Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 90.6% → 94.0%

Time: 10.7s

Alternatives: 12

Speedup: 0.6×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+279}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{x}}{y}}\\ \end{array} \end{array} \]

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) -2e+166)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) 4e+279)
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
     (/ 0.5 (/ (/ a x) 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) {
	double tmp;
	if ((x * y) <= -2e+166) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 4e+279) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 / ((a / x) / y);
	}
	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 * y) <= (-2d+166)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= 4d+279) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = 0.5d0 / ((a / x) / y)
    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 * y) <= -2e+166) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 4e+279) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 / ((a / x) / y);
	}
	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) <= -2e+166:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= 4e+279:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = 0.5 / ((a / x) / y)
	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) <= -2e+166)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= 4e+279)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 / Float64(Float64(a / x) / y));
	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) <= -2e+166)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= 4e+279)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = 0.5 / ((a / x) / y);
	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], -2e+166], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+279], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999988e166

   1. Initial program 83.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 83.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 87.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   6. Simplified 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.99999999999999988e166 < (*.f64 x y) < 4.00000000000000023e279

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   if 4.00000000000000023e279 < (*.f64 x y)

   1. Initial program 78.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 78.8%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in a around 0 78.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.8%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 78.8%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 78.8%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 78.8%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 78.8%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   6. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 78.8%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/r* 100.0%

         \[\leadsto \frac{0.5}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

   9. Simplified 100.0%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+279}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{x}}{y}}\\ \end{array} \]

Alternative 2: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+279}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4.5 \cdot t, z, x \cdot \left(y \cdot 0.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{x}}{y}}\\ \end{array} \end{array} \]

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) 4e+279)
   (/ (fma (* -4.5 t) z (* x (* y 0.5))) a)
   (/ 0.5 (/ (/ a x) 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) {
	double tmp;
	if ((x * y) <= 4e+279) {
		tmp = fma((-4.5 * t), z, (x * (y * 0.5))) / a;
	} else {
		tmp = 0.5 / ((a / x) / y);
	}
	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) <= 4e+279)
		tmp = Float64(fma(Float64(-4.5 * t), z, Float64(x * Float64(y * 0.5))) / a);
	else
		tmp = Float64(0.5 / Float64(Float64(a / x) / y));
	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[N[(x * y), $MachinePrecision], 4e+279], N[(N[(N[(-4.5 * t), $MachinePrecision] * z + N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.5 / N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 4.00000000000000023e279

   1. Initial program 94.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 94.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 92.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]

   5. Taylor expanded in a around -inf 94.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 94.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. mul-1-neg 94.9%

         \[\leadsto \frac{\color{blue}{-\left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. +-commutative 94.9%

         \[\leadsto \frac{-\color{blue}{\left(4.5 \cdot \left(t \cdot z\right) + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      4. associate-*r* 94.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(4.5 \cdot t\right) \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      5. *-commutative 94.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(t \cdot 4.5\right)} \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      6. fma-def 95.3%

         \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      7. associate-*r* 95.3%

         \[\leadsto \frac{-\mathsf{fma}\left(t \cdot 4.5, z, \color{blue}{\left(-0.5 \cdot x\right) \cdot y}\right)}{a} \]

   7. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(t \cdot 4.5, z, \left(-0.5 \cdot x\right) \cdot y\right)}{a}} \]

   8. Taylor expanded in a around 0 94.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 94.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. +-commutative 94.9%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(4.5 \cdot \left(t \cdot z\right) + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      3. associate-*r* 94.9%

         \[\leadsto \frac{-1 \cdot \left(\color{blue}{\left(4.5 \cdot t\right) \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      4. *-commutative 94.9%

         \[\leadsto \frac{-1 \cdot \left(\color{blue}{\left(t \cdot 4.5\right)} \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      5. fma-def 95.3%

         \[\leadsto \frac{-1 \cdot \color{blue}{\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      6. neg-mul-1 95.3%

         \[\leadsto \frac{\color{blue}{-\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      7. fma-def 94.9%

         \[\leadsto \frac{-\color{blue}{\left(\left(t \cdot 4.5\right) \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      8. distribute-neg-in 94.9%

         \[\leadsto \frac{\color{blue}{\left(-\left(t \cdot 4.5\right) \cdot z\right) + \left(--0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      9. distribute-lft-neg-in 94.9%

         \[\leadsto \frac{\color{blue}{\left(-t \cdot 4.5\right) \cdot z} + \left(--0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      10. fma-def 95.3%

