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

Percentage Accurate: 90.9% → 97.0%

Time: 9.6s

Alternatives: 13

Speedup: 0.4×

• 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: 90.9% 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: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+238}:\\ \;\;\;\;t\_1 - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ a y))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 -5e+238)
     (- t_1 (/ z (/ a t)))
     (if (<= t_2 2e+306) (/ t_2 a) (- t_1 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
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 / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+238) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 2e+306) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = x / (a / y)
    t_2 = (x * y) - (z * t)
    if (t_2 <= (-5d+238)) then
        tmp = t_1 - (z / (a / t))
    else if (t_2 <= 2d+306) then
        tmp = t_2 / a
    else
        tmp = t_1 - (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = x / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+238) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 2e+306) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -5e+238:
		tmp = t_1 - (z / (a / t))
	elif t_2 <= 2e+306:
		tmp = t_2 / a
	else:
		tmp = t_1 - (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+238)
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	elseif (t_2 <= 2e+306)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -5e+238)
		tmp = t_1 - (z / (a / t));
	elseif (t_2 <= 2e+306)
		tmp = t_2 / a;
	else
		tmp = t_1 - (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.
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[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+238], N[(t$95$1 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], N[(t$95$2 / a), $MachinePrecision], N[(t$95$1 - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.99999999999999995e238

   1. Initial program 80.8%

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

      1. div-sub 78.5%

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

      2. associate-/l* 86.9%

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

      3. associate-/l* 97.5%

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

   4. Applied egg-rr 97.5%

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

   if -4.99999999999999995e238 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000003e306

   1. Initial program 98.4%

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

   if 2.00000000000000003e306 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 62.4%

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

      1. div-sub 62.4%

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

      2. associate-/l* 71.4%

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

      3. associate-/l* 89.7%

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

   4. Applied egg-rr 89.7%

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

      1. associate-/r/ 86.5%

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

      2. associate-*l/ 71.4%

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

      3. add-sqr-sqrt 30.5%

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

      4. sqrt-unprod 60.4%

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

      5. sqr-neg 60.4%

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

      6. sqrt-unprod 33.2%

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

      7. add-sqr-sqrt 49.9%

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

      8. add-sqr-sqrt 16.7%

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

      9. sqrt-unprod 50.9%

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

      10. sqr-neg 50.9%

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

      11. sqrt-unprod 40.9%

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

      12. add-sqr-sqrt 71.4%

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

      13. distribute-lft-neg-in 71.4%

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

      14. *-commutative 71.4%

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

      15. distribute-rgt-neg-out 71.4%

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

      16. remove-double-neg 71.4%

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

      17. associate-*l/ 89.8%

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

   6. Applied egg-rr 89.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+238}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 7.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\sqrt{a}} \cdot \frac{t}{\sqrt{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 7.2e-61)
   (/ (fma x y (* z (- t))) a)
   (- (/ x (/ a y)) (* (/ z (sqrt a)) (/ t (sqrt a))))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 7.2e-61) {
		tmp = fma(x, y, (z * -t)) / a;
	} else {
		tmp = (x / (a / y)) - ((z / sqrt(a)) * (t / sqrt(a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 7.2e-61)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(Float64(z / sqrt(a)) * Float64(t / sqrt(a))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 7.2e-61], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(N[(z / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(t / N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.20000000000000028e-61

