Average Error: 4.6 → 4.9
Time: 9.0s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.11347096139749 \cdot 10^{-298}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right) + \frac{-x}{\frac{1.0 - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + \frac{-x}{\frac{1.0 - z}{t}}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.11347096139749 \cdot 10^{-298}:\\
\;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right) + \frac{-x}{\frac{1.0 - z}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}} + \frac{-x}{\frac{1.0 - z}{t}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r8371524 = x;
        double r8371525 = y;
        double r8371526 = z;
        double r8371527 = r8371525 / r8371526;
        double r8371528 = t;
        double r8371529 = 1.0;
        double r8371530 = r8371529 - r8371526;
        double r8371531 = r8371528 / r8371530;
        double r8371532 = r8371527 - r8371531;
        double r8371533 = r8371524 * r8371532;
        return r8371533;
}
↓
double f(double x, double y, double z, double t) {
        double r8371534 = t;
        double r8371535 = -4.11347096139749e-298;
        bool r8371536 = r8371534 <= r8371535;
        double r8371537 = 1.0;
        double r8371538 = z;
        double r8371539 = r8371537 / r8371538;
        double r8371540 = x;
        double r8371541 = y;
        double r8371542 = r8371540 * r8371541;
        double r8371543 = r8371539 * r8371542;
        double r8371544 = -r8371540;
        double r8371545 = 1.0;
        double r8371546 = r8371545 - r8371538;
        double r8371547 = r8371546 / r8371534;
        double r8371548 = r8371544 / r8371547;
        double r8371549 = r8371543 + r8371548;
        double r8371550 = r8371538 / r8371541;
        double r8371551 = r8371540 / r8371550;
        double r8371552 = r8371551 + r8371548;
        double r8371553 = r8371536 ? r8371549 : r8371552;
        return r8371553;
}

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

Original4.6
Target4.2
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1.0 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.11347096139749e-298

    1. Initial program 4.5

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied clear-num4.7

      \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{\frac{1}{\frac{1.0 - z}{t}}}\right)\]
    4. Using strategy rm

    5. Applied sub-neg4.7

      \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{1}{\frac{1.0 - z}{t}}\right)\right)}\]

    6. Applied distribute-lft-in4.7

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} + x \cdot \left(-\frac{1}{\frac{1.0 - z}{t}}\right)}\]

    7. Simplified4.6

      \[\leadsto x \cdot \frac{y}{z} + \color{blue}{\frac{x \cdot -1}{\frac{1.0 - z}{t}}}\]
    8. Using strategy rm

    9. Applied associate-*r/5.3

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} + \frac{x \cdot -1}{\frac{1.0 - z}{t}}\]
    10. Using strategy rm

    11. Applied div-inv5.4

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}} + \frac{x \cdot -1}{\frac{1.0 - z}{t}}\]

    if -4.11347096139749e-298 < t

    1. Initial program 4.6

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied clear-num4.7

      \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{\frac{1}{\frac{1.0 - z}{t}}}\right)\]
    4. Using strategy rm

    5. Applied sub-neg4.7

      \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{1}{\frac{1.0 - z}{t}}\right)\right)}\]

    6. Applied distribute-lft-in4.7

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} + x \cdot \left(-\frac{1}{\frac{1.0 - z}{t}}\right)}\]

    7. Simplified4.7

      \[\leadsto x \cdot \frac{y}{z} + \color{blue}{\frac{x \cdot -1}{\frac{1.0 - z}{t}}}\]
    8. Using strategy rm

    9. Applied associate-*r/5.6

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} + \frac{x \cdot -1}{\frac{1.0 - z}{t}}\]
    10. Using strategy rm

    11. Applied associate-/l*4.5

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{x \cdot -1}{\frac{1.0 - z}{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.11347096139749 \cdot 10^{-298}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right) + \frac{-x}{\frac{1.0 - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + \frac{-x}{\frac{1.0 - z}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))