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

Percentage Accurate: 90.9% → 92.9%

Time: 9.3s

Alternatives: 8

Speedup: 0.8×

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

Specification

Math

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

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: 90.9% 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: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+294}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+294)
   (* y (/ (* x 0.5) a))
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+294) {
		tmp = y * ((x * 0.5) / a);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x and y 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+294)) then
        tmp = y * ((x * 0.5d0) / a)
    else
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+294) {
		tmp = y * ((x * 0.5) / a);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+294:
		tmp = y * ((x * 0.5) / a)
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+294)
		tmp = Float64(y * Float64(Float64(x * 0.5) / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+294)
		tmp = y * ((x * 0.5) / a);
	else
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+294], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000013e294

   1. Initial program 69.6%

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

      1. sub-neg 69.6%

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

      2. +-commutative 69.6%

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

      3. neg-sub0 69.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 69.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 69.6%

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

      6. neg-mul-1 69.6%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 69.5%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 69.6%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 69.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 69.6%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 69.6%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 69.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 69.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 69.6%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 69.6%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 69.6%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 69.6%

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

      1. associate-*r/ 69.6%

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

      2. clear-num 69.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 69.5%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-*l* 78.7%

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

      4. associate-*r/ 95.6%

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

   8. Simplified 95.6%

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

   if -2.00000000000000013e294 < (*.f64 x y)

   1. Initial program 96.1%

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

      1. associate-*l* 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+294}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 91.3% accurate, 0.1× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (/ (fma z (* t -9.0) (* x y)) (* a 2.0)))

C

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

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	return Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0))
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.8%

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

   1. sub-neg 93.8%

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

   2. +-commutative 93.8%

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

   3. associate-*l* 93.9%

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

   4. distribute-rgt-neg-in 93.9%

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

   5. fma-def 94.6%

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

   6. *-commutative 94.6%

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

   7. distribute-rgt-neg-in 94.6%

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

   8. metadata-eval 94.6%

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

3. Simplified 94.6%

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

4. Final simplification 94.6%

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

Alternative 3: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-152}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-43}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5000:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e-114)
   (* y (/ (* x 0.5) a))
   (if (<= (* x y) 1e-152)
     (* -4.5 (/ (* z t) a))
     (if (<= (* x y) 5e-43)
       (* 0.5 (/ (* x y) a))
       (if (<= (* x y) 5000.0)
         (/ (* t (* z -4.5)) a)
         (* x (* 0.5 (/ y a))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-114) {
		tmp = y * ((x * 0.5) / a);
	} else if ((x * y) <= 1e-152) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e-43) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5000.0) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = x * (0.5 * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x and y 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) <= (-5d-114)) then
        tmp = y * ((x * 0.5d0) / a)
    else if ((x * y) <= 1d-152) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d-43) then
        tmp = 0.5d0 * ((x * y) / a)
    else if ((x * y) <= 5000.0d0) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = x * (0.5d0 * (y / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-114) {
		tmp = y * ((x * 0.5) / a);
	} else if ((x * y) <= 1e-152) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e-43) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5000.0) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = x * (0.5 * (y / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e-114:
		tmp = y * ((x * 0.5) / a)
	elif (x * y) <= 1e-152:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e-43:
		tmp = 0.5 * ((x * y) / a)
	elif (x * y) <= 5000.0:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = x * (0.5 * (y / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e-114)
		tmp = Float64(y * Float64(Float64(x * 0.5) / a));
	elseif (Float64(x * y) <= 1e-152)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e-43)
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	elseif (Float64(x * y) <= 5000.0)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(x * Float64(0.5 * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e-114)
		tmp = y * ((x * 0.5) / a);
	elseif ((x * y) <= 1e-152)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e-43)
		tmp = 0.5 * ((x * y) / a);
	elseif ((x * y) <= 5000.0)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = x * (0.5 * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e-114], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-152], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-43], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5000.0], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.99999999999999989e-114

   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. sub-neg 91.1%

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

      2. +-commutative 91.1%

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

      3. neg-sub0 91.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 91.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 91.1%

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

      6. neg-mul-1 91.1%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 91.1%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 91.0%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 91.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 91.0%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 91.0%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 91.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 91.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 91.0%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 91.0%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 91.0%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 91.0%

