Average Error: 4.5 → 4.5
Time: 11.6s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[x \cdot \left(\frac{y}{z} - 1 \cdot \frac{t}{1 - z}\right)\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
x \cdot \left(\frac{y}{z} - 1 \cdot \frac{t}{1 - z}\right)
double f(double x, double y, double z, double t) {
        double r486056 = x;
        double r486057 = y;
        double r486058 = z;
        double r486059 = r486057 / r486058;
        double r486060 = t;
        double r486061 = 1.0;
        double r486062 = r486061 - r486058;
        double r486063 = r486060 / r486062;
        double r486064 = r486059 - r486063;
        double r486065 = r486056 * r486064;
        return r486065;
}
↓
double f(double x, double y, double z, double t) {
        double r486066 = x;
        double r486067 = y;
        double r486068 = z;
        double r486069 = r486067 / r486068;
        double r486070 = 1.0;
        double r486071 = t;
        double r486072 = 1.0;
        double r486073 = r486072 - r486068;
        double r486074 = r486071 / r486073;
        double r486075 = r486070 * r486074;
        double r486076 = r486069 - r486075;
        double r486077 = r486066 * r486076;
        return r486077;
}

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

Original4.5
Target4.2
Herbie4.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.623226303312042442144691872793570510727 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.413394492770230216018398633584271456447 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.091203968982807e-269 or 8.493095129058636e-198 < z

    1. Initial program 3.6

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

    3. Applied *-un-lft-identity3.6

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

    4. Applied *-un-lft-identity3.6

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

    5. Applied times-frac3.6

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

    6. Simplified3.6

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

    if -2.091203968982807e-269 < z < 8.493095129058636e-198

    1. Initial program 14.2

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

    3. Applied frac-sub14.3

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

    4. Applied associate-*r/9.4

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

  4. Final simplification4.5

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

Reproduce

herbie shell --seed 2019303 
(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)))) -7.62322630331204244e-196) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 1.41339449277023022e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z)))))))

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