Average Error: 8.2 → 8.2
Time: 6.8s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a} \]
↓
\[\frac{y \cdot x}{a} - \frac{t \cdot z}{a} \]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{y \cdot x}{a} - \frac{t \cdot z}{a}

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))
↓
(FPCore (x y z t a) :precision binary64 (- (/ (* y x) a) (/ (* t z) a)))
double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((y * x) / a) - ((t * z) / a);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.2
Target6.6
Herbie8.2
\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array} \]

Derivation

  1. Initial program 8.2

    \[\frac{x \cdot y - z \cdot t}{a} \]

  2. Taylor expanded in x around 0 8.2

    \[\leadsto \color{blue}{\frac{y \cdot x}{a} - \frac{t \cdot z}{a}} \]

  3. Final simplification8.2

    \[\leadsto \frac{y \cdot x}{a} - \frac{t \cdot z}{a} \]

Reproduce

herbie shell --seed 2022076 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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