Average Error: 4.8 → 4.8
Time: 11.5s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)
double f(double x, double y, double z, double t) {
        double r481584 = x;
        double r481585 = y;
        double r481586 = z;
        double r481587 = r481585 / r481586;
        double r481588 = t;
        double r481589 = 1.0;
        double r481590 = r481589 - r481586;
        double r481591 = r481588 / r481590;
        double r481592 = r481587 - r481591;
        double r481593 = r481584 * r481592;
        return r481593;
}
↓
double f(double x, double y, double z, double t) {
        double r481594 = x;
        double r481595 = y;
        double r481596 = z;
        double r481597 = r481595 / r481596;
        double r481598 = t;
        double r481599 = 1.0;
        double r481600 = 1.0;
        double r481601 = r481600 - r481596;
        double r481602 = r481599 / r481601;
        double r481603 = r481598 * r481602;
        double r481604 = r481597 - r481603;
        double r481605 = r481594 * r481604;
        return r481605;
}

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

Original4.8
Target4.4
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. Initial program 4.8

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

  3. Applied div-inv4.8

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

  4. Final simplification4.8

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))))