Average Error: 7.4 → 5.7
Time: 4.1s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \le -3.18624459217187986 \cdot 10^{52}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \cdot t \le -9.7526479675253164 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t \cdot z}{a}\\ \mathbf{elif}\;z \cdot t \le 5.1148514294461227 \cdot 10^{247}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \le -3.18624459217187986 \cdot 10^{52}:\\
\;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\

\mathbf{elif}\;z \cdot t \le -9.7526479675253164 \cdot 10^{-297}:\\
\;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t \cdot z}{a}\\

\mathbf{elif}\;z \cdot t \le 5.1148514294461227 \cdot 10^{247}:\\
\;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (z * t)) <= -3.18624459217188e+52)) {
		VAR = ((double) (((double) (((double) (x * y)) / a)) - ((double) (t / ((double) (a / z))))));
	} else {
		double VAR_1;
		if ((((double) (z * t)) <= -9.752647967525316e-297)) {
			VAR_1 = ((double) (((double) (x / ((double) (a / y)))) - ((double) (((double) (t * z)) / a))));
		} else {
			double VAR_2;
			if ((((double) (z * t)) <= 5.114851429446123e+247)) {
				VAR_2 = ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (1.0 / a))));
			} else {
				VAR_2 = ((double) (((double) (((double) (x * y)) / a)) - ((double) (t / ((double) (a / z))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original7.4
Target6.0
Herbie5.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z t) < -3.18624459217187986e52 or 5.1148514294461227e247 < (* z t)

    1. Initial program 20.7

      \[\frac{x \cdot y - z \cdot t}{a}\]
    2. Using strategy rm

    3. Applied div-sub20.7

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

    4. Simplified20.7

      \[\leadsto \frac{x \cdot y}{a} - \color{blue}{\frac{t \cdot z}{a}}\]
    5. Using strategy rm

    6. Applied associate-/l*7.6

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

    if -3.18624459217187986e52 < (* z t) < -9.7526479675253164e-297

    1. Initial program 3.1

      \[\frac{x \cdot y - z \cdot t}{a}\]
    2. Using strategy rm

    3. Applied div-sub3.1

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

    4. Simplified3.1

      \[\leadsto \frac{x \cdot y}{a} - \color{blue}{\frac{t \cdot z}{a}}\]
    5. Using strategy rm

    6. Applied associate-/l*6.4

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

    if -9.7526479675253164e-297 < (* z t) < 5.1148514294461227e247

    1. Initial program 4.5

      \[\frac{x \cdot y - z \cdot t}{a}\]
    2. Using strategy rm

    3. Applied div-inv4.5

      \[\leadsto \color{blue}{\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification5.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \le -3.18624459217187986 \cdot 10^{52}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \cdot t \le -9.7526479675253164 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t \cdot z}{a}\\ \mathbf{elif}\;z \cdot t \le 5.1148514294461227 \cdot 10^{247}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(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))