Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.7% → 96.6%

Time: 10.2s

Alternatives: 12

Speedup: 0.7×

• 27.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := \mathsf{fma}\left(\frac{y}{a}, x, -t \cdot \frac{z}{a}\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+197}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))) (t_2 (fma (/ y a) x (- (* t (/ z a))))))
   (if (<= t_1 -1e+223) t_2 (if (<= t_1 2e+197) (/ t_1 a) t_2))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double t_2 = fma((y / a), x, -(t * (z / a)));
	double tmp;
	if (t_1 <= -1e+223) {
		tmp = t_2;
	} else if (t_1 <= 2e+197) {
		tmp = t_1 / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = fma(Float64(y / a), x, Float64(-Float64(t * Float64(z / a))))
	tmp = 0.0
	if (t_1 <= -1e+223)
		tmp = t_2;
	elseif (t_1 <= 2e+197)
		tmp = Float64(t_1 / a);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * x + (-N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+223], t$95$2, If[LessEqual[t$95$1, 2e+197], N[(t$95$1 / a), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.00000000000000005e223 or 1.9999999999999999e197 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 84.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(\frac{z \cdot t}{a}\right)\right)} \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, x, \mathsf{neg}\left(\frac{z \cdot t}{a}\right)\right) \]

      7. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\mathsf{neg}\left(\frac{z \cdot t}{a}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{a}}\right)\right) \]

      9. *-lowering-*.f64 89.0

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

   4. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, x, -\frac{z \cdot t}{a}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(\color{blue}{z \cdot \frac{t}{a}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(\color{blue}{\frac{z}{\frac{a}{t}}}\right)\right) \]

      4. distribute-frac-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\frac{\mathsf{neg}\left(z\right)}{\frac{a}{t}}}\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t}\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\left(\mathsf{neg}\left(\frac{z}{a}\right)\right)} \cdot t\right) \]

      8. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\frac{z}{\mathsf{neg}\left(a\right)}} \cdot t\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\frac{z}{\mathsf{neg}\left(a\right)}} \cdot t\right) \]

      10. neg-lowering-neg.f64 97.5

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

   6. Applied egg-rr 97.5%

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

   if -1.00000000000000005e223 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.9999999999999999e197

   1. Initial program 98.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -1 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, -t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+197}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, -t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 530000000:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+189}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a}, \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, -\frac{z \cdot t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 530000000.0)
   (/ (- (* x y) (* z t)) a)
   (if (<= a 1.05e+189)
     (fma (- t) (/ z a) (/ (* x y) a))
     (fma (/ y a) x (- (/ (* z t) a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 530000000.0) {
		tmp = ((x * y) - (z * t)) / a;
	} else if (a <= 1.05e+189) {
		tmp = fma(-t, (z / a), ((x * y) / a));
	} else {
		tmp = fma((y / a), x, -((z * t) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 530000000.0)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	elseif (a <= 1.05e+189)
		tmp = fma(Float64(-t), Float64(z / a), Float64(Float64(x * y) / a));
	else
		tmp = fma(Float64(y / a), x, Float64(-Float64(Float64(z * t) / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 530000000.0], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 1.05e+189], N[((-t) * N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x + (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 5.3e8

   1. Initial program 94.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.3e8 < a < 1.04999999999999996e189

   1. Initial program 92.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(t\right), \frac{z}{a}, \frac{x \cdot y}{a}\right)} \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, \frac{z}{a}, \frac{x \cdot y}{a}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), \color{blue}{\frac{z}{a}}, \frac{x \cdot y}{a}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), \frac{z}{a}, \color{blue}{\frac{x \cdot y}{a}}\right) \]

      11. *-lowering-*.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   if 1.04999999999999996e189 < a

   1. Initial program 90.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(\frac{z \cdot t}{a}\right)\right)} \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, x, \mathsf{neg}\left(\frac{z \cdot t}{a}\right)\right) \]

      7. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\mathsf{neg}\left(\frac{z \cdot t}{a}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{a}}\right)\right) \]

      9. *-lowering-*.f64 98.8

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

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, x, -\frac{z \cdot t}{a}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 92.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 530000000:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a}, \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, -\frac{z \cdot t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 530000000.0)
   (/ (- (* x y) (* z t)) a)
   (if (<= a 3.1e+168)
     (fma (- t) (/ z a) (/ (* x y) a))
     (fma (/ x a) y (- (/ (* z t) a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 530000000.0) {
		tmp = ((x * y) - (z * t)) / a;
	} else if (a <= 3.1e+168) {
		tmp = fma(-t, (z / a), ((x * y) / a));
	} else {
		tmp = fma((x / a), y, -((z * t) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 530000000.0)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	elseif (a <= 3.1e+168)
		tmp = fma(Float64(-t), Float64(z / a), Float64(Float64(x * y) / a));
	else
		tmp = fma(Float64(x / a), y, Float64(-Float64(Float64(z * t) / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 530000000.0], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 3.1e+168], N[((-t) * N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y + (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 5.3e8

