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

Percentage Accurate: 91.4% → 94.3%

Time: 8.9s

Alternatives: 12

Speedup: 0.6×

• 28.4% 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: 91.4% 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: 94.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - \frac{t}{\frac{a\_m}{z}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= a_m 6.3e+106)
    (/ (fma x y (* z (- t))) a_m)
    (- (* x (/ y a_m)) (/ t (/ a_m z))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 6.3e+106) {
		tmp = fma(x, y, (z * -t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (t / (a_m / z));
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (a_m <= 6.3e+106)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(t / Float64(a_m / z)));
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[a$95$m, 6.3e+106], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 6.29999999999999974e106

   1. Initial program 94.4%

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

      1. div-sub 91.6%

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

      2. *-commutative 91.6%

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

      3. div-sub 94.4%

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

      4. *-commutative 94.4%

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

      5. fma-neg 94.4%

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

      6. distribute-rgt-neg-out 94.4%

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

   3. Simplified 94.4%

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

   if 6.29999999999999974e106 < a

   1. Initial program 74.4%

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

      1. div-sub 74.4%

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

      2. associate-/l* 89.7%

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

      3. associate-/l* 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. div-inv 92.7%

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

      2. add-sqr-sqrt 47.9%

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

      3. sqrt-unprod 59.9%

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

      4. sqr-neg 59.9%

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

      5. sqrt-unprod 27.0%

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

      6. add-sqr-sqrt 55.1%

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

      7. associate-*l* 55.0%

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

      8. *-commutative 55.0%

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

      9. div-inv 55.0%

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

      10. associate-/l* 55.0%

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

      11. clear-num 55.0%

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

      12. un-div-inv 55.0%

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

      13. add-sqr-sqrt 27.1%

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

      14. sqrt-unprod 60.9%

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

      15. sqr-neg 60.9%

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

      16. sqrt-unprod 51.1%

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

      17. add-sqr-sqrt 93.8%

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

   6. Applied egg-rr 93.8%

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

Alternative 2: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{-1}{\frac{\frac{a\_m}{t}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -5e+145)
    (/ x (/ a_m y))
    (if (<= (* x y) -2e+57)
      (/ (* z (- t)) a_m)
      (if (<= (* x y) -2e-32)
        (/ (* x y) a_m)
        (if (<= (* x y) 5e-30) (/ -1.0 (/ (/ a_m t) z)) (* x (/ y a_m))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = (z * -t) / a_m;
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-30) {
		tmp = -1.0 / ((a_m / t) / z);
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-5d+145)) then
        tmp = x / (a_m / y)
    else if ((x * y) <= (-2d+57)) then
        tmp = (z * -t) / a_m
    else if ((x * y) <= (-2d-32)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 5d-30) then
        tmp = (-1.0d0) / ((a_m / t) / z)
    else
        tmp = x * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = (z * -t) / a_m;
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-30) {
		tmp = -1.0 / ((a_m / t) / z);
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -5e+145:
		tmp = x / (a_m / y)
	elif (x * y) <= -2e+57:
		tmp = (z * -t) / a_m
	elif (x * y) <= -2e-32:
		tmp = (x * y) / a_m
	elif (x * y) <= 5e-30:
		tmp = -1.0 / ((a_m / t) / z)
	else:
		tmp = x * (y / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -5e+145)
		tmp = Float64(x / Float64(a_m / y));
	elseif (Float64(x * y) <= -2e+57)
		tmp = Float64(Float64(z * Float64(-t)) / a_m);
	elseif (Float64(x * y) <= -2e-32)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 5e-30)
		tmp = Float64(-1.0 / Float64(Float64(a_m / t) / z));
	else
		tmp = Float64(x * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -5e+145)
		tmp = x / (a_m / y);
	elseif ((x * y) <= -2e+57)
		tmp = (z * -t) / a_m;
	elseif ((x * y) <= -2e-32)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 5e-30)
		tmp = -1.0 / ((a_m / t) / z);
	else
		tmp = x * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+145], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+57], N[(N[(z * (-t)), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-32], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-30], N[(-1.0 / N[(N[(a$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.99999999999999967e145

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.5%

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

   7. Applied egg-rr 83.5%

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

   if -4.99999999999999967e145 < (*.f64 x y) < -2.0000000000000001e57

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 77.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(t \cdot z\right)}}{a} \]
   4. Step-by-step derivation

