 - r39197746;
        double r39197748 = r39197744 / r39197747;
        double r39197749 = a;
        double r39197750 = 120.0;
        double r39197751 = r39197749 * r39197750;
        double r39197752 = r39197748 + r39197751;
        return r39197752;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r39197753 = x;
        double r39197754 = y;
        double r39197755 = r39197753 - r39197754;
        double r39197756 = 60.0;
        double r39197757 = z;
        double r39197758 = t;
        double r39197759 = r39197757 - r39197758;
        double r39197760 = r39197756 / r39197759;
        double r39197761 = r39197755 * r39197760;
        double r39197762 = a;
        double r39197763 = 120.0;
        double r39197764 = r39197762 * r39197763;
        double r39197765 = r39197761 + r39197764;
        return r39197765;
}

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

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 fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 +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)))