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

      1. associate-*r/ 91.1%

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

      2. clear-num 91.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 91.1%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 91.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*l* 75.7%

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

      4. associate-*r/ 76.9%

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

   8. Simplified 76.9%

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

   if -4.99999999999999989e-114 < (*.f64 x y) < 1.00000000000000007e-152

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. +-commutative 97.4%

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

      3. neg-sub0 97.4%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.4%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.4%

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

      6. neg-mul-1 97.4%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 97.4%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 97.2%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 97.2%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 97.2%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 97.2%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 97.2%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.2%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.2%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 97.2%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 97.2%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 97.4%

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

   4. Taylor expanded in x around 0 90.2%

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

   if 1.00000000000000007e-152 < (*.f64 x y) < 5.00000000000000019e-43

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. neg-sub0 99.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 99.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 99.3%

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

      6. neg-mul-1 99.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 99.3%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 99.0%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 99.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 99.0%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 99.0%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 99.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 99.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 99.0%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 99.0%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 99.0%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 79.0%

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

   if 5.00000000000000019e-43 < (*.f64 x y) < 5e3

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 99.6%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 99.6%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 99.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 99.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 99.6%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 99.6%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 99.6%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 99.8%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 99.9%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around 0 70.9%

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

      1. associate-*r/ 70.9%

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

   8. Simplified 70.9%

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

      1. expm1-log1p-u 23.1%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-4.5 \cdot \left(t \cdot z\right)\right)\right)}}{a} \]

      2. expm1-udef 22.6%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(-4.5 \cdot \left(t \cdot z\right)\right)} - 1}}{a} \]

      3. *-commutative 22.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(-4.5 \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1}{a} \]

   10. Applied egg-rr 22.6%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(-4.5 \cdot \left(z \cdot t\right)\right)} - 1}}{a} \]
   11. Step-by-step derivation

       1. expm1-def 23.1%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-4.5 \cdot \left(z \cdot t\right)\right)\right)}}{a} \]

       2. expm1-log1p 70.9%

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

       3. *-commutative 70.9%

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

       4. associate-*r* 71.0%

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

       5. *-commutative 71.0%

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

       6. associate-*l* 70.7%

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

   12. Simplified 70.7%

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

   if 5e3 < (*.f64 x y)

   1. Initial program 90.3%

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

      1. sub-neg 90.3%

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

      2. +-commutative 90.3%

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

      3. neg-sub0 90.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 90.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 90.3%

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

      6. neg-mul-1 90.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 90.2%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 90.1%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 90.1%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 90.1%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 90.1%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 90.1%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 90.1%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 90.1%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 90.1%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 90.1%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 90.1%

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

      1. associate-*r/ 90.3%

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

      2. clear-num 90.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 90.2%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 90.2%

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

      1. *-commutative 90.2%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      2. metadata-eval 90.2%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(\color{blue}{\left(-9\right)} \cdot t\right)\right)}} \]

      3. distribute-lft-neg-in 90.2%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      4. distribute-rgt-neg-in 90.2%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, \color{blue}{-z \cdot \left(9 \cdot t\right)}\right)}} \]

