Average Error: 11.6 → 1.0
Time: 3.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.38115760978392342 \cdot 10^{253} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le -3.3290513729027525 \cdot 10^{-272} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 3.7548645609617997 \cdot 10^{-176} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 1.5701424637407852 \cdot 10^{181}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.38115760978392342 \cdot 10^{253} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le -3.3290513729027525 \cdot 10^{-272} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 3.7548645609617997 \cdot 10^{-176} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 1.5701424637407852 \cdot 10^{181}\right)\right)\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r578564 = x;
        double r578565 = y;
        double r578566 = z;
        double r578567 = r578565 - r578566;
        double r578568 = r578564 * r578567;
        double r578569 = t;
        double r578570 = r578569 - r578566;
        double r578571 = r578568 / r578570;
        return r578571;
}
↓
double f(double x, double y, double z, double t) {
        double r578572 = x;
        double r578573 = y;
        double r578574 = z;
        double r578575 = r578573 - r578574;
        double r578576 = r578572 * r578575;
        double r578577 = t;
        double r578578 = r578577 - r578574;
        double r578579 = r578576 / r578578;
        double r578580 = -3.3811576097839234e+253;
        bool r578581 = r578579 <= r578580;
        double r578582 = -3.3290513729027525e-272;
        bool r578583 = r578579 <= r578582;
        double r578584 = 3.7548645609618e-176;
        bool r578585 = r578579 <= r578584;
        double r578586 = 1.5701424637407852e+181;
        bool r578587 = r578579 <= r578586;
        double r578588 = !r578587;
        bool r578589 = r578585 || r578588;
        double r578590 = !r578589;
        bool r578591 = r578583 || r578590;
        double r578592 = !r578591;
        bool r578593 = r578581 || r578592;
        double r578594 = r578575 / r578578;
        double r578595 = r578572 * r578594;
        double r578596 = r578593 ? r578595 : r578579;
        return r578596;
}

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

Original11.6
Target2.1
Herbie1.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) (- t z)) < -3.3811576097839234e+253 or -3.3290513729027525e-272 < (/ (* x (- y z)) (- t z)) < 3.7548645609618e-176 or 1.5701424637407852e+181 < (/ (* x (- y z)) (- t z))

    1. Initial program 27.0

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

    3. Applied *-un-lft-identity27.0

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

      \[\leadsto \color{blue}{x} \cdot \frac{y - z}{t - z}\]

    if -3.3811576097839234e+253 < (/ (* x (- y z)) (- t z)) < -3.3290513729027525e-272 or 3.7548645609618e-176 < (/ (* x (- y z)) (- t z)) < 1.5701424637407852e+181

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity0.3

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

    4. Applied times-frac2.2

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

    5. Simplified2.2

      \[\leadsto \color{blue}{x} \cdot \frac{y - z}{t - z}\]
    6. Using strategy rm

    7. Applied associate-*r/0.3

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.38115760978392342 \cdot 10^{253} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le -3.3290513729027525 \cdot 10^{-272} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 3.7548645609617997 \cdot 10^{-176} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 1.5701424637407852 \cdot 10^{181}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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