Average Error: 6.8 → 5.6
Time: 17.5s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;\left(\frac{y}{a} \cdot x\right) \cdot 0.5 - \frac{t \cdot z}{a} \cdot 4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot 2.0} \cdot \left(x \cdot y - \left(t \cdot 9.0\right) \cdot z\right)\\ \end{array}\]
\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -\infty:\\
\;\;\;\;\left(\frac{y}{a} \cdot x\right) \cdot 0.5 - \frac{t \cdot z}{a} \cdot 4.5\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{a \cdot 2.0} \cdot \left(x \cdot y - \left(t \cdot 9.0\right) \cdot z\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r41729132 = x;
        double r41729133 = y;
        double r41729134 = r41729132 * r41729133;
        double r41729135 = z;
        double r41729136 = 9.0;
        double r41729137 = r41729135 * r41729136;
        double r41729138 = t;
        double r41729139 = r41729137 * r41729138;
        double r41729140 = r41729134 - r41729139;
        double r41729141 = a;
        double r41729142 = 2.0;
        double r41729143 = r41729141 * r41729142;
        double r41729144 = r41729140 / r41729143;
        return r41729144;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r41729145 = x;
        double r41729146 = y;
        double r41729147 = r41729145 * r41729146;
        double r41729148 = -inf.0;
        bool r41729149 = r41729147 <= r41729148;
        double r41729150 = a;
        double r41729151 = r41729146 / r41729150;
        double r41729152 = r41729151 * r41729145;
        double r41729153 = 0.5;
        double r41729154 = r41729152 * r41729153;
        double r41729155 = t;
        double r41729156 = z;
        double r41729157 = r41729155 * r41729156;
        double r41729158 = r41729157 / r41729150;
        double r41729159 = 4.5;
        double r41729160 = r41729158 * r41729159;
        double r41729161 = r41729154 - r41729160;
        double r41729162 = 1.0;
        double r41729163 = 2.0;
        double r41729164 = r41729150 * r41729163;
        double r41729165 = r41729162 / r41729164;
        double r41729166 = 9.0;
        double r41729167 = r41729155 * r41729166;
        double r41729168 = r41729167 * r41729156;
        double r41729169 = r41729147 - r41729168;
        double r41729170 = r41729165 * r41729169;
        double r41729171 = r41729149 ? r41729161 : r41729170;
        return r41729171;
}

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

Original6.8
Target5.2
Herbie5.6
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9.0 \cdot t\right)}{a \cdot 2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -inf.0

    1. Initial program 60.3

      \[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]

    2. Taylor expanded around 0 60.3

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity60.3

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{\color{blue}{1 \cdot a}} - 4.5 \cdot \frac{t \cdot z}{a}\]

    5. Applied times-frac8.5

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{y}{a}\right)} - 4.5 \cdot \frac{t \cdot z}{a}\]

    6. Simplified8.5

      \[\leadsto 0.5 \cdot \left(\color{blue}{x} \cdot \frac{y}{a}\right) - 4.5 \cdot \frac{t \cdot z}{a}\]

    if -inf.0 < (* x y)

    1. Initial program 5.4

      \[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]
    2. Using strategy rm

    3. Applied associate-*l*5.4

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9.0 \cdot t\right)}}{a \cdot 2.0}\]
    4. Using strategy rm

    5. Applied div-inv5.5

      \[\leadsto \color{blue}{\left(x \cdot y - z \cdot \left(9.0 \cdot t\right)\right) \cdot \frac{1}{a \cdot 2.0}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;\left(\frac{y}{a} \cdot x\right) \cdot 0.5 - \frac{t \cdot z}{a} \cdot 4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot 2.0} \cdot \left(x \cdot y - \left(t \cdot 9.0\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"

  :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 (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))