      5. fma-def 90.2%

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

      6. +-commutative 90.2%

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

      7. distribute-rgt-neg-in 90.2%

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

      8. distribute-lft-neg-in 90.2%

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

      9. metadata-eval 90.2%

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

      10. *-commutative 90.2%

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

   7. Applied egg-rr 90.2%

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

   8. Taylor expanded in z around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*r/ 84.5%

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

      4. associate-*l* 84.5%

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

   10. Simplified 84.5%

       \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-152}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-43}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5000:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 4: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{z \cdot t}{a}\\ t_2 := 0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+73} \lor \neg \left(y \leq 1.35 \cdot 10^{+102}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ (* z t) a))) (t_2 (* 0.5 (/ (* x y) a))))
   (if (<= y -6.8e-153)
     t_2
     (if (<= y 1.8e-134)
       t_1
       (if (<= y 5.2e-120)
         t_2
         (if (<= y 0.0105)
           t_1
           (if (or (<= y 9.8e+73) (not (<= y 1.35e+102)))
             t_2
             (* -4.5 (* z (/ t a))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = 0.5 * ((x * y) / a);
	double tmp;
	if (y <= -6.8e-153) {
		tmp = t_2;
	} else if (y <= 1.8e-134) {
		tmp = t_1;
	} else if (y <= 5.2e-120) {
		tmp = t_2;
	} else if (y <= 0.0105) {
		tmp = t_1;
	} else if ((y <= 9.8e+73) || !(y <= 1.35e+102)) {
		tmp = t_2;
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.5d0) * ((z * t) / a)
    t_2 = 0.5d0 * ((x * y) / a)
    if (y <= (-6.8d-153)) then
        tmp = t_2
    else if (y <= 1.8d-134) then
        tmp = t_1
    else if (y <= 5.2d-120) then
        tmp = t_2
    else if (y <= 0.0105d0) then
        tmp = t_1
    else if ((y <= 9.8d+73) .or. (.not. (y <= 1.35d+102))) then
        tmp = t_2
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = 0.5 * ((x * y) / a);
	double tmp;
	if (y <= -6.8e-153) {
		tmp = t_2;
	} else if (y <= 1.8e-134) {
		tmp = t_1;
	} else if (y <= 5.2e-120) {
		tmp = t_2;
	} else if (y <= 0.0105) {
		tmp = t_1;
	} else if ((y <= 9.8e+73) || !(y <= 1.35e+102)) {
		tmp = t_2;
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = -4.5 * ((z * t) / a)
	t_2 = 0.5 * ((x * y) / a)
	tmp = 0
	if y <= -6.8e-153:
		tmp = t_2
	elif y <= 1.8e-134:
		tmp = t_1
	elif y <= 5.2e-120:
		tmp = t_2
	elif y <= 0.0105:
		tmp = t_1
	elif (y <= 9.8e+73) or not (y <= 1.35e+102):
		tmp = t_2
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(Float64(z * t) / a))
	t_2 = Float64(0.5 * Float64(Float64(x * y) / a))
	tmp = 0.0
	if (y <= -6.8e-153)
		tmp = t_2;
	elseif (y <= 1.8e-134)
		tmp = t_1;
	elseif (y <= 5.2e-120)
		tmp = t_2;
	elseif (y <= 0.0105)
		tmp = t_1;
	elseif ((y <= 9.8e+73) || !(y <= 1.35e+102))
		tmp = t_2;
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * ((z * t) / a);
	t_2 = 0.5 * ((x * y) / a);
	tmp = 0.0;
	if (y <= -6.8e-153)
		tmp = t_2;
	elseif (y <= 1.8e-134)
		tmp = t_1;
	elseif (y <= 5.2e-120)
		tmp = t_2;
	elseif (y <= 0.0105)
		tmp = t_1;
	elseif ((y <= 9.8e+73) || ~((y <= 1.35e+102)))
		tmp = t_2;
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e-153], t$95$2, If[LessEqual[y, 1.8e-134], t$95$1, If[LessEqual[y, 5.2e-120], t$95$2, If[LessEqual[y, 0.0105], t$95$1, If[Or[LessEqual[y, 9.8e+73], N[Not[LessEqual[y, 1.35e+102]], $MachinePrecision]], t$95$2, N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999997e-153 or 1.79999999999999995e-134 < y < 5.2000000000000002e-120 or 0.0105000000000000007 < y < 9.7999999999999998e73 or 1.3500000000000001e102 < y

   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. sub-neg 92.6%

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

      2. +-commutative 92.6%

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

      3. neg-sub0 92.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 92.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 92.6%

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

      6. neg-mul-1 92.6%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 92.6%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 92.5%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 92.5%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 92.5%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 92.5%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 92.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 92.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 92.5%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 92.5%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 92.5%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 67.4%

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

   if -6.7999999999999997e-153 < y < 1.79999999999999995e-134 or 5.2000000000000002e-120 < y < 0.0105000000000000007

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. neg-sub0 97.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.3%

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

      6. neg-mul-1 97.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 97.2%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 97.0%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 97.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 97.0%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 97.0%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 97.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.0%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 97.0%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 97.0%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 97.1%

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

   4. Taylor expanded in x around 0 73.1%

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

   if 9.7999999999999998e73 < y < 1.3500000000000001e102

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. +-commutative 80.8%

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

      3. neg-sub0 80.8%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 80.8%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 80.8%