      1. associate-*r* 77.3%

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

      2. mul-1-neg 77.3%

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

   5. Simplified 77.3%

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

   if -2.0000000000000001e57 < (*.f64 x y) < -2.00000000000000011e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.3%

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

   if -2.00000000000000011e-32 < (*.f64 x y) < 4.99999999999999972e-30

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 82.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(t \cdot z\right)}}{a} \]
   4. Step-by-step derivation

      1. associate-*r* 82.9%

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

      2. mul-1-neg 82.9%

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

   5. Simplified 82.9%

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

      1. *-commutative 82.9%

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

      2. distribute-rgt-neg-out 82.9%

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

      3. distribute-neg-frac 82.9%

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

      4. associate-*r/ 79.2%

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

      5. *-commutative 79.2%

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

      6. distribute-rgt-neg-in 79.2%

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

   7. Applied egg-rr 79.2%

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

      1. distribute-rgt-neg-out 79.2%

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

      2. associate-*l/ 82.9%

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

      3. clear-num 82.4%

         \[\leadsto -\color{blue}{\frac{1}{\frac{a}{t \cdot z}}} \]

      4. distribute-neg-frac 82.4%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a}{t \cdot z}}} \]

      5. metadata-eval 82.4%

         \[\leadsto \frac{\color{blue}{-1}}{\frac{a}{t \cdot z}} \]

      6. associate-/r* 79.8%

         \[\leadsto \frac{-1}{\color{blue}{\frac{\frac{a}{t}}{z}}} \]

   9. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{\frac{-1}{\frac{\frac{a}{t}}{z}}} \]

   if 4.99999999999999972e-30 < (*.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 73.7%

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

      1. associate-*r/ 76.3%

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

   5. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{-1}{\frac{\frac{a}{t}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-t\right)}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ (* z (- t)) a_m)))
   (*
    a_s
    (if (<= (* x y) -5e+145)
      (/ x (/ a_m y))
      (if (<= (* x y) -2e+57)
        t_1
        (if (<= (* x y) -2e-32)
          (/ (* x y) a_m)
          (if (<= (* x y) 5e-30) t_1 (* x (/ y a_m)))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (z * -t) / a_m;
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = t_1;
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-30) {
		tmp = t_1;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * -t) / a_m
    if ((x * y) <= (-5d+145)) then
        tmp = x / (a_m / y)
    else if ((x * y) <= (-2d+57)) then
        tmp = t_1
    else if ((x * y) <= (-2d-32)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 5d-30) then
        tmp = t_1
    else
        tmp = x * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (z * -t) / a_m;
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = t_1;
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-30) {
		tmp = t_1;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	t_1 = (z * -t) / a_m
	tmp = 0
	if (x * y) <= -5e+145:
		tmp = x / (a_m / y)
	elif (x * y) <= -2e+57:
		tmp = t_1
	elif (x * y) <= -2e-32:
		tmp = (x * y) / a_m
	elif (x * y) <= 5e-30:
		tmp = t_1
	else:
		tmp = x * (y / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(z * Float64(-t)) / a_m)
	tmp = 0.0
	if (Float64(x * y) <= -5e+145)
		tmp = Float64(x / Float64(a_m / y));
	elseif (Float64(x * y) <= -2e+57)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-32)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 5e-30)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (z * -t) / a_m;
	tmp = 0.0;
	if ((x * y) <= -5e+145)
		tmp = x / (a_m / y);
	elseif ((x * y) <= -2e+57)
		tmp = t_1;
	elseif ((x * y) <= -2e-32)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 5e-30)
		tmp = t_1;
	else
		tmp = x * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(z * (-t)), $MachinePrecision] / a$95$m), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+145], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+57], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-32], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-30], t$95$1, N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.99999999999999967e145

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.5%

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

   7. Applied egg-rr 83.5%

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

   if -4.99999999999999967e145 < (*.f64 x y) < -2.0000000000000001e57 or -2.00000000000000011e-32 < (*.f64 x y) < 4.99999999999999972e-30

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 82.4%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(t \cdot z\right)}}{a} \]
   4. Step-by-step derivation

      1. associate-*r* 82.4%

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

      2. mul-1-neg 82.4%

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

   5. Simplified 82.4%

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

   if -2.0000000000000001e57 < (*.f64 x y) < -2.00000000000000011e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.3%

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

   if 4.99999999999999972e-30 < (*.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 73.7%

