Average Error: 8.0 → 8.0
Time: 3.7s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a} \cdot \frac{1}{2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a} \cdot \frac{1}{2}
double f(double x, double y, double z, double t, double a) {
        double r764120 = x;
        double r764121 = y;
        double r764122 = r764120 * r764121;
        double r764123 = z;
        double r764124 = 9.0;
        double r764125 = r764123 * r764124;
        double r764126 = t;
        double r764127 = r764125 * r764126;
        double r764128 = r764122 - r764127;
        double r764129 = a;
        double r764130 = 2.0;
        double r764131 = r764129 * r764130;
        double r764132 = r764128 / r764131;
        return r764132;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r764133 = x;
        double r764134 = y;
        double r764135 = r764133 * r764134;
        double r764136 = z;
        double r764137 = 9.0;
        double r764138 = r764136 * r764137;
        double r764139 = t;
        double r764140 = r764138 * r764139;
        double r764141 = r764135 - r764140;
        double r764142 = a;
        double r764143 = r764141 / r764142;
        double r764144 = 1.0;
        double r764145 = 2.0;
        double r764146 = r764144 / r764145;
        double r764147 = r764143 * r764146;
        return r764147;
}

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

Original8.0
Target5.9
Herbie8.0
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 8.0

    \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity8.0

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2}\]

  4. Applied times-frac8.1

    \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}\]
  5. Using strategy rm

  6. Applied div-inv8.1

    \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{2}\right)}\]

  7. Applied associate-*r*8.1

    \[\leadsto \color{blue}{\left(\frac{1}{a} \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \cdot \frac{1}{2}}\]

  8. Simplified8.0

    \[\leadsto \color{blue}{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a}} \cdot \frac{1}{2}\]

  9. Final simplification8.0

    \[\leadsto \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a} \cdot \frac{1}{2}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))