Average Error: 22.5 → 22.5
Time: 5.7s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\frac{\left(x \cdot y + t \cdot z\right) + z \cdot \left(-a\right)}{y + z \cdot \left(b - y\right)}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\frac{\left(x \cdot y + t \cdot z\right) + z \cdot \left(-a\right)}{y + z \cdot \left(b - y\right)}
double code(double x, double y, double z, double t, double a, double b) {
	return (((x * y) + (z * (t - a))) / (y + (z * (b - y))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((((x * y) + (t * z)) + (z * -a)) / (y + (z * (b - y))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original22.5
Target17.4
Herbie22.5
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Initial program 22.5

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

  3. Applied sub-neg22.5

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

  4. Applied distribute-lft-in22.5

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

  5. Applied associate-+r+22.5

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

  6. Simplified22.5

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

  7. Final simplification22.5

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

Reproduce

herbie shell --seed 2020105 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))