Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.8% → 98.8%

Time: 16.7s

Alternatives: 17

Speedup: 0.8×

• 32.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (fma y x (* (* a b) -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = fma(y, x, ((a * b) * -0.25));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = fma(y, x, Float64(Float64(a * b) * -0.25));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(y * x + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 54.5%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 54.5%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.5%

         \[\leadsto \color{blue}{y \cdot x} - 0.25 \cdot \left(a \cdot b\right) \]

      2. fma-neg 63.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -0.25 \cdot \left(a \cdot b\right)\right)} \]

      3. *-commutative 63.6%

         \[\leadsto \mathsf{fma}\left(y, x, -\color{blue}{\left(a \cdot b\right) \cdot 0.25}\right) \]

      4. distribute-rgt-neg-in 63.6%

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(a \cdot b\right) \cdot \left(-0.25\right)}\right) \]

      5. metadata-eval 63.6%

         \[\leadsto \mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot \color{blue}{-0.25}\right) \]

   5. Applied egg-rr 63.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)\\ \end{array} \]

Alternative 2: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma x y (fma (/ z 16.0) t (fma (/ a -4.0) b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, fma((z / 16.0), t, fma((a / -4.0), b, c)));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(x, y, fma(Float64(z / 16.0), t, fma(Float64(a / -4.0), b, c)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * y + N[(N[(z / 16.0), $MachinePrecision] * t + N[(N[(a / -4.0), $MachinePrecision] * b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 95.7%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. associate--l+ 95.7%

      \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   3. fma-def 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   4. associate-*l/ 96.5%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   5. fma-neg 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