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-t \cdot 4.5, z, --0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      11. *-commutative 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(-\color{blue}{4.5 \cdot t}, z, --0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      12. distribute-lft-neg-in 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4.5\right) \cdot t}, z, --0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      13. metadata-eval 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{-4.5} \cdot t, z, --0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      14. distribute-lft-neg-in 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(-4.5 \cdot t, z, \color{blue}{\left(--0.5\right) \cdot \left(x \cdot y\right)}\right)}{a} \]

      15. metadata-eval 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(-4.5 \cdot t, z, \color{blue}{0.5} \cdot \left(x \cdot y\right)\right)}{a} \]

      16. associate-*r* 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(-4.5 \cdot t, z, \color{blue}{\left(0.5 \cdot x\right) \cdot y}\right)}{a} \]

      17. *-commutative 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(-4.5 \cdot t, z, \color{blue}{\left(x \cdot 0.5\right)} \cdot y\right)}{a} \]

      18. associate-*l* 95.3%

          \[\leadsto \frac{\mathsf{fma}\left(-4.5 \cdot t, z, \color{blue}{x \cdot \left(0.5 \cdot y\right)}\right)}{a} \]

   10. Simplified 95.3%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4.5 \cdot t, z, x \cdot \left(0.5 \cdot y\right)\right)}{a}} \]

   if 4.00000000000000023e279 < (*.f64 x y)

   1. Initial program 78.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 78.8%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in a around 0 78.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.8%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 78.8%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 78.8%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 78.8%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 78.8%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 78.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 78.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   6. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 78.8%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/r* 100.0%

         \[\leadsto \frac{0.5}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

   9. Simplified 100.0%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+279}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4.5 \cdot t, z, x \cdot \left(y \cdot 0.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{x}}{y}}\\ \end{array} \]

Alternative 3: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+96}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \end{array} \]

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 (<= y -1.25e-101)
   (* y (* x (/ 0.5 a)))
   (if (<= y 6e+96) (/ (* z (* t -9.0)) (* a 2.0)) (/ y (/ a (* x 0.5))))))

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 (y <= -1.25e-101) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 6e+96) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 (y <= (-1.25d-101)) then
        tmp = y * (x * (0.5d0 / a))
    else if (y <= 6d+96) then
        tmp = (z * (t * (-9.0d0))) / (a * 2.0d0)
    else
        tmp = y / (a / (x * 0.5d0))
    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 (y <= -1.25e-101) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 6e+96) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 y <= -1.25e-101:
		tmp = y * (x * (0.5 / a))
	elif y <= 6e+96:
		tmp = (z * (t * -9.0)) / (a * 2.0)
	else:
		tmp = y / (a / (x * 0.5))
	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 (y <= -1.25e-101)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (y <= 6e+96)
		tmp = Float64(Float64(z * Float64(t * -9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(y / Float64(a / Float64(x * 0.5)));
	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 (y <= -1.25e-101)
		tmp = y * (x * (0.5 / a));
	elseif (y <= 6e+96)
		tmp = (z * (t * -9.0)) / (a * 2.0);
	else
		tmp = y / (a / (x * 0.5));
	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[y, -1.25e-101], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+96], N[(N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e-101

   1. Initial program 92.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 92.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 92.2%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. fma-def 92.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   6. Simplified 92.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   7. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 61.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. associate-*l/ 61.2%

         \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 63.3%

         \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   if -1.25e-101 < y < 6.0000000000000001e96

   1. Initial program 95.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.4%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. associate-*r* 74.4%

         \[\leadsto \frac{\color{blue}{\left(-9 \cdot t\right) \cdot z}}{a \cdot 2} \]

      2. *-commutative 74.4%

         \[\leadsto \frac{\color{blue}{z \cdot \left(-9 \cdot t\right)}}{a \cdot 2} \]

      3. *-commutative 74.4%

         \[\leadsto \frac{z \cdot \color{blue}{\left(t \cdot -9\right)}}{a \cdot 2} \]

   6. Simplified 74.4%

      \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

   if 6.0000000000000001e96 < y

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 80.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]