   1. Initial program 94.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.3e8 < a < 3.09999999999999996e168

   1. Initial program 92.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(t\right), \frac{z}{a}, \frac{x \cdot y}{a}\right)} \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, \frac{z}{a}, \frac{x \cdot y}{a}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), \color{blue}{\frac{z}{a}}, \frac{x \cdot y}{a}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), \frac{z}{a}, \color{blue}{\frac{x \cdot y}{a}}\right) \]

      11. *-lowering-*.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   if 3.09999999999999996e168 < a

   1. Initial program 91.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a}, y, \mathsf{neg}\left(\frac{z \cdot t}{a}\right)\right)} \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{x}{a}}, y, \mathsf{neg}\left(\frac{z \cdot t}{a}\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, y, \color{blue}{\mathsf{neg}\left(\frac{z \cdot t}{a}\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, y, \mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{a}}\right)\right) \]

      10. *-lowering-*.f64 99.9

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

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a}, y, -\frac{z \cdot t}{a}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{-z}}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -5e+23)
   (/ t (/ a (- z)))
   (if (<= (* z t) 2e+61) (/ (* x y) a) (- (/ z (/ a t))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = t / (a / -z);
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = -(z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= (-5d+23)) then
        tmp = t / (a / -z)
    else if ((z * t) <= 2d+61) then
        tmp = (x * y) / a
    else
        tmp = -(z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = t / (a / -z);
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = -(z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -5e+23:
		tmp = t / (a / -z)
	elif (z * t) <= 2e+61:
		tmp = (x * y) / a
	else:
		tmp = -(z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -5e+23)
		tmp = Float64(t / Float64(a / Float64(-z)));
	elseif (Float64(z * t) <= 2e+61)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(-Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -5e+23)
		tmp = t / (a / -z);
	elseif ((z * t) <= 2e+61)
		tmp = (x * y) / a;
	else
		tmp = -(z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+23], N[(t / N[(a / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+61], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], (-N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999999e23

   1. Initial program 88.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 88.3

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 81.1

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

   7. Simplified 81.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \frac{\mathsf{neg}\left(z\right)}{a}} \]

      5. clear-num N/A

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      6. un-div-inv N/A

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \frac{t}{\color{blue}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      9. neg-lowering-neg.f64 86.3

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

   9. Applied egg-rr 86.3%

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

   if -4.9999999999999999e23 < (*.f64 z t) < 1.9999999999999999e61

   1. Initial program 96.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 78.1

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

   5. Simplified 78.1%

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

   if 1.9999999999999999e61 < (*.f64 z t)

   1. Initial program 92.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 92.6

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 83.6

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

   7. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{\frac{a}{t}}} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{\frac{a}{t}}} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z\right)}}{\frac{a}{t}} \]

      7. /-lowering-/.f64 90.7

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

   9. Applied egg-rr 90.7%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{-z}}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{-z}}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a (- z)))))
   (if (<= (* z t) -5e+23) t_1 (if (<= (* z t) 2e+61) (/ (* x y) a) t_1))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / -z);
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = t_1;
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / -z)
    if ((z * t) <= (-5d+23)) then
        tmp = t_1
    else if ((z * t) <= 2d+61) then
        tmp = (x * y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / -z);
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = t_1;
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t / (a / -z)
	tmp = 0
	if (z * t) <= -5e+23:
		tmp = t_1
	elif (z * t) <= 2e+61:
		tmp = (x * y) / a
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / Float64(-z)))
	tmp = 0.0
	if (Float64(z * t) <= -5e+23)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e+61)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / -z);
	tmp = 0.0;
	if ((z * t) <= -5e+23)
		tmp = t_1;
	elseif ((z * t) <= 2e+61)
		tmp = (x * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+23], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e+61], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999999e23 or 1.9999999999999999e61 < (*.f64 z t)

   1. Initial program 90.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 90.0

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 82.1

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

   7. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \frac{\mathsf{neg}\left(z\right)}{a}} \]

      5. clear-num N/A

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      6. un-div-inv N/A

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \frac{t}{\color{blue}{\frac{a}{\mathsf{neg}\left(z\right)}}} \]