   1. Initial program 92.7%

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

      1. div-sub 90.0%

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

      2. *-commutative 90.0%

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

      3. div-sub 92.7%

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

      4. fma-neg 92.7%

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

      5. *-commutative 92.7%

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

      6. distribute-rgt-neg-out 92.7%

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

   3. Simplified 92.7%

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

   if 7.20000000000000028e-61 < a

   1. Initial program 87.1%

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

      1. div-sub 87.1%

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

      2. associate-/l* 88.4%

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

      3. associate-/l* 95.5%

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

   4. Applied egg-rr 95.5%

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

      1. div-inv 95.6%

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

      2. clear-num 95.6%

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

      3. add-sqr-sqrt 37.6%

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

      4. sqrt-unprod 52.2%

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

      5. sqr-neg 52.2%

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

      6. sqrt-unprod 26.4%

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

      7. add-sqr-sqrt 49.5%

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

      8. div-inv 49.5%

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

      9. associate-*l* 49.5%

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

      10. *-commutative 49.5%

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

      11. div-inv 49.5%

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

      12. add-sqr-sqrt 49.5%

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

      13. *-commutative 49.5%

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

      14. times-frac 49.6%

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

      15. add-sqr-sqrt 26.5%

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

      16. sqrt-unprod 52.0%

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

      17. sqr-neg 52.0%

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

      18. sqrt-unprod 37.5%

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

      19. add-sqr-sqrt 94.3%

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

   6. Applied egg-rr 94.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\sqrt{a}} \cdot \frac{t}{\sqrt{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a}{z}}\\ t_2 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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))) (t_2 (/ x (/ a y))))
   (if (<= (* x y) -1e+67)
     t_2
     (if (<= (* x y) 5e-113)
       t_1
       (if (<= (* x y) 2e+15)
         (/ (* x y) a)
         (if (<= (* x y) 7e+99) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a);
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 t_2 = x / (a / y);
	double tmp;
	if ((x * y) <= -1e+67) {
		tmp = t_2;
	} else if ((x * y) <= 5e-113) {
		tmp = t_1;
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = -t / (a / z)
    t_2 = x / (a / y)
    if ((x * y) <= (-1d+67)) then
        tmp = t_2
    else if ((x * y) <= 5d-113) then
        tmp = t_1
    else if ((x * y) <= 2d+15) then
        tmp = (x * y) / a
    else if ((x * y) <= 7d+99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 t_2 = x / (a / y);
	double tmp;
	if ((x * y) <= -1e+67) {
		tmp = t_2;
	} else if ((x * y) <= 5e-113) {
		tmp = t_1;
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -t / (a / z)
	t_2 = x / (a / y)
	tmp = 0
	if (x * y) <= -1e+67:
		tmp = t_2
	elif (x * y) <= 5e-113:
		tmp = t_1
	elif (x * y) <= 2e+15:
		tmp = (x * y) / a
	elif (x * y) <= 7e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(a / z))
	t_2 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+67)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-113)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 7e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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);
	t_2 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -1e+67)
		tmp = t_2;
	elseif ((x * y) <= 5e-113)
		tmp = t_1;
	elseif ((x * y) <= 2e+15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 7e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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]}, Block[{t$95$2 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+67], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-113], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999983e66 or 6.9999999999999995e99 < (*.f64 x y)

   1. Initial program 84.9%

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

   3. Taylor expanded in x around inf 78.3%

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

      1. associate-*l/ 83.8%

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

   5. Simplified 83.8%

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

      1. associate-/r/ 81.3%

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

   7. Applied egg-rr 81.3%

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

   if -9.99999999999999983e66 < (*.f64 x y) < 4.9999999999999997e-113 or 2e15 < (*.f64 x y) < 6.9999999999999995e99