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

      1. associate-*r/ 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{-t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -5e+145)
    (/ x (/ a_m y))
    (if (<= (* x y) -2e+57)
      (* (- t) (/ z a_m))
      (if (<= (* x y) -2e-32)
        (/ (* x y) a_m)
        (if (<= (* x y) 5e-30) (* z (/ (- t) a_m)) (* x (/ y a_m))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = -t * (z / a_m);
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-30) {
		tmp = z * (-t / a_m);
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-5d+145)) then
        tmp = x / (a_m / y)
    else if ((x * y) <= (-2d+57)) then
        tmp = -t * (z / a_m)
    else if ((x * y) <= (-2d-32)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 5d-30) then
        tmp = z * (-t / a_m)
    else
        tmp = x * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = -t * (z / a_m);
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-30) {
		tmp = z * (-t / a_m);
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -5e+145:
		tmp = x / (a_m / y)
	elif (x * y) <= -2e+57:
		tmp = -t * (z / a_m)
	elif (x * y) <= -2e-32:
		tmp = (x * y) / a_m
	elif (x * y) <= 5e-30:
		tmp = z * (-t / a_m)
	else:
		tmp = x * (y / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -5e+145)
		tmp = Float64(x / Float64(a_m / y));
	elseif (Float64(x * y) <= -2e+57)
		tmp = Float64(Float64(-t) * Float64(z / a_m));
	elseif (Float64(x * y) <= -2e-32)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 5e-30)
		tmp = Float64(z * Float64(Float64(-t) / a_m));
	else
		tmp = Float64(x * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -5e+145)
		tmp = x / (a_m / y);
	elseif ((x * y) <= -2e+57)
		tmp = -t * (z / a_m);
	elseif ((x * y) <= -2e-32)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 5e-30)
		tmp = z * (-t / a_m);
	else
		tmp = x * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+145], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+57], N[((-t) * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-32], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-30], N[(z * N[((-t) / a$95$m), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.99999999999999967e145

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.5%

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

   7. Applied egg-rr 83.5%

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

   if -4.99999999999999967e145 < (*.f64 x y) < -2.0000000000000001e57

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-/l* 77.0%

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

      3. distribute-rgt-neg-in 77.0%

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

      4. distribute-neg-frac2 77.0%

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

   5. Simplified 77.0%

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

   if -2.0000000000000001e57 < (*.f64 x y) < -2.00000000000000011e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.3%

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

   if -2.00000000000000011e-32 < (*.f64 x y) < 4.99999999999999972e-30

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 82.9%

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

      1. *-commutative 82.9%

         \[\leadsto -1 \cdot \frac{\color{blue}{z \cdot t}}{a} \]

      2. associate-*r/ 79.2%

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

      3. neg-mul-1 79.2%

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

      4. distribute-rgt-neg-in 79.2%

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

      5. distribute-frac-neg 79.2%

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

   5. Simplified 79.2%

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

   if 4.99999999999999972e-30 < (*.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 73.7%

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

      1. associate-*r/ 76.3%

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

   5. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \frac{z}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (- t) (/ z a_m))))
   (*
    a_s
    (if (<= (* x y) -5e+145)
      (/ x (/ a_m y))
      (if (<= (* x y) -2e+57)
        t_1
        (if (<= (* x y) -2e-32)
          (/ (* x y) a_m)
          (if (<= (* x y) 5e-49) t_1 (* x (/ y a_m)))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = -t * (z / a_m);
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = t_1;
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-49) {
		tmp = t_1;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t * (z / a_m)
    if ((x * y) <= (-5d+145)) then
        tmp = x / (a_m / y)
    else if ((x * y) <= (-2d+57)) then
        tmp = t_1
    else if ((x * y) <= (-2d-32)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 5d-49) then
        tmp = t_1
    else
        tmp = x * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = -t * (z / a_m);
	double tmp;
	if ((x * y) <= -5e+145) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= -2e+57) {
		tmp = t_1;
	} else if ((x * y) <= -2e-32) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 5e-49) {
		tmp = t_1;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	t_1 = -t * (z / a_m)
	tmp = 0
	if (x * y) <= -5e+145:
		tmp = x / (a_m / y)
	elif (x * y) <= -2e+57:
		tmp = t_1
	elif (x * y) <= -2e-32:
		tmp = (x * y) / a_m
	elif (x * y) <= 5e-49:
		tmp = t_1
	else:
		tmp = x * (y / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(-t) * Float64(z / a_m))
	tmp = 0.0
	if (Float64(x * y) <= -5e+145)
		tmp = Float64(x / Float64(a_m / y));
	elseif (Float64(x * y) <= -2e+57)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-32)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 5e-49)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = -t * (z / a_m);
	tmp = 0.0;
	if ((x * y) <= -5e+145)
		tmp = x / (a_m / y);
	elseif ((x * y) <= -2e+57)
		tmp = t_1;
	elseif ((x * y) <= -2e-32)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 5e-49)
		tmp = t_1;
	else
		tmp = x * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[((-t) * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+145], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+57], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-32], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-49], t$95$1, N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.99999999999999967e145