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

      6. neg-mul-1 80.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 80.5%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 80.5%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 80.5%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 80.5%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 80.5%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 80.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 80.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 80.5%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 80.5%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 80.5%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 81.1%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-153}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+73} \lor \neg \left(y \leq 1.35 \cdot 10^{+102}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 5: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{z \cdot t}{a}\\ t_2 := x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.0006:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ (* z t) a))) (t_2 (* x (* 0.5 (/ y a)))))
   (if (<= y -7e-153)
     t_2
     (if (<= y 1.8e-134)
       t_1
       (if (<= y 5.2e-120)
         t_2
         (if (<= y 0.0006)
           t_1
           (if (<= y 9.8e+73)
             t_2
             (if (<= y 4.5e+101)
               (* -4.5 (* z (/ t a)))
               (* 0.5 (/ (* x y) a))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = x * (0.5 * (y / a));
	double tmp;
	if (y <= -7e-153) {
		tmp = t_2;
	} else if (y <= 1.8e-134) {
		tmp = t_1;
	} else if (y <= 5.2e-120) {
		tmp = t_2;
	} else if (y <= 0.0006) {
		tmp = t_1;
	} else if (y <= 9.8e+73) {
		tmp = t_2;
	} else if (y <= 4.5e+101) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.5d0) * ((z * t) / a)
    t_2 = x * (0.5d0 * (y / a))
    if (y <= (-7d-153)) then
        tmp = t_2
    else if (y <= 1.8d-134) then
        tmp = t_1
    else if (y <= 5.2d-120) then
        tmp = t_2
    else if (y <= 0.0006d0) then
        tmp = t_1
    else if (y <= 9.8d+73) then
        tmp = t_2
    else if (y <= 4.5d+101) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = 0.5d0 * ((x * y) / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = x * (0.5 * (y / a));
	double tmp;
	if (y <= -7e-153) {
		tmp = t_2;
	} else if (y <= 1.8e-134) {
		tmp = t_1;
	} else if (y <= 5.2e-120) {
		tmp = t_2;
	} else if (y <= 0.0006) {
		tmp = t_1;
	} else if (y <= 9.8e+73) {
		tmp = t_2;
	} else if (y <= 4.5e+101) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = -4.5 * ((z * t) / a)
	t_2 = x * (0.5 * (y / a))
	tmp = 0
	if y <= -7e-153:
		tmp = t_2
	elif y <= 1.8e-134:
		tmp = t_1
	elif y <= 5.2e-120:
		tmp = t_2
	elif y <= 0.0006:
		tmp = t_1
	elif y <= 9.8e+73:
		tmp = t_2
	elif y <= 4.5e+101:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * ((x * y) / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(Float64(z * t) / a))
	t_2 = Float64(x * Float64(0.5 * Float64(y / a)))
	tmp = 0.0
	if (y <= -7e-153)
		tmp = t_2;
	elseif (y <= 1.8e-134)
		tmp = t_1;
	elseif (y <= 5.2e-120)
		tmp = t_2;
	elseif (y <= 0.0006)
		tmp = t_1;
	elseif (y <= 9.8e+73)
		tmp = t_2;
	elseif (y <= 4.5e+101)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * ((z * t) / a);
	t_2 = x * (0.5 * (y / a));
	tmp = 0.0;
	if (y <= -7e-153)
		tmp = t_2;
	elseif (y <= 1.8e-134)
		tmp = t_1;
	elseif (y <= 5.2e-120)
		tmp = t_2;
	elseif (y <= 0.0006)
		tmp = t_1;
	elseif (y <= 9.8e+73)
		tmp = t_2;
	elseif (y <= 4.5e+101)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * ((x * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e-153], t$95$2, If[LessEqual[y, 1.8e-134], t$95$1, If[LessEqual[y, 5.2e-120], t$95$2, If[LessEqual[y, 0.0006], t$95$1, If[LessEqual[y, 9.8e+73], t$95$2, If[LessEqual[y, 4.5e+101], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.99999999999999961e-153 or 1.79999999999999995e-134 < y < 5.2000000000000002e-120 or 5.99999999999999947e-4 < y < 9.7999999999999998e73