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

   if 4.9999999999999997e-113 < (*.f64 x y) < 2e15

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 71.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ a y))))
   (if (<= (* x y) -1e-28)
     t_1
     (if (<= (* x y) 5e-113)
       (* z (/ (- t) a))
       (if (<= (* x y) 2e+15)
         (/ (* x y) a)
         (if (<= (* x y) 7e+99) (/ (- t) (/ a z)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
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 / (a / y);
	double tmp;
	if ((x * y) <= -1e-28) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = z * (-t / a);
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = -t / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = x / (a / y)
    if ((x * y) <= (-1d-28)) then
        tmp = t_1
    else if ((x * y) <= 5d-113) then
        tmp = z * (-t / a)
    else if ((x * y) <= 2d+15) then
        tmp = (x * y) / a
    else if ((x * y) <= 7d+99) then
        tmp = -t / (a / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = x / (a / y);
	double tmp;
	if ((x * y) <= -1e-28) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = z * (-t / a);
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = -t / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	tmp = 0
	if (x * y) <= -1e-28:
		tmp = t_1
	elif (x * y) <= 5e-113:
		tmp = z * (-t / a)
	elif (x * y) <= 2e+15:
		tmp = (x * y) / a
	elif (x * y) <= 7e+99:
		tmp = -t / (a / z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -1e-28)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-113)
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (Float64(x * y) <= 2e+15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 7e+99)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -1e-28)
		tmp = t_1;
	elseif ((x * y) <= 5e-113)
		tmp = z * (-t / a);
	elseif ((x * y) <= 2e+15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 7e+99)
		tmp = -t / (a / z);
	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.
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[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e-28], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-113], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7e+99], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999971e-29 or 6.9999999999999995e99 < (*.f64 x y)

   1. Initial program 87.7%

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

   3. Taylor expanded in x around inf 72.6%

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

      1. associate-*l/ 75.1%

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

   5. Simplified 75.1%

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

      1. associate-/r/ 72.0%

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

   7. Applied egg-rr 72.0%

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

   if -9.99999999999999971e-29 < (*.f64 x y) < 4.9999999999999997e-113

   1. Initial program 94.4%

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

      1. div-sub 94.4%

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

      2. associate-/l* 91.1%

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

      3. associate-/l* 90.4%

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

   4. Applied egg-rr 90.4%

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

      1. div-inv 90.4%

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

      2. clear-num 90.4%

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

      3. add-sqr-sqrt 36.4%

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

      4. sqrt-unprod 44.0%

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

      5. sqr-neg 44.0%

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

      6. sqrt-unprod 11.5%

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

      7. add-sqr-sqrt 20.6%

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

      8. div-inv 20.6%

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

      9. associate-*l* 20.6%

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

      10. *-commutative 20.6%

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

      11. div-inv 20.6%

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

      12. add-sqr-sqrt 12.4%

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

      13. *-commutative 12.4%

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

      14. times-frac 12.4%

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

      15. add-sqr-sqrt 6.8%

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

      16. sqrt-unprod 21.9%

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

      17. sqr-neg 21.9%

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

      18. sqrt-unprod 16.1%

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

      19. add-sqr-sqrt 41.8%

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

   6. Applied egg-rr 41.8%

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

   7. Taylor expanded in x around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. associate-*l/ 80.9%

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

      3. distribute-rgt-neg-in 80.9%

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

   9. Simplified 80.9%

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

   if 4.9999999999999997e-113 < (*.f64 x y) < 2e15

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 71.4%

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

   if 2e15 < (*.f64 x y) < 6.9999999999999995e99

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

      \[\leadsto \color{blue}{-\frac{t}{\frac{a}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ a y))))
   (if (<= (* x y) -1e+67)
     t_1
     (if (<= (* x y) 5e-113)
       (* t (/ (- z) a))
       (if (<= (* x y) 2e+15)
         (/ (* x y) a)
         (if (<= (* x y) 7e+99) (/ (- t) (/ a z)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
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 / (a / y);
	double tmp;
	if ((x * y) <= -1e+67) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = -t / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = x / (a / y)
    if ((x * y) <= (-1d+67)) then
        tmp = t_1
    else if ((x * y) <= 5d-113) then
        tmp = t * (-z / a)
    else if ((x * y) <= 2d+15) then
        tmp = (x * y) / a
    else if ((x * y) <= 7d+99) then
        tmp = -t / (a / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = x / (a / y);
	double tmp;
	if ((x * y) <= -1e+67) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = -t / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	tmp = 0
	if (x * y) <= -1e+67:
		tmp = t_1
	elif (x * y) <= 5e-113:
		tmp = t * (-z / a)
	elif (x * y) <= 2e+15:
		tmp = (x * y) / a
	elif (x * y) <= 7e+99:
		tmp = -t / (a / z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+67)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-113)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(x * y) <= 2e+15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 7e+99)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -1e+67)
		tmp = t_1;
	elseif ((x * y) <= 5e-113)
		tmp = t * (-z / a);
	elseif ((x * y) <= 2e+15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 7e+99)
		tmp = -t / (a / z);
	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.
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[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+67], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-113], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7e+99], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999983e66 or 6.9999999999999995e99 < (*.f64 x y)