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.5%

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

   7. Applied egg-rr 83.5%

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

   if -4.99999999999999967e145 < (*.f64 x y) < -2.0000000000000001e57 or -2.00000000000000011e-32 < (*.f64 x y) < 4.9999999999999999e-49

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. associate-/l* 84.2%

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

      3. distribute-rgt-neg-in 84.2%

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

      4. distribute-neg-frac2 84.2%

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

   5. Simplified 84.2%

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

   if -2.0000000000000001e57 < (*.f64 x y) < -2.00000000000000011e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.3%

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

   if 4.9999999999999999e-49 < (*.f64 x y)

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 71.9%

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

      1. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{x \cdot y}{t} - z}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* z t) 2e+274)
    (/ (- (* x y) (* z t)) a_m)
    (* t (/ (- (/ (* x y) t) z) a_m)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= 2e+274) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = t * ((((x * y) / t) - z) / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((z * t) <= 2d+274) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = t * ((((x * y) / t) - z) / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= 2e+274) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = t * ((((x * y) / t) - z) / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (z * t) <= 2e+274:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = t * ((((x * y) / t) - z) / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(z * t) <= 2e+274)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(t * Float64(Float64(Float64(Float64(x * y) / t) - z) / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((z * t) <= 2e+274)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = t * ((((x * y) / t) - z) / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(z * t), $MachinePrecision], 2e+274], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(t * N[(N[(N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision] - z), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.99999999999999984e274

   1. Initial program 93.8%

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

   if 1.99999999999999984e274 < (*.f64 z t)

   1. Initial program 55.2%

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

   3. Taylor expanded in t around inf 89.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \frac{z}{a} + \frac{x \cdot y}{a \cdot t}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 89.2%

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

      2. mul-1-neg 89.2%

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

      3. unsub-neg 89.2%

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

      4. times-frac 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in a around 0 94.5%

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

Alternative 7: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - \frac{t}{\frac{a\_m}{z}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= a_m 7.5e+106)
    (/ (- (* x y) (* z t)) a_m)
    (- (* x (/ y a_m)) (/ t (/ a_m z))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 7.5e+106) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (t / (a_m / z));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (a_m <= 7.5d+106) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = (x * (y / a_m)) - (t / (a_m / z))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 7.5e+106) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (t / (a_m / z));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if a_m <= 7.5e+106:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = (x * (y / a_m)) - (t / (a_m / z))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (a_m <= 7.5e+106)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(t / Float64(a_m / z)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (a_m <= 7.5e+106)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = (x * (y / a_m)) - (t / (a_m / z));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[a$95$m, 7.5e+106], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 7.50000000000000058e106

   1. Initial program 94.4%

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

   if 7.50000000000000058e106 < a

   1. Initial program 74.4%

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

      1. div-sub 74.4%

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

      2. associate-/l* 89.7%

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

      3. associate-/l* 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. div-inv 92.7%

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

      2. add-sqr-sqrt 47.9%

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

      3. sqrt-unprod 59.9%

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

      4. sqr-neg 59.9%

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

      5. sqrt-unprod 27.0%

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

      6. add-sqr-sqrt 55.1%

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

      7. associate-*l* 55.0%

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

      8. *-commutative 55.0%

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

      9. div-inv 55.0%

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

      10. associate-/l* 55.0%

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

      11. clear-num 55.0%

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

      12. un-div-inv 55.0%

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

      13. add-sqr-sqrt 27.1%

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

      14. sqrt-unprod 60.9%

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

      15. sqr-neg 60.9%

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

      16. sqrt-unprod 51.1%

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

      17. add-sqr-sqrt 93.8%

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

   6. Applied egg-rr 93.8%

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

Alternative 8: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - z \cdot \frac{t}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= a_m 1.4e-5)
    (/ (- (* x y) (* z t)) a_m)
    (- (* x (/ y a_m)) (* z (/ t a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 1.4e-5) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (a_m <= 1.4d-5) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = (x * (y / a_m)) - (z * (t / a_m))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 1.4e-5) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if a_m <= 1.4e-5:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = (x * (y / a_m)) - (z * (t / a_m))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (a_m <= 1.4e-5)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(z * Float64(t / a_m)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (a_m <= 1.4e-5)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[a$95$m, 1.4e-5], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 1.39999999999999998e-5

