Average Error: 7.7 → 7.7
Time: 5.6s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a} \]
↓
\[\frac{x \cdot y - t \cdot z}{a} \]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{x \cdot y - 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 (/ (- (* x y) (* 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 ((x * y) - (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

Original7.7
Target6.3
Herbie7.7
\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array} \]

Derivation

  1. Initial program 7.7

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

  2. Applied sub-neg_binary647.7

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

  3. Simplified7.7

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

  4. Final simplification7.7

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

Reproduce

herbie shell --seed 2022067 
(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))