Average Error: 4.9 → 4.9
Time: 5.0s
Precision: binary64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) ((y / z) - (t / ((double) (1.0 - z)))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) ((y / z) - (t / ((double) (1.0 - z)))))));
}

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

Original4.9
Target4.4
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Initial program 4.9

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

  2. Final simplification4.9

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

Reproduce

herbie shell --seed 2020199 
(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 (- 1.0 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)))))