      9. neg-lowering-neg.f64 84.2

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

   9. Applied egg-rr 84.2%

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

   if -4.9999999999999999e23 < (*.f64 z t) < 1.9999999999999999e61

   1. Initial program 96.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 78.1

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

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 92.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a}, \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -1e+103)
   (fma (- t) (/ z a) (/ (* x y) a))
   (/ (fma (- z) t (* x y)) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -1e+103) {
		tmp = fma(-t, (z / a), ((x * y) / a));
	} else {
		tmp = fma(-z, t, (x * y)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -1e+103)
		tmp = fma(Float64(-t), Float64(z / a), Float64(Float64(x * y) / a));
	else
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+103], N[((-t) * N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1e103

   1. Initial program 87.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(t\right), \frac{z}{a}, \frac{x \cdot y}{a}\right)} \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, \frac{z}{a}, \frac{x \cdot y}{a}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), \color{blue}{\frac{z}{a}}, \frac{x \cdot y}{a}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), \frac{z}{a}, \color{blue}{\frac{x \cdot y}{a}}\right) \]

      11. *-lowering-*.f64 97.6

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

   4. Applied egg-rr 97.6%

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

   if -1e103 < (*.f64 z t)

   1. Initial program 95.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 95.3

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

   4. Applied egg-rr 95.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-z, t, x \cdot y\right)}}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -5e+23)
   (- (* t (/ z a)))
   (if (<= (* z t) 2e+61) (/ (* x y) a) (- (* z (/ t a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = -(t * (z / a));
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = -(z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= (-5d+23)) then
        tmp = -(t * (z / a))
    else if ((z * t) <= 2d+61) then
        tmp = (x * y) / a
    else
        tmp = -(z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = -(t * (z / a));
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = -(z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -5e+23:
		tmp = -(t * (z / a))
	elif (z * t) <= 2e+61:
		tmp = (x * y) / a
	else:
		tmp = -(z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -5e+23)
		tmp = Float64(-Float64(t * Float64(z / a)));
	elseif (Float64(z * t) <= 2e+61)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(-Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -5e+23)
		tmp = -(t * (z / a));
	elseif ((z * t) <= 2e+61)
		tmp = (x * y) / a;
	else
		tmp = -(z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+23], (-N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(z * t), $MachinePrecision], 2e+61], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], (-N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999999e23

   1. Initial program 88.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 88.3

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 81.1

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

   7. Simplified 81.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      5. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(a\right)}} \cdot t \]

      6. remove-double-neg N/A

         \[\leadsto \frac{\color{blue}{z}}{\mathsf{neg}\left(a\right)} \cdot t \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{\mathsf{neg}\left(a\right)}} \cdot t \]

      8. neg-lowering-neg.f64 86.3

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

   9. Applied egg-rr 86.3%

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

   if -4.9999999999999999e23 < (*.f64 z t) < 1.9999999999999999e61

   1. Initial program 96.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 78.1

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

   5. Simplified 78.1%

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

   if 1.9999999999999999e61 < (*.f64 z t)

   1. Initial program 92.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 92.6

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 83.6

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

   7. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{z \cdot \frac{\mathsf{neg}\left(t\right)}{a}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(t\right)}{a} \cdot z} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(t\right)}{a} \cdot z} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(t\right)}{a}} \cdot z \]

      5. neg-lowering-neg.f64 88.2

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

   9. Applied egg-rr 88.2%

      \[\leadsto \color{blue}{\frac{-t}{a} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := -t \cdot \frac{z}{a}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* t (/ z a)))))
   (if (<= (* z t) -5e+23) t_1 (if (<= (* z t) 2e+61) (/ (* x y) a) t_1))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t * (z / a));
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = t_1;
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(t * (z / a))
    if ((z * t) <= (-5d+23)) then
        tmp = t_1
    else if ((z * t) <= 2d+61) then
        tmp = (x * y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t * (z / a));
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = t_1;
	} else if ((z * t) <= 2e+61) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -(t * (z / a))
	tmp = 0
	if (z * t) <= -5e+23:
		tmp = t_1
	elif (z * t) <= 2e+61:
		tmp = (x * y) / a
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(-Float64(t * Float64(z / a)))
	tmp = 0.0
	if (Float64(z * t) <= -5e+23)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e+61)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -(t * (z / a));
	tmp = 0.0;
	if ((z * t) <= -5e+23)
		tmp = t_1;
	elseif ((z * t) <= 2e+61)
		tmp = (x * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+23], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e+61], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999999e23 or 1.9999999999999999e61 < (*.f64 z t)

   1. Initial program 90.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 90.0

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 82.1

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

   7. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      5. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(a\right)}} \cdot t \]