   5. Taylor expanded in a around -inf 88.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. mul-1-neg 88.9%

         \[\leadsto \frac{\color{blue}{-\left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. +-commutative 88.9%

         \[\leadsto \frac{-\color{blue}{\left(4.5 \cdot \left(t \cdot z\right) + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      4. associate-*r* 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(4.5 \cdot t\right) \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      5. *-commutative 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(t \cdot 4.5\right)} \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      6. fma-def 88.9%

         \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      7. associate-*r* 88.9%

         \[\leadsto \frac{-\mathsf{fma}\left(t \cdot 4.5, z, \color{blue}{\left(-0.5 \cdot x\right) \cdot y}\right)}{a} \]

   7. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(t \cdot 4.5, z, \left(-0.5 \cdot x\right) \cdot y\right)}{a}} \]

   8. Taylor expanded in t around 0 71.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 71.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 0.5}}{a} \]

      3. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(y \cdot x\right)} \cdot 0.5}{a} \]

      4. associate-*r* 71.0%

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 0.5\right)}}{a} \]

      5. associate-/l* 75.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x \cdot 0.5}}} \]

      6. *-commutative 75.3%

         \[\leadsto \frac{y}{\frac{a}{\color{blue}{0.5 \cdot x}}} \]

   10. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{0.5 \cdot x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+96}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \]

Alternative 4: 68.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-86} \lor \neg \left(y \leq 9 \cdot 10^{+94}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \end{array} \end{array} \]

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 (or (<= y -2.3e-86) (not (<= y 9e+94)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (/ (* t z) 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 ((y <= -2.3e-86) || !(y <= 9e+94)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((t * z) / 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 ((y <= (-2.3d-86)) .or. (.not. (y <= 9d+94))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * ((t * z) / 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 ((y <= -2.3e-86) || !(y <= 9e+94)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((t * z) / 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 (y <= -2.3e-86) or not (y <= 9e+94):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * ((t * z) / 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 ((y <= -2.3e-86) || !(y <= 9e+94))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(t * z) / 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 ((y <= -2.3e-86) || ~((y <= 9e+94)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * ((t * z) / 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[Or[LessEqual[y, -2.3e-86], N[Not[LessEqual[y, 9e+94]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.29999999999999996e-86 or 8.99999999999999944e94 < y

   1. Initial program 91.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 63.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 69.9%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)} \]

   6. Simplified 69.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

   if -2.29999999999999996e-86 < y < 8.99999999999999944e94

   1. Initial program 95.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 72.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-86} \lor \neg \left(y \leq 9 \cdot 10^{+94}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \end{array} \]

Alternative 5: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-101} \lor \neg \left(y \leq 9.2 \cdot 10^{+94}\right):\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \end{array} \end{array} \]

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 (or (<= y -4.8e-101) (not (<= y 9.2e+94)))
   (* y (* x (/ 0.5 a)))
   (* -4.5 (/ (* t z) 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 ((y <= -4.8e-101) || !(y <= 9.2e+94)) {
		tmp = y * (x * (0.5 / a));
	} else {
		tmp = -4.5 * ((t * z) / 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 ((y <= (-4.8d-101)) .or. (.not. (y <= 9.2d+94))) then
        tmp = y * (x * (0.5d0 / a))
    else
        tmp = (-4.5d0) * ((t * z) / 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 ((y <= -4.8e-101) || !(y <= 9.2e+94)) {
		tmp = y * (x * (0.5 / a));
	} else {
		tmp = -4.5 * ((t * z) / 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 (y <= -4.8e-101) or not (y <= 9.2e+94):
		tmp = y * (x * (0.5 / a))
	else:
		tmp = -4.5 * ((t * z) / 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 ((y <= -4.8e-101) || !(y <= 9.2e+94))
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(t * z) / 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 ((y <= -4.8e-101) || ~((y <= 9.2e+94)))
		tmp = y * (x * (0.5 / a));
	else
		tmp = -4.5 * ((t * z) / 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[Or[LessEqual[y, -4.8e-101], N[Not[LessEqual[y, 9.2e+94]], $MachinePrecision]], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e-101 or 9.1999999999999999e94 < y

   1. Initial program 91.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 91.3%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. fma-def 91.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   6. Simplified 91.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   7. Taylor expanded in t around 0 64.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 64.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. associate-*l/ 63.9%

