Average Error: 7.1 → 2.3
Time: 4.0s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.25339538517550107 \cdot 10^{44}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y \cdot \frac{z}{t \cdot z - x}\right) - \frac{x}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.25339538517550107 \cdot 10^{44}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r745656 = x;
        double r745657 = y;
        double r745658 = z;
        double r745659 = r745657 * r745658;
        double r745660 = r745659 - r745656;
        double r745661 = t;
        double r745662 = r745661 * r745658;
        double r745663 = r745662 - r745656;
        double r745664 = r745660 / r745663;
        double r745665 = r745656 + r745664;
        double r745666 = 1.0;
        double r745667 = r745656 + r745666;
        double r745668 = r745665 / r745667;
        return r745668;
}
↓
double f(double x, double y, double z, double t) {
        double r745669 = t;
        double r745670 = -1.253395385175501e+44;
        bool r745671 = r745669 <= r745670;
        double r745672 = x;
        double r745673 = y;
        double r745674 = r745673 / r745669;
        double r745675 = r745672 + r745674;
        double r745676 = 1.0;
        double r745677 = r745672 + r745676;
        double r745678 = r745675 / r745677;
        double r745679 = z;
        double r745680 = r745669 * r745679;
        double r745681 = r745680 - r745672;
        double r745682 = r745679 / r745681;
        double r745683 = r745673 * r745682;
        double r745684 = r745672 + r745683;
        double r745685 = r745672 / r745681;
        double r745686 = r745684 - r745685;
        double r745687 = r745686 / r745677;
        double r745688 = r745671 ? r745678 : r745687;
        return r745688;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.1
Target0.3
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.253395385175501e+44

    1. Initial program 9.6

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

    2. Taylor expanded around inf 5.0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1}\]

    if -1.253395385175501e+44 < t

    1. Initial program 6.4

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
    2. Using strategy rm

    3. Applied div-sub6.4

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

    4. Applied associate-+r-6.4

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

    6. Applied *-un-lft-identity6.4

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

    7. Applied times-frac1.5

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

    8. Simplified1.5

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.25339538517550107 \cdot 10^{44}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y \cdot \frac{z}{t \cdot z - x}\right) - \frac{x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))