   1. Initial program 93.8%

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

   if 1.39999999999999998e-5 < a

   1. Initial program 82.8%

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

      1. div-sub 82.8%

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

      2. associate-/l* 93.0%

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

      3. associate-/l* 93.7%

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

   4. Applied egg-rr 93.7%

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

Alternative 9: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* z t) 2e+274) (/ (- (* x y) (* z t)) a_m) (* (- t) (/ z a_m)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= 2e+274) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = -t * (z / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((z * t) <= 2d+274) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = -t * (z / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= 2e+274) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = -t * (z / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (z * t) <= 2e+274:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = -t * (z / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(z * t) <= 2e+274)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(Float64(-t) * Float64(z / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((z * t) <= 2e+274)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = -t * (z / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(z * t), $MachinePrecision], 2e+274], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[((-t) * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.99999999999999984e274

   1. Initial program 93.8%

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

   if 1.99999999999999984e274 < (*.f64 z t)

   1. Initial program 55.2%

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

   3. Taylor expanded in x around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 94.4%

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

      3. distribute-rgt-neg-in 94.4%

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

      4. distribute-neg-frac2 94.4%

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

   5. Simplified 94.4%

      \[\leadsto \color{blue}{t \cdot \frac{z}{-a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 1.35 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= a_m 1.35e+94) (/ (* x y) a_m) (/ x (/ a_m y)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 1.35e+94) {
		tmp = (x * y) / a_m;
	} else {
		tmp = x / (a_m / y);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (a_m <= 1.35d+94) then
        tmp = (x * y) / a_m
    else
        tmp = x / (a_m / y)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 1.35e+94) {
		tmp = (x * y) / a_m;
	} else {
		tmp = x / (a_m / y);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if a_m <= 1.35e+94:
		tmp = (x * y) / a_m
	else:
		tmp = x / (a_m / y)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (a_m <= 1.35e+94)
		tmp = Float64(Float64(x * y) / a_m);
	else
		tmp = Float64(x / Float64(a_m / y));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (a_m <= 1.35e+94)
		tmp = (x * y) / a_m;
	else
		tmp = x / (a_m / y);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[a$95$m, 1.35e+94], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 1.3500000000000001e94

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 48.3%

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

   if 1.3500000000000001e94 < a

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 41.6%

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

      1. associate-*r/ 55.6%

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

   5. Simplified 55.6%

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

      1. clear-num 54.0%

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

      2. un-div-inv 54.2%

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

   7. Applied egg-rr 54.2%

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

Alternative 11: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= z -4.4e-184) (* x (/ y a_m)) (* y (/ x a_m)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -4.4e-184) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (z <= (-4.4d-184)) then
        tmp = x * (y / a_m)
    else
        tmp = y * (x / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -4.4e-184) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if z <= -4.4e-184:
		tmp = x * (y / a_m)
	else:
		tmp = y * (x / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (z <= -4.4e-184)
		tmp = Float64(x * Float64(y / a_m));
	else
		tmp = Float64(y * Float64(x / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (z <= -4.4e-184)
		tmp = x * (y / a_m);
	else
		tmp = y * (x / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[z, -4.4e-184], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999984e-184

   1. Initial program 91.7%

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

   3. Taylor expanded in x around inf 40.8%

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

      1. associate-*r/ 41.6%

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

   5. Simplified 41.6%

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

   if -4.39999999999999984e-184 < z

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 77.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot y} + \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. fma-define 77.4%

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

      2. times-frac 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in t around 0 54.2%

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

Alternative 12: 51.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \left(x \cdot \frac{y}{a\_m}\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* x (/ y a_m))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * (x * (y / a_m))
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
def code(a_s, x, y, z, t, a_m):
	return a_s * (x * (y / a_m))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(x * Float64(y / a_m)))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (x * (y / a_m));
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

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

3. Taylor expanded in x around inf 47.1%

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

   1. associate-*r/ 48.6%

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

5. Simplified 48.6%

   \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
6. Add Preprocessing

Developer target: 90.9% accurate, 0.4× 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 2024085 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (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))