         \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 66.6%

         \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   9. Simplified 66.6%

      \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   if -4.8e-101 < y < 9.1999999999999999e94

   1. Initial program 95.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-101} \lor \neg \left(y \leq 9.2 \cdot 10^{+94}\right):\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \end{array} \]

Alternative 6: 68.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-86}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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 (<= y -2.9e-86)
   (* 0.5 (* x (/ y a)))
   (if (<= y 7.5e+95) (* -4.5 (/ (* t z) a)) (* 0.5 (/ 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) {
	double tmp;
	if (y <= -2.9e-86) {
		tmp = 0.5 * (x * (y / a));
	} else if (y <= 7.5e+95) {
		tmp = -4.5 * ((t * z) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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 (y <= (-2.9d-86)) then
        tmp = 0.5d0 * (x * (y / a))
    else if (y <= 7.5d+95) then
        tmp = (-4.5d0) * ((t * z) / a)
    else
        tmp = 0.5d0 * (x / (a / y))
    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 (y <= -2.9e-86) {
		tmp = 0.5 * (x * (y / a));
	} else if (y <= 7.5e+95) {
		tmp = -4.5 * ((t * z) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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 y <= -2.9e-86:
		tmp = 0.5 * (x * (y / a))
	elif y <= 7.5e+95:
		tmp = -4.5 * ((t * z) / a)
	else:
		tmp = 0.5 * (x / (a / y))
	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 (y <= -2.9e-86)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (y <= 7.5e+95)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	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 (y <= -2.9e-86)
		tmp = 0.5 * (x * (y / a));
	elseif (y <= 7.5e+95)
		tmp = -4.5 * ((t * z) / a);
	else
		tmp = 0.5 * (x / (a / y));
	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[y, -2.9e-86], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+95], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999999e-86

   1. Initial program 91.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.8%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 60.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 65.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)} \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

   if -2.8999999999999999e-86 < y < 7.5000000000000001e95

   1. Initial program 95.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 72.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 7.5000000000000001e95 < y

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 71.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 81.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   6. Simplified 81.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-86}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+94}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{x}}{y}}\\ \end{array} \end{array} \]

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 (<= y -5.6e-104)
   (* y (* x (/ 0.5 a)))
   (if (<= y 9e+94) (* -4.5 (/ (* t z) a)) (/ 0.5 (/ (/ a x) 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) {
	double tmp;
	if (y <= -5.6e-104) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 9e+94) {
		tmp = -4.5 * ((t * z) / a);
	} else {
		tmp = 0.5 / ((a / x) / y);
	}
	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 (y <= (-5.6d-104)) then
        tmp = y * (x * (0.5d0 / a))
    else if (y <= 9d+94) then
        tmp = (-4.5d0) * ((t * z) / a)
    else
        tmp = 0.5d0 / ((a / x) / y)
    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 (y <= -5.6e-104) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 9e+94) {
		tmp = -4.5 * ((t * z) / a);
	} else {
		tmp = 0.5 / ((a / x) / y);
	}
	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 y <= -5.6e-104:
		tmp = y * (x * (0.5 / a))
	elif y <= 9e+94:
		tmp = -4.5 * ((t * z) / a)
	else:
		tmp = 0.5 / ((a / x) / y)
	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 (y <= -5.6e-104)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (y <= 9e+94)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	else
		tmp = Float64(0.5 / Float64(Float64(a / x) / y));
	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 (y <= -5.6e-104)
		tmp = y * (x * (0.5 / a));
	elseif (y <= 9e+94)
		tmp = -4.5 * ((t * z) / a);
	else
		tmp = 0.5 / ((a / x) / y);
	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[y, -5.6e-104], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+94], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6e-104

   1. Initial program 92.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 92.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 92.3%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. fma-def 92.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   6. Simplified 92.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   7. Taylor expanded in t around 0 61.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 61.7%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. associate-*l/ 61.6%

         \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 63.7%

         \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   9. Simplified 63.7%

      \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   if -5.6e-104 < y < 8.99999999999999944e94

