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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -6.685209076129246292924560996375942465453 \cdot 10^{161}:\\ \;\;\;\;\frac{y}{z} \cdot x + \sqrt[3]{x} \cdot \left(\frac{t}{1 - z} \cdot \left(-\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\\ \mathbf{elif}\;z \le 2.185888032045070132087342276027611687031 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot x}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x + \sqrt[3]{x} \cdot \left(\frac{t}{1 - z} \cdot \left(-\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\\ \end{array}\]

x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)

↓

\begin{array}{l}
\mathbf{if}\;z \le -6.685209076129246292924560996375942465453 \cdot 10^{161}:\\
\;\;\;\;\frac{y}{z} \cdot x + \sqrt[3]{x} \cdot \left(\frac{t}{1 - z} \cdot \left(-\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\\

\mathbf{elif}\;z \le 2.185888032045070132087342276027611687031 \cdot 10^{-209}:\\
\;\;\;\;\frac{y \cdot x}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{z} \cdot x + \sqrt[3]{x} \cdot \left(\frac{t}{1 - z} \cdot \left(-\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\\

\end{array}

double f(double x, double y, double z, double t) {
        double r15321994 = x;
        double r15321995 = y;
        double r15321996 = z;
        double r15321997 = r15321995 / r15321996;
        double r15321998 = t;
        double r15321999 = 1.0;
        double r15322000 = r15321999 - r15321996;
        double r15322001 = r15321998 / r15322000;
        double r15322002 = r15321997 - r15322001;
        double r15322003 = r15321994 * r15322002;
        return r15322003;
}

↓

double f(double x, double y, double z, double t) {
        double r15322004 = z;
        double r15322005 = -6.685209076129246e+161;
        bool r15322006 = r15322004 <= r15322005;
        double r15322007 = y;
        double r15322008 = r15322007 / r15322004;
        double r15322009 = x;
        double r15322010 = r15322008 * r15322009;
        double r15322011 = cbrt(r15322009);
        double r15322012 = t;
        double r15322013 = 1.0;
        double r15322014 = r15322013 - r15322004;
        double r15322015 = r15322012 / r15322014;
        double r15322016 = r15322011 * r15322011;
        double r15322017 = -r15322016;
        double r15322018 = r15322015 * r15322017;
        double r15322019 = r15322011 * r15322018;
        double r15322020 = r15322010 + r15322019;
        double r15322021 = 2.18588803204507e-209;
        bool r15322022 = r15322004 <= r15322021;
        double r15322023 = r15322007 * r15322009;
        double r15322024 = r15322023 / r15322004;
        double r15322025 = -r15322015;
        double r15322026 = r15322009 * r15322025;
        double r15322027 = r15322024 + r15322026;
        double r15322028 = r15322022 ? r15322027 : r15322020;
        double r15322029 = r15322006 ? r15322020 : r15322028;
        return r15322029;
}

Original	4.5
Target	4.3
Herbie	3.8

Derivation

Split input into 2 regimes
if z < -6.685209076129246e+161 or 2.18588803204507e-209 < z
1. Initial program 3.1
  \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
2. Using strategy rm
3. Applied sub-neg3.1
  \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{t}{1 - z}\right)\right)}\]
4. Applied distribute-rgt-in3.1
  \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \left(-\frac{t}{1 - z}\right) \cdot x}\]
5. Using strategy rm
6. Applied add-cube-cbrt3.5
  \[\leadsto \frac{y}{z} \cdot x + \left(-\frac{t}{1 - z}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)}\]
7. Applied associate-*r*3.5
  \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(\left(-\frac{t}{1 - z}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}}\]
if -6.685209076129246e+161 < z < 2.18588803204507e-209
1. Initial program 6.7
  \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
2. Using strategy rm
3. Applied sub-neg6.7
  \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{t}{1 - z}\right)\right)}\]
4. Applied distribute-rgt-in6.7
  \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \left(-\frac{t}{1 - z}\right) \cdot x}\]
5. Taylor expanded around 0 4.2
  \[\leadsto \color{blue}{\frac{x \cdot y}{z}} + \left(-\frac{t}{1 - z}\right) \cdot x\]
Recombined 2 regimes into one program.
Final simplification3.8
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.685209076129246292924560996375942465453 \cdot 10^{161}:\\ \;\;\;\;\frac{y}{z} \cdot x + \sqrt[3]{x} \cdot \left(\frac{t}{1 - z} \cdot \left(-\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\\ \mathbf{elif}\;z \le 2.185888032045070132087342276027611687031 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot x}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x + \sqrt[3]{x} \cdot \left(\frac{t}{1 - z} \cdot \left(-\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(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 (/ 1.0 (- 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 (/ 1.0 (- 1.0 z)))))))

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

Error

Try it out

Target

Derivation

`if z < -6.685209076129246e+161 or 2.18588803204507e-209 < z`

`if -6.685209076129246e+161 < z < 2.18588803204507e-209`

Reproduce

In
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