   1. Initial program 84.9%

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

   3. Taylor expanded in x around inf 78.3%

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

      1. associate-*l/ 83.8%

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

   5. Simplified 83.8%

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

      1. associate-/r/ 81.3%

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

   7. Applied egg-rr 81.3%

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

   if -9.99999999999999983e66 < (*.f64 x y) < 4.9999999999999997e-113

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*l/ 70.4%

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

      4. distribute-rgt-neg-in 70.4%

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

   5. Simplified 70.4%

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

   if 4.9999999999999997e-113 < (*.f64 x y) < 2e15

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 71.4%

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

   if 2e15 < (*.f64 x y) < 6.9999999999999995e99

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

      \[\leadsto \color{blue}{-\frac{t}{\frac{a}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ a y))))
   (if (<= (* x y) -2e+17)
     t_1
     (if (<= (* x y) 5e-113)
       (/ (* z (- t)) a)
       (if (<= (* x y) 2e+15)
         (/ (* x y) a)
         (if (<= (* x y) 7e+99) (/ (- t) (/ a z)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
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 / (a / y);
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = -t / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = x / (a / y)
    if ((x * y) <= (-2d+17)) then
        tmp = t_1
    else if ((x * y) <= 5d-113) then
        tmp = (z * -t) / a
    else if ((x * y) <= 2d+15) then
        tmp = (x * y) / a
    else if ((x * y) <= 7d+99) then
        tmp = -t / (a / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = x / (a / y);
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 2e+15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = -t / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	tmp = 0
	if (x * y) <= -2e+17:
		tmp = t_1
	elif (x * y) <= 5e-113:
		tmp = (z * -t) / a
	elif (x * y) <= 2e+15:
		tmp = (x * y) / a
	elif (x * y) <= 7e+99:
		tmp = -t / (a / z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -2e+17)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-113)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	elseif (Float64(x * y) <= 2e+15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 7e+99)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -2e+17)
		tmp = t_1;
	elseif ((x * y) <= 5e-113)
		tmp = (z * -t) / a;
	elseif ((x * y) <= 2e+15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 7e+99)
		tmp = -t / (a / z);
	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.
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[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-113], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7e+99], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e17 or 6.9999999999999995e99 < (*.f64 x y)

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf 74.9%

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

      1. associate-*l/ 78.5%

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

   5. Simplified 78.5%

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

      1. associate-/r/ 76.7%

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

   7. Applied egg-rr 76.7%

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

   if -2e17 < (*.f64 x y) < 4.9999999999999997e-113

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. distribute-rgt-neg-in 77.1%

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

   5. Simplified 77.1%

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

   if 4.9999999999999997e-113 < (*.f64 x y) < 2e15

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 71.4%

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

   if 2e15 < (*.f64 x y) < 6.9999999999999995e99

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

      \[\leadsto \color{blue}{-\frac{t}{\frac{a}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+306)))
     (- (/ x (/ a y)) (* z (/ t a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
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 tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+306)) {
		tmp = (x / (a / y)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
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 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+306)) {
		tmp = (x / (a / y)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+306):
		tmp = (x / (a / y)) - (z * (t / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+306))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+306)))
		tmp = (x / (a / y)) - (z * (t / a));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+306]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 2.00000000000000003e306 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.2%