   1. Initial program 95.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 8.99999999999999944e94 < y

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in a around 0 88.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 88.9%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 88.9%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 88.9%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 88.9%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 88.8%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 88.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 88.8%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 88.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 88.8%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 88.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 88.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 88.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 88.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 88.8%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   6. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 71.0%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/r* 75.3%

         \[\leadsto \frac{0.5}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

   9. Simplified 75.3%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+94}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{x}}{y}}\\ \end{array} \]

Alternative 8: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \end{array} \]

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 (<= y -4.9e-101)
   (* y (* x (/ 0.5 a)))
   (if (<= y 2.5e+98) (* -4.5 (/ (* t z) a)) (/ y (/ a (* x 0.5))))))

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 (y <= -4.9e-101) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 2.5e+98) {
		tmp = -4.5 * ((t * z) / a);
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 (y <= (-4.9d-101)) then
        tmp = y * (x * (0.5d0 / a))
    else if (y <= 2.5d+98) then
        tmp = (-4.5d0) * ((t * z) / a)
    else
        tmp = y / (a / (x * 0.5d0))
    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 (y <= -4.9e-101) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 2.5e+98) {
		tmp = -4.5 * ((t * z) / a);
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 y <= -4.9e-101:
		tmp = y * (x * (0.5 / a))
	elif y <= 2.5e+98:
		tmp = -4.5 * ((t * z) / a)
	else:
		tmp = y / (a / (x * 0.5))
	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 (y <= -4.9e-101)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (y <= 2.5e+98)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	else
		tmp = Float64(y / Float64(a / Float64(x * 0.5)));
	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 (y <= -4.9e-101)
		tmp = y * (x * (0.5 / a));
	elseif (y <= 2.5e+98)
		tmp = -4.5 * ((t * z) / a);
	else
		tmp = y / (a / (x * 0.5));
	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[y, -4.9e-101], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+98], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9e-101

   1. Initial program 92.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 92.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 92.2%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. fma-def 92.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   6. Simplified 92.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   7. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 61.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. associate-*l/ 61.2%

         \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 63.3%

         \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   if -4.9e-101 < y < 2.4999999999999999e98

   1. Initial program 95.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 2.4999999999999999e98 < y

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 80.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]

   5. Taylor expanded in a around -inf 88.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. mul-1-neg 88.9%

         \[\leadsto \frac{\color{blue}{-\left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. +-commutative 88.9%

         \[\leadsto \frac{-\color{blue}{\left(4.5 \cdot \left(t \cdot z\right) + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      4. associate-*r* 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(4.5 \cdot t\right) \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      5. *-commutative 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(t \cdot 4.5\right)} \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      6. fma-def 88.9%

         \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      7. associate-*r* 88.9%

         \[\leadsto \frac{-\mathsf{fma}\left(t \cdot 4.5, z, \color{blue}{\left(-0.5 \cdot x\right) \cdot y}\right)}{a} \]

   7. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(t \cdot 4.5, z, \left(-0.5 \cdot x\right) \cdot y\right)}{a}} \]

   8. Taylor expanded in t around 0 71.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 71.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 0.5}}{a} \]

      3. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(y \cdot x\right)} \cdot 0.5}{a} \]

      4. associate-*r* 71.0%

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 0.5\right)}}{a} \]

      5. associate-/l* 75.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x \cdot 0.5}}} \]

      6. *-commutative 75.3%

         \[\leadsto \frac{y}{\frac{a}{\color{blue}{0.5 \cdot x}}} \]

   10. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{0.5 \cdot x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \]

Alternative 9: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{t \cdot \left(-4.5 \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \end{array} \]

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 (<= y -1.65e-111)
   (* y (* x (/ 0.5 a)))
   (if (<= y 6.5e+95) (/ (* t (* -4.5 z)) a) (/ y (/ a (* x 0.5))))))