   1. Initial program 93.8%

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

      1. sub-neg 93.8%

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

      2. +-commutative 93.8%

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

      3. neg-sub0 93.8%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 93.8%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 93.8%

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

      6. neg-mul-1 93.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 93.8%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 93.7%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 93.7%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 93.7%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 93.7%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 93.7%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 93.7%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 93.7%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 93.7%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 93.7%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 93.7%

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

      1. associate-*r/ 93.8%

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

      2. clear-num 93.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 93.8%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 93.8%

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

      1. *-commutative 93.8%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      2. metadata-eval 93.8%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(\color{blue}{\left(-9\right)} \cdot t\right)\right)}} \]

      3. distribute-lft-neg-in 93.8%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      4. distribute-rgt-neg-in 93.8%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, \color{blue}{-z \cdot \left(9 \cdot t\right)}\right)}} \]

      5. fma-def 93.8%

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

      6. +-commutative 93.8%

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

      7. distribute-rgt-neg-in 93.8%

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

      8. distribute-lft-neg-in 93.8%

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

      9. metadata-eval 93.8%

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

      10. *-commutative 93.8%

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

   7. Applied egg-rr 93.8%

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

   8. Taylor expanded in z around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*r/ 67.7%

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

      4. associate-*l* 67.7%

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

   10. Simplified 67.7%

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

   if -6.99999999999999961e-153 < y < 1.79999999999999995e-134 or 5.2000000000000002e-120 < y < 5.99999999999999947e-4

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. neg-sub0 97.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.3%

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

      6. neg-mul-1 97.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 97.2%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 97.0%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 97.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 97.0%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 97.0%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 97.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.0%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 97.0%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 97.0%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 97.1%

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

   4. Taylor expanded in x around 0 72.7%

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

   if 9.7999999999999998e73 < y < 4.5000000000000002e101

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. +-commutative 80.8%

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

      3. neg-sub0 80.8%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 80.8%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 80.8%

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

      6. neg-mul-1 80.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 80.5%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 80.5%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 80.5%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 80.5%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 80.5%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 80.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 80.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 80.5%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 80.5%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 80.5%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 81.1%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 80.3%

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

   6. Simplified 80.3%

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

   if 4.5000000000000002e101 < y

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. +-commutative 89.3%

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

      3. neg-sub0 89.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 89.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 89.3%

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

      6. neg-mul-1 89.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 89.3%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 89.2%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 89.2%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 89.2%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 89.2%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 89.2%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 89.2%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 89.2%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 89.2%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 89.2%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 89.3%

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

   4. Taylor expanded in x around inf 66.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 0.0006:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]