      6. remove-double-neg N/A

         \[\leadsto \frac{\color{blue}{z}}{\mathsf{neg}\left(a\right)} \cdot t \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{\mathsf{neg}\left(a\right)}} \cdot t \]

      8. neg-lowering-neg.f64 84.4

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

   9. Applied egg-rr 84.4%

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

   if -4.9999999999999999e23 < (*.f64 z t) < 1.9999999999999999e61

   1. Initial program 96.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 78.1

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

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+204}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -1e+204) (- (* t (/ z a))) (/ (fma (- z) t (* x y)) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -1e+204) {
		tmp = -(t * (z / a));
	} else {
		tmp = fma(-z, t, (x * y)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -1e+204)
		tmp = Float64(-Float64(t * Float64(z / a)));
	else
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+204], (-N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999989e203

   1. Initial program 78.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 78.3

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

   4. Applied egg-rr 78.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 78.2

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

   7. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      5. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(a\right)}} \cdot t \]

      6. remove-double-neg N/A

         \[\leadsto \frac{\color{blue}{z}}{\mathsf{neg}\left(a\right)} \cdot t \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{\mathsf{neg}\left(a\right)}} \cdot t \]

      8. neg-lowering-neg.f64 96.1

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

   9. Applied egg-rr 96.1%

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

   if -9.99999999999999989e203 < (*.f64 z t)

   1. Initial program 95.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 95.6

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

   4. Applied egg-rr 95.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-z, t, x \cdot y\right)}}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+204}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+204}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -1e+204) (- (* t (/ z a))) (/ (- (* x y) (* z t)) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -1e+204) {
		tmp = -(t * (z / a));
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= (-1d+204)) then
        tmp = -(t * (z / a))
    else
        tmp = ((x * y) - (z * t)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -1e+204) {
		tmp = -(t * (z / a));
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -1e+204:
		tmp = -(t * (z / a))
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -1e+204)
		tmp = Float64(-Float64(t * Float64(z / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -1e+204)
		tmp = -(t * (z / a));
	else
		tmp = ((x * y) - (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+204], (-N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999989e203

   1. Initial program 78.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), t, x \cdot y\right)}}{a} \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, t, x \cdot y\right)}{a} \]

      6. *-lowering-*.f64 78.3

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

   4. Applied egg-rr 78.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot z}}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(-1 \cdot t\right)}}{a} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}}{a} \]

      7. neg-lowering-neg.f64 78.2

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

   7. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{z \cdot \left(-t\right)}{a}} \]
   8. Step-by-step derivation

      1. distribute-rgt-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z \cdot t\right)}}{a} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}}{a} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z\right)}{a} \cdot t} \]

      5. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(a\right)}} \cdot t \]

      6. remove-double-neg N/A

         \[\leadsto \frac{\color{blue}{z}}{\mathsf{neg}\left(a\right)} \cdot t \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{\mathsf{neg}\left(a\right)}} \cdot t \]

      8. neg-lowering-neg.f64 96.1

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

   9. Applied egg-rr 96.1%

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

   if -9.99999999999999989e203 < (*.f64 z t)

   1. Initial program 95.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+204}:\\ \;\;\;\;-t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.45 \cdot 10^{+120}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 2.45e+120) (/ (* x y) a) (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.45e+120) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 2.45d+120) then
        tmp = (x * y) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.45e+120) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.45e+120:
		tmp = (x * y) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.45e+120)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 2.45e+120)
		tmp = (x * y) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.45e+120], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.45000000000000005e120

   1. Initial program 94.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 56.8

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

   5. Simplified 56.8%

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

   if 2.45000000000000005e120 < a

   1. Initial program 92.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 52.2

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

   5. Simplified 52.2%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

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

      2. clear-num N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      3. un-div-inv N/A

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

      4. associate-/r/ N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 57.5

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

   7. Applied egg-rr 57.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.45 \cdot 10^{+120}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ y \cdot \frac{x}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* y (/ x a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = y * (x / a)
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return y * (x / a)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(y * Float64(x / a))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = y * (x / a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 N/A

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

   2. *-lowering-*.f64 56.2

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

5. Simplified 56.2%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
6. Step-by-step derivation

   1. associate-/l* N/A

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

   2. clear-num N/A

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

   3. un-div-inv N/A

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   4. associate-/r/ N/A

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

   5. *-lowering-*.f64 N/A

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

   6. /-lowering-/.f64 53.8

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

7. Applied egg-rr 53.8%

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

8. Final simplification 53.8%

   \[\leadsto y \cdot \frac{x}{a} \]
9. Add Preprocessing

Developer Target 1: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

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