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 (y <= -1.65e-111) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 6.5e+95) {
		tmp = (t * (-4.5 * z)) / a;
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 (y <= (-1.65d-111)) then
        tmp = y * (x * (0.5d0 / a))
    else if (y <= 6.5d+95) then
        tmp = (t * ((-4.5d0) * z)) / a
    else
        tmp = y / (a / (x * 0.5d0))
    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 (y <= -1.65e-111) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 6.5e+95) {
		tmp = (t * (-4.5 * z)) / a;
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 y <= -1.65e-111:
		tmp = y * (x * (0.5 / a))
	elif y <= 6.5e+95:
		tmp = (t * (-4.5 * z)) / a
	else:
		tmp = y / (a / (x * 0.5))
	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 (y <= -1.65e-111)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (y <= 6.5e+95)
		tmp = Float64(Float64(t * Float64(-4.5 * z)) / a);
	else
		tmp = Float64(y / Float64(a / Float64(x * 0.5)));
	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 (y <= -1.65e-111)
		tmp = y * (x * (0.5 / a));
	elseif (y <= 6.5e+95)
		tmp = (t * (-4.5 * z)) / a;
	else
		tmp = y / (a / (x * 0.5));
	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[y, -1.65e-111], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+95], N[(N[(t * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y / N[(a / N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-111

   1. Initial program 92.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 92.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 92.6%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. fma-def 92.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   6. Simplified 92.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   7. Taylor expanded in t around 0 61.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 61.9%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. associate-*l/ 61.8%

         \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 63.9%

         \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   9. Simplified 63.9%

      \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   if -1.65e-111 < y < 6.5e95

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 74.4%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. *-commutative 74.4%

         \[\leadsto \frac{-4.5 \cdot \color{blue}{\left(z \cdot t\right)}}{a} \]

      3. associate-*r* 74.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot z\right) \cdot t}}{a} \]

   6. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{\left(-4.5 \cdot z\right) \cdot t}{a}} \]

   if 6.5e95 < y

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 80.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]

   5. Taylor expanded in a around -inf 88.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. mul-1-neg 88.9%

         \[\leadsto \frac{\color{blue}{-\left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. +-commutative 88.9%

         \[\leadsto \frac{-\color{blue}{\left(4.5 \cdot \left(t \cdot z\right) + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      4. associate-*r* 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(4.5 \cdot t\right) \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      5. *-commutative 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(t \cdot 4.5\right)} \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      6. fma-def 88.9%

         \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      7. associate-*r* 88.9%

         \[\leadsto \frac{-\mathsf{fma}\left(t \cdot 4.5, z, \color{blue}{\left(-0.5 \cdot x\right) \cdot y}\right)}{a} \]

   7. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(t \cdot 4.5, z, \left(-0.5 \cdot x\right) \cdot y\right)}{a}} \]

   8. Taylor expanded in t around 0 71.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 71.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 0.5}}{a} \]

      3. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(y \cdot x\right)} \cdot 0.5}{a} \]

      4. associate-*r* 71.0%

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 0.5\right)}}{a} \]

      5. associate-/l* 75.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x \cdot 0.5}}} \]

      6. *-commutative 75.3%

         \[\leadsto \frac{y}{\frac{a}{\color{blue}{0.5 \cdot x}}} \]

   10. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{0.5 \cdot x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{t \cdot \left(-4.5 \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \]

Alternative 10: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \end{array} \]

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 (<= y -2.1e-106)
   (* y (* x (/ 0.5 a)))
   (if (<= y 5.6e+96) (/ (* -4.5 (* t z)) a) (/ y (/ a (* x 0.5))))))

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 (y <= -2.1e-106) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 5.6e+96) {
		tmp = (-4.5 * (t * z)) / a;
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 (y <= (-2.1d-106)) then
        tmp = y * (x * (0.5d0 / a))
    else if (y <= 5.6d+96) then
        tmp = ((-4.5d0) * (t * z)) / a
    else
        tmp = y / (a / (x * 0.5d0))
    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 (y <= -2.1e-106) {
		tmp = y * (x * (0.5 / a));
	} else if (y <= 5.6e+96) {
		tmp = (-4.5 * (t * z)) / a;
	} else {
		tmp = y / (a / (x * 0.5));
	}
	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 y <= -2.1e-106:
		tmp = y * (x * (0.5 / a))
	elif y <= 5.6e+96:
		tmp = (-4.5 * (t * z)) / a
	else:
		tmp = y / (a / (x * 0.5))
	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 (y <= -2.1e-106)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (y <= 5.6e+96)
		tmp = Float64(Float64(-4.5 * Float64(t * z)) / a);
	else
		tmp = Float64(y / Float64(a / Float64(x * 0.5)));
	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 (y <= -2.1e-106)
		tmp = y * (x * (0.5 / a));
	elseif (y <= 5.6e+96)
		tmp = (-4.5 * (t * z)) / a;
	else
		tmp = y / (a / (x * 0.5));
	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[y, -2.1e-106], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+96], N[(N[(-4.5 * N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y / N[(a / N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000003e-106