Alternative 6: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{z \cdot t}{a}\\ t_2 := x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ (* z t) a))) (t_2 (* x (* 0.5 (/ y a)))))
   (if (<= y -7e-153)
     t_2
     (if (<= y 1e-134)
       t_1
       (if (<= y 3.8e-120)
         t_2
         (if (<= y 6.2e-12)
           t_1
           (if (<= y 1.02e+74)
             (* y (/ (* x 0.5) a))
             (if (<= y 4.5e+101)
               (* -4.5 (* z (/ t a)))
               (* 0.5 (/ (* x y) a))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = x * (0.5 * (y / a));
	double tmp;
	if (y <= -7e-153) {
		tmp = t_2;
	} else if (y <= 1e-134) {
		tmp = t_1;
	} else if (y <= 3.8e-120) {
		tmp = t_2;
	} else if (y <= 6.2e-12) {
		tmp = t_1;
	} else if (y <= 1.02e+74) {
		tmp = y * ((x * 0.5) / a);
	} else if (y <= 4.5e+101) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.5d0) * ((z * t) / a)
    t_2 = x * (0.5d0 * (y / a))
    if (y <= (-7d-153)) then
        tmp = t_2
    else if (y <= 1d-134) then
        tmp = t_1
    else if (y <= 3.8d-120) then
        tmp = t_2
    else if (y <= 6.2d-12) then
        tmp = t_1
    else if (y <= 1.02d+74) then
        tmp = y * ((x * 0.5d0) / a)
    else if (y <= 4.5d+101) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = 0.5d0 * ((x * y) / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = x * (0.5 * (y / a));
	double tmp;
	if (y <= -7e-153) {
		tmp = t_2;
	} else if (y <= 1e-134) {
		tmp = t_1;
	} else if (y <= 3.8e-120) {
		tmp = t_2;
	} else if (y <= 6.2e-12) {
		tmp = t_1;
	} else if (y <= 1.02e+74) {
		tmp = y * ((x * 0.5) / a);
	} else if (y <= 4.5e+101) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = -4.5 * ((z * t) / a)
	t_2 = x * (0.5 * (y / a))
	tmp = 0
	if y <= -7e-153:
		tmp = t_2
	elif y <= 1e-134:
		tmp = t_1
	elif y <= 3.8e-120:
		tmp = t_2
	elif y <= 6.2e-12:
		tmp = t_1
	elif y <= 1.02e+74:
		tmp = y * ((x * 0.5) / a)
	elif y <= 4.5e+101:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * ((x * y) / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(Float64(z * t) / a))
	t_2 = Float64(x * Float64(0.5 * Float64(y / a)))
	tmp = 0.0
	if (y <= -7e-153)
		tmp = t_2;
	elseif (y <= 1e-134)
		tmp = t_1;
	elseif (y <= 3.8e-120)
		tmp = t_2;
	elseif (y <= 6.2e-12)
		tmp = t_1;
	elseif (y <= 1.02e+74)
		tmp = Float64(y * Float64(Float64(x * 0.5) / a));
	elseif (y <= 4.5e+101)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * ((z * t) / a);
	t_2 = x * (0.5 * (y / a));
	tmp = 0.0;
	if (y <= -7e-153)
		tmp = t_2;
	elseif (y <= 1e-134)
		tmp = t_1;
	elseif (y <= 3.8e-120)
		tmp = t_2;
	elseif (y <= 6.2e-12)
		tmp = t_1;
	elseif (y <= 1.02e+74)
		tmp = y * ((x * 0.5) / a);
	elseif (y <= 4.5e+101)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * ((x * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e-153], t$95$2, If[LessEqual[y, 1e-134], t$95$1, If[LessEqual[y, 3.8e-120], t$95$2, If[LessEqual[y, 6.2e-12], t$95$1, If[LessEqual[y, 1.02e+74], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+101], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.99999999999999961e-153 or 1.00000000000000004e-134 < y < 3.7999999999999997e-120

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. +-commutative 93.4%

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

      3. neg-sub0 93.4%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 93.4%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 93.4%

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

      6. neg-mul-1 93.4%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 93.4%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 93.3%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 93.3%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 93.3%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 93.3%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 93.3%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 93.3%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 93.3%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 93.3%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 93.3%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 93.3%

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

      1. associate-*r/ 93.4%

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

      2. clear-num 93.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 93.3%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 93.3%

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

      1. *-commutative 93.3%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      2. metadata-eval 93.3%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(\color{blue}{\left(-9\right)} \cdot t\right)\right)}} \]

      3. distribute-lft-neg-in 93.3%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      4. distribute-rgt-neg-in 93.3%

         \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, \color{blue}{-z \cdot \left(9 \cdot t\right)}\right)}} \]

      5. fma-def 93.3%

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

      6. +-commutative 93.3%

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

      7. distribute-rgt-neg-in 93.3%

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

      8. distribute-lft-neg-in 93.3%

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

      9. metadata-eval 93.3%

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

      10. *-commutative 93.3%

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

   7. Applied egg-rr 93.3%

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

   8. Taylor expanded in z around 0 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-*r/ 64.7%

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

      4. associate-*l* 64.7%

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

   10. Simplified 64.7%

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

   if -6.99999999999999961e-153 < y < 1.00000000000000004e-134 or 3.7999999999999997e-120 < y < 6.2000000000000002e-12

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. neg-sub0 97.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.3%

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

      6. neg-mul-1 97.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 97.2%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 97.0%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 97.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 97.0%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 97.0%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 97.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.0%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 97.0%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 97.0%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 97.1%

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

   4. Taylor expanded in x around 0 72.7%

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

   if 6.2000000000000002e-12 < y < 1.02000000000000005e74

   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. sub-neg 95.6%

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

      2. +-commutative 95.6%

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

      3. neg-sub0 95.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 95.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 95.6%