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

      1. div-sub 65.5%

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

      2. associate-/l* 76.2%

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

      3. associate-/l* 93.2%

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

   4. Applied egg-rr 93.2%

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

      1. associate-/r/ 91.5%

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

      2. associate-*l/ 76.2%

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

      3. add-sqr-sqrt 27.1%

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

      4. sqrt-unprod 50.5%

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

      5. sqr-neg 50.5%

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

      6. sqrt-unprod 26.6%

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

      7. add-sqr-sqrt 45.0%

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

      8. add-sqr-sqrt 18.3%

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

      9. sqrt-unprod 62.5%

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

      10. sqr-neg 62.5%

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

      11. sqrt-unprod 49.1%

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

      12. add-sqr-sqrt 76.2%

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

      13. distribute-lft-neg-in 76.2%

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

      14. *-commutative 76.2%

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

      15. distribute-rgt-neg-out 76.2%

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

      16. remove-double-neg 76.2%

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

      17. associate-*l/ 93.2%

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

   6. Applied egg-rr 93.2%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000003e306

   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 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+180}:\\ \;\;\;\;t\_1 - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ a y))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 -1e+180)
     (- t_1 (/ t (/ a z)))
     (if (<= t_2 2e+306) (/ t_2 a) (- t_1 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
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 / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -1e+180) {
		tmp = t_1 - (t / (a / z));
	} else if (t_2 <= 2e+306) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = x / (a / y)
    t_2 = (x * y) - (z * t)
    if (t_2 <= (-1d+180)) then
        tmp = t_1 - (t / (a / z))
    else if (t_2 <= 2d+306) then
        tmp = t_2 / a
    else
        tmp = t_1 - (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = x / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -1e+180) {
		tmp = t_1 - (t / (a / z));
	} else if (t_2 <= 2e+306) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -1e+180:
		tmp = t_1 - (t / (a / z))
	elif t_2 <= 2e+306:
		tmp = t_2 / a
	else:
		tmp = t_1 - (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -1e+180)
		tmp = Float64(t_1 - Float64(t / Float64(a / z)));
	elseif (t_2 <= 2e+306)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -1e+180)
		tmp = t_1 - (t / (a / z));
	elseif (t_2 <= 2e+306)
		tmp = t_2 / a;
	else
		tmp = t_1 - (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.
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[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+180], N[(t$95$1 - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], N[(t$95$2 / a), $MachinePrecision], N[(t$95$1 - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1e180

   1. Initial program 85.1%

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

      1. div-sub 83.3%

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

      2. associate-/l* 89.9%

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

      3. associate-/l* 94.8%

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

   4. Applied egg-rr 94.8%

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

      1. div-inv 94.8%

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

      2. clear-num 94.8%

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

      3. add-sqr-sqrt 31.6%

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

      4. sqrt-unprod 40.5%

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

      5. sqr-neg 40.5%

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

      6. sqrt-unprod 22.3%

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

      7. add-sqr-sqrt 39.9%

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

      8. div-inv 39.9%

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

      9. associate-*l* 40.5%

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

      10. *-commutative 40.5%

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

      11. div-inv 40.5%

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

      12. add-sqr-sqrt 26.3%

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

      13. *-commutative 26.3%

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

      14. times-frac 26.3%

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

      15. add-sqr-sqrt 14.0%

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

      16. sqrt-unprod 21.6%

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

      17. sqr-neg 21.6%

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

      18. sqrt-unprod 15.9%

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

      19. add-sqr-sqrt 50.9%

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

   6. Applied egg-rr 50.9%

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

      1. frac-times 52.5%

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

      2. *-commutative 52.5%

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

      3. add-sqr-sqrt 89.9%

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

      4. associate-/l* 98.1%

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

   8. Applied egg-rr 98.1%

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

   if -1e180 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000003e306

   1. Initial program 98.3%

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

   if 2.00000000000000003e306 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 62.4%