   1. Initial program 92.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 92.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 92.4%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. fma-def 92.4%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   6. Simplified 92.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, t \cdot z, x \cdot y\right)}}{a \cdot 2} \]

   7. Taylor expanded in t around 0 62.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.2%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. associate-*l/ 62.1%

         \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 64.1%

         \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   9. Simplified 64.1%

      \[\leadsto \color{blue}{\left(\frac{0.5}{a} \cdot x\right) \cdot y} \]

   if -2.10000000000000003e-106 < y < 5.59999999999999999e96

   1. Initial program 95.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 73.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 69.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   7. Step-by-step derivation

      1. associate-/l* 73.9%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t \cdot z}{a}} \]

      2. *-commutative 73.9%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} \]

      3. associate-*l/ 74.0%

         \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} \]

   8. Applied egg-rr 74.0%

      \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} \]

   if 5.59999999999999999e96 < y

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 80.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]

   5. Taylor expanded in a around -inf 88.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. mul-1-neg 88.9%

         \[\leadsto \frac{\color{blue}{-\left(-0.5 \cdot \left(x \cdot y\right) + 4.5 \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. +-commutative 88.9%

         \[\leadsto \frac{-\color{blue}{\left(4.5 \cdot \left(t \cdot z\right) + -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      4. associate-*r* 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(4.5 \cdot t\right) \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      5. *-commutative 88.9%

         \[\leadsto \frac{-\left(\color{blue}{\left(t \cdot 4.5\right)} \cdot z + -0.5 \cdot \left(x \cdot y\right)\right)}{a} \]

      6. fma-def 88.9%

         \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(t \cdot 4.5, z, -0.5 \cdot \left(x \cdot y\right)\right)}}{a} \]

      7. associate-*r* 88.9%

         \[\leadsto \frac{-\mathsf{fma}\left(t \cdot 4.5, z, \color{blue}{\left(-0.5 \cdot x\right) \cdot y}\right)}{a} \]

   7. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(t \cdot 4.5, z, \left(-0.5 \cdot x\right) \cdot y\right)}{a}} \]

   8. Taylor expanded in t around 0 71.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 71.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{a}} \]

      2. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 0.5}}{a} \]

      3. *-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(y \cdot x\right)} \cdot 0.5}{a} \]

      4. associate-*r* 71.0%

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 0.5\right)}}{a} \]

      5. associate-/l* 75.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x \cdot 0.5}}} \]

      6. *-commutative 75.3%

         \[\leadsto \frac{y}{\frac{a}{\color{blue}{0.5 \cdot x}}} \]

   10. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{0.5 \cdot x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x \cdot 0.5}}\\ \end{array} \]

Alternative 11: 51.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \end{array} \]

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 (* -4.5 (* 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) {
	return -4.5 * (z * (t / 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 = (-4.5d0) * (z * (t / 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 -4.5 * (z * (t / 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 -4.5 * (z * (t / 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(-4.5 * Float64(z * Float64(t / 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 = -4.5 * (z * (t / 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[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.5%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Step-by-step derivation

   1. associate-*l* 93.5%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

3. Simplified 93.5%

   \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

4. Taylor expanded in x around 0 55.9%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
5. Step-by-step derivation

   1. associate-/l* 52.4%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

6. Simplified 52.4%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
7. Step-by-step derivation

   1. associate-/r/ 55.2%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

8. Applied egg-rr 55.2%

   \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

9. Final simplification 55.2%

   \[\leadsto -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \]

Alternative 12: 49.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \frac{t \cdot z}{a} \end{array} \]

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 (* -4.5 (/ (* t z) 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 -4.5 * ((t * z) / 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 = (-4.5d0) * ((t * z) / 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 -4.5 * ((t * z) / 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 -4.5 * ((t * z) / 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(-4.5 * Float64(Float64(t * z) / 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 = -4.5 * ((t * z) / 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[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.5%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Step-by-step derivation

   1. associate-*l* 93.5%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

3. Simplified 93.5%

   \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

4. Taylor expanded in x around 0 55.9%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

5. Final simplification 55.9%

   \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} \]

Developer target: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	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) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))