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

      6. neg-mul-1 95.6%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 95.7%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 95.4%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 95.4%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 95.4%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 95.4%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 95.4%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 95.4%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 95.4%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 95.4%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 95.4%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 95.4%

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

      1. associate-*r/ 95.6%

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

      2. clear-num 95.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 95.7%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. *-commutative 80.8%

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

      3. associate-*l* 80.8%

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

      4. associate-*r/ 84.9%

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

   8. Simplified 84.9%

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

   if 1.02000000000000005e74 < y < 4.5000000000000002e101

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. +-commutative 80.8%

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

      3. neg-sub0 80.8%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 80.8%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 80.8%

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

      6. neg-mul-1 80.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 80.5%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 80.5%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 80.5%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 80.5%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 80.5%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 80.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 80.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 80.5%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 80.5%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 80.5%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 81.1%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 80.3%

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

   6. Simplified 80.3%

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

   if 4.5000000000000002e101 < y

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. +-commutative 89.3%

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

      3. neg-sub0 89.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 89.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 89.3%

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

      6. neg-mul-1 89.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 89.3%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 89.2%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 89.2%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 89.2%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 89.2%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 89.2%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 89.2%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 89.2%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 89.2%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 89.2%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 89.3%

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

   4. Taylor expanded in x around inf 66.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 10^{-134}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]

Alternative 7: 51.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 950:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 950.0) (* -4.5 (/ (* z t) a)) (* -4.5 (* z (/ t a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 950.0) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= 950.0d0) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 950.0) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if y <= 950.0:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 950.0)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 950.0)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 950.0], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 950

   1. Initial program 95.1%

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

      1. sub-neg 95.1%

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

      2. +-commutative 95.1%

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

      3. neg-sub0 95.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 95.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 95.1%

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

      6. neg-mul-1 95.1%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 95.0%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 94.9%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 94.9%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 94.9%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 94.9%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 94.9%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 94.9%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 94.9%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 94.9%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 94.9%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 95.0%

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

   4. Taylor expanded in x around 0 56.2%

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

   if 950 < y

   1. Initial program 90.6%

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

      1. sub-neg 90.6%

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

      2. +-commutative 90.6%

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

      3. neg-sub0 90.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 90.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 90.6%

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

      6. neg-mul-1 90.6%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      7. associate-/l* 90.5%

         \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

      8. associate-/r/ 90.4%

         \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

      9. *-commutative 90.4%

         \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

      10. sub-neg 90.4%

          \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      11. +-commutative 90.4%

          \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

      12. neg-sub0 90.4%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 90.4%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 90.4%

          \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      15. distribute-lft-neg-out 90.4%

          \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

      16. distribute-rgt-neg-in 90.4%

          \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 30.7%

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

      1. associate-/l* 33.2%

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

      2. associate-/r/ 32.1%

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

   6. Simplified 32.1%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 950:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 8: 51.8% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x and y 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);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Fortran

NOTE: x and y 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;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	return -4.5 * (z * (t / a))

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(z * Float64(t / a)))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z * (t / a));
end

Wolfram

NOTE: x and y 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 93.8%

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

   1. sub-neg 93.8%

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

   2. +-commutative 93.8%

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

   3. neg-sub0 93.8%

      \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

   4. associate-+l- 93.8%

      \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

   5. sub0-neg 93.8%

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

   6. neg-mul-1 93.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

   7. associate-/l* 93.8%

      \[\leadsto \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]

   8. associate-/r/ 93.6%

      \[\leadsto \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]

   9. *-commutative 93.6%

      \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]

   10. sub-neg 93.6%

       \[\leadsto \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

   11. +-commutative 93.6%

       \[\leadsto \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]

   12. neg-sub0 93.6%

       \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

   13. associate-+l- 93.6%

       \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

   14. sub0-neg 93.6%

       \[\leadsto \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

   15. distribute-lft-neg-out 93.6%

       \[\leadsto \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]

   16. distribute-rgt-neg-in 93.6%

       \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

3. Simplified 93.7%

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

4. Taylor expanded in x around 0 49.1%

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

   1. associate-/l* 48.5%

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

   2. associate-/r/ 48.5%

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

6. Simplified 48.5%

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

7. Final simplification 48.5%

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

Developer target: 93.4% 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 2023195 
(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)))