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

      1. div-sub 62.4%

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

      2. associate-/l* 71.4%

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

      3. associate-/l* 89.7%

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

   4. Applied egg-rr 89.7%

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

      1. associate-/r/ 86.5%

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

      2. associate-*l/ 71.4%

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

      3. add-sqr-sqrt 30.5%

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

      4. sqrt-unprod 60.4%

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

      5. sqr-neg 60.4%

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

      6. sqrt-unprod 33.2%

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

      7. add-sqr-sqrt 49.9%

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

      8. add-sqr-sqrt 16.7%

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

      9. sqrt-unprod 50.9%

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

      10. sqr-neg 50.9%

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

      11. sqrt-unprod 40.9%

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

      12. add-sqr-sqrt 71.4%

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

      13. distribute-lft-neg-in 71.4%

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

      14. *-commutative 71.4%

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

      15. distribute-rgt-neg-out 71.4%

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

      16. remove-double-neg 71.4%

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

      17. associate-*l/ 89.8%

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

   6. Applied egg-rr 89.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -1 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+273}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= (* x y) (- INFINITY))
   (/ y (/ a x))
   (if (<= (* x y) 1e+273) (/ (- (* x y) (* z t)) a) (* y (/ x a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1e+273) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
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 ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1e+273) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y / (a / x)
	elif (x * y) <= 1e+273:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 1e+273)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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])){:}
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 ((x * y) <= -Inf)
		tmp = y / (a / x);
	elseif ((x * y) <= 1e+273)
		tmp = ((x * y) - (z * t)) / 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.
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[(x * y), $MachinePrecision], (-Infinity)], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+273], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 62.6%

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

   3. Taylor expanded in x around inf 69.2%

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

      1. associate-*l/ 97.6%

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

   5. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. clear-num 97.5%

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

      3. un-div-inv 97.6%

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

   7. Applied egg-rr 97.6%

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

   if -inf.0 < (*.f64 x y) < 9.99999999999999945e272

   1. Initial program 94.9%

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

   if 9.99999999999999945e272 < (*.f64 x y)

   1. Initial program 70.1%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-*l/ 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+273}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+216}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= x -2.25e+216) (/ x (/ a y)) (/ (* x y) a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.25e+216) {
		tmp = x / (a / y);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (x <= (-2.25d+216)) then
        tmp = x / (a / y)
    else
        tmp = (x * y) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 (x <= -2.25e+216) {
		tmp = x / (a / y);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.25e+216:
		tmp = x / (a / y)
	else:
		tmp = (x * y) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.25e+216)
		tmp = Float64(x / Float64(a / y));
	else
		tmp = Float64(Float64(x * y) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 (x <= -2.25e+216)
		tmp = x / (a / y);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[x, -2.25e+216], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25000000000000012e216

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf 81.0%

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

      1. associate-*l/ 73.2%

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

   5. Simplified 73.2%

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

      1. associate-/r/ 87.6%

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

   7. Applied egg-rr 87.6%

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

   if -2.25000000000000012e216 < x

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 48.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+216}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.6% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 91.2%

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

3. Taylor expanded in x around inf 51.8%

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

   1. associate-*l/ 50.9%

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

5. Simplified 50.9%

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

6. Final simplification 50.9%

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

Alternative 12: 50.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

3. Taylor expanded in x around inf 51.8%

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

   1. associate-/l* 50.2%

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

   2. div-inv 49.8%

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

   3. *-commutative 49.8%

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

   4. clear-num 49.8%

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

5. Applied egg-rr 49.8%

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

6. Final simplification 49.8%

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

Alternative 13: 50.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

3. Taylor expanded in x around inf 51.8%

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

   1. associate-*l/ 50.9%

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

5. Simplified 50.9%

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

   1. associate-/r/ 50.2%

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

7. Applied egg-rr 50.2%

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

8. Final simplification 50.2%

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

Developer target: 91.5% 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 2024027 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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