Average Error: 4.7 → 4.8
Time: 6.6s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.67227397293114902 \cdot 10^{32}:\\ \;\;\;\;\frac{x}{z} \cdot y + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{elif}\;t \le -5.07013430888526762 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + \left(t \cdot x\right) \cdot \left(-\frac{1}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{1}{x \cdot y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.67227397293114902 \cdot 10^{32}:\\
\;\;\;\;\frac{x}{z} \cdot y + x \cdot \left(-\frac{t}{1 - z}\right)\\

\mathbf{elif}\;t \le -5.07013430888526762 \cdot 10^{-249}:\\
\;\;\;\;\frac{x}{\frac{z}{y}} + \left(t \cdot x\right) \cdot \left(-\frac{1}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r375709 = x;
        double r375710 = y;
        double r375711 = z;
        double r375712 = r375710 / r375711;
        double r375713 = t;
        double r375714 = 1.0;
        double r375715 = r375714 - r375711;
        double r375716 = r375713 / r375715;
        double r375717 = r375712 - r375716;
        double r375718 = r375709 * r375717;
        return r375718;
}
↓
double f(double x, double y, double z, double t) {
        double r375719 = t;
        double r375720 = -8.672273972931149e+32;
        bool r375721 = r375719 <= r375720;
        double r375722 = x;
        double r375723 = z;
        double r375724 = r375722 / r375723;
        double r375725 = y;
        double r375726 = r375724 * r375725;
        double r375727 = 1.0;
        double r375728 = r375727 - r375723;
        double r375729 = r375719 / r375728;
        double r375730 = -r375729;
        double r375731 = r375722 * r375730;
        double r375732 = r375726 + r375731;
        double r375733 = -5.070134308885268e-249;
        bool r375734 = r375719 <= r375733;
        double r375735 = r375723 / r375725;
        double r375736 = r375722 / r375735;
        double r375737 = r375719 * r375722;
        double r375738 = 1.0;
        double r375739 = r375738 / r375728;
        double r375740 = -r375739;
        double r375741 = r375737 * r375740;
        double r375742 = r375736 + r375741;
        double r375743 = r375722 * r375725;
        double r375744 = r375738 / r375743;
        double r375745 = r375723 * r375744;
        double r375746 = r375738 / r375745;
        double r375747 = r375746 + r375731;
        double r375748 = r375734 ? r375742 : r375747;
        double r375749 = r375721 ? r375732 : r375748;
        return r375749;
}

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

Original4.7
Target4.3
Herbie4.8
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -8.672273972931149e+32

    1. Initial program 4.2

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
    2. Using strategy rm

    3. Applied sub-neg4.2

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

    4. Applied distribute-lft-in4.2

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

    5. Simplified4.0

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

    7. Applied associate-/l*3.8

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

    9. Applied associate-/r/3.0

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

    if -8.672273972931149e+32 < t < -5.070134308885268e-249

    1. Initial program 5.1

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
    2. Using strategy rm

    3. Applied sub-neg5.1

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

    4. Applied distribute-lft-in5.1

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

    5. Simplified6.0

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

    7. Applied associate-/l*4.8

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

    9. Applied div-inv4.8

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

    10. Applied distribute-rgt-neg-in4.8

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

    11. Applied associate-*r*4.1

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

    12. Simplified4.1

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

    if -5.070134308885268e-249 < t

    1. Initial program 4.7

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
    2. Using strategy rm

    3. Applied sub-neg4.7

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

    4. Applied distribute-lft-in4.7

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

    5. Simplified5.4

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

    7. Applied clear-num5.6

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

    9. Applied div-inv5.9

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

  4. Final simplification4.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.67227397293114902 \cdot 10^{32}:\\ \;\;\;\;\frac{x}{z} \cdot y + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{elif}\;t \le -5.07013430888526762 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + \left(t \cdot x\right) \cdot \left(-\frac{1}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{1}{x \cdot y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

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