   6. sub-neg 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

   7. distribute-neg-in 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

   8. remove-double-neg 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

   9. associate-/l* 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

   10. distribute-frac-neg 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

   11. associate-/r/ 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

   12. fma-def 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

   13. neg-mul-1 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

   14. *-commutative 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

   15. associate-/l* 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

   16. metadata-eval 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

3. Simplified 98.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]

4. Final simplification 98.0%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \]

Alternative 3: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + x \cdot y\\ t_3 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -0.00044:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.05 \cdot 10^{-196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t))))
        (t_2 (+ c (* x y)))
        (t_3 (+ c (* a (* b -0.25)))))
   (if (<= (* x y) -5.2e+204)
     t_2
     (if (<= (* x y) -6.2e+165)
       t_1
       (if (<= (* x y) -2.2e+81)
         t_2
         (if (<= (* x y) -0.00044)
           t_3
           (if (<= (* x y) -4.4e-304)
             t_1
             (if (<= (* x y) 2.05e-196)
               t_3
               (if (<= (* x y) 4.3e-83)
                 t_1
                 (if (<= (* x y) 1.9e+14)
                   t_3
                   (if (<= (* x y) 1e+80)
                     t_1
                     (if (<= (* x y) 3.8e+119) t_3 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double t_2 = c + (x * y);
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -5.2e+204) {
		tmp = t_2;
	} else if ((x * y) <= -6.2e+165) {
		tmp = t_1;
	} else if ((x * y) <= -2.2e+81) {
		tmp = t_2;
	} else if ((x * y) <= -0.00044) {
		tmp = t_3;
	} else if ((x * y) <= -4.4e-304) {
		tmp = t_1;
	} else if ((x * y) <= 2.05e-196) {
		tmp = t_3;
	} else if ((x * y) <= 4.3e-83) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e+14) {
		tmp = t_3;
	} else if ((x * y) <= 1e+80) {
		tmp = t_1;
	} else if ((x * y) <= 3.8e+119) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (0.0625d0 * (z * t))
    t_2 = c + (x * y)
    t_3 = c + (a * (b * (-0.25d0)))
    if ((x * y) <= (-5.2d+204)) then
        tmp = t_2
    else if ((x * y) <= (-6.2d+165)) then
        tmp = t_1
    else if ((x * y) <= (-2.2d+81)) then
        tmp = t_2
    else if ((x * y) <= (-0.00044d0)) then
        tmp = t_3
    else if ((x * y) <= (-4.4d-304)) then
        tmp = t_1
    else if ((x * y) <= 2.05d-196) then
        tmp = t_3
    else if ((x * y) <= 4.3d-83) then
        tmp = t_1
    else if ((x * y) <= 1.9d+14) then
        tmp = t_3
    else if ((x * y) <= 1d+80) then
        tmp = t_1
    else if ((x * y) <= 3.8d+119) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double t_2 = c + (x * y);
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -5.2e+204) {
		tmp = t_2;
	} else if ((x * y) <= -6.2e+165) {
		tmp = t_1;
	} else if ((x * y) <= -2.2e+81) {
		tmp = t_2;
	} else if ((x * y) <= -0.00044) {
		tmp = t_3;
	} else if ((x * y) <= -4.4e-304) {
		tmp = t_1;
	} else if ((x * y) <= 2.05e-196) {
		tmp = t_3;
	} else if ((x * y) <= 4.3e-83) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e+14) {
		tmp = t_3;
	} else if ((x * y) <= 1e+80) {
		tmp = t_1;
	} else if ((x * y) <= 3.8e+119) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (z * t))
	t_2 = c + (x * y)
	t_3 = c + (a * (b * -0.25))
	tmp = 0
	if (x * y) <= -5.2e+204:
		tmp = t_2
	elif (x * y) <= -6.2e+165:
		tmp = t_1
	elif (x * y) <= -2.2e+81:
		tmp = t_2
	elif (x * y) <= -0.00044:
		tmp = t_3
	elif (x * y) <= -4.4e-304:
		tmp = t_1
	elif (x * y) <= 2.05e-196:
		tmp = t_3
	elif (x * y) <= 4.3e-83:
		tmp = t_1
	elif (x * y) <= 1.9e+14:
		tmp = t_3
	elif (x * y) <= 1e+80:
		tmp = t_1
	elif (x * y) <= 3.8e+119:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_2 = Float64(c + Float64(x * y))
	t_3 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -5.2e+204)
		tmp = t_2;
	elseif (Float64(x * y) <= -6.2e+165)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.2e+81)
		tmp = t_2;
	elseif (Float64(x * y) <= -0.00044)
		tmp = t_3;
	elseif (Float64(x * y) <= -4.4e-304)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.05e-196)
		tmp = t_3;
	elseif (Float64(x * y) <= 4.3e-83)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.9e+14)
		tmp = t_3;
	elseif (Float64(x * y) <= 1e+80)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.8e+119)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (0.0625 * (z * t));
	t_2 = c + (x * y);
	t_3 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((x * y) <= -5.2e+204)
		tmp = t_2;
	elseif ((x * y) <= -6.2e+165)
		tmp = t_1;
	elseif ((x * y) <= -2.2e+81)
		tmp = t_2;
	elseif ((x * y) <= -0.00044)
		tmp = t_3;
	elseif ((x * y) <= -4.4e-304)
		tmp = t_1;
	elseif ((x * y) <= 2.05e-196)
		tmp = t_3;
	elseif ((x * y) <= 4.3e-83)
		tmp = t_1;
	elseif ((x * y) <= 1.9e+14)
		tmp = t_3;
	elseif ((x * y) <= 1e+80)
		tmp = t_1;
	elseif ((x * y) <= 3.8e+119)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5.2e+204], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -6.2e+165], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.2e+81], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -0.00044], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -4.4e-304], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.05e-196], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 4.3e-83], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.9e+14], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1e+80], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+119], t$95$3, t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.2000000000000002e204 or -6.2000000000000003e165 < (*.f64 x y) < -2.19999999999999987e81 or 3.7999999999999999e119 < (*.f64 x y)

   1. Initial program 90.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 86.7%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if -5.2000000000000002e204 < (*.f64 x y) < -6.2000000000000003e165 or -4.40000000000000016e-4 < (*.f64 x y) < -4.4e-304 or 2.05000000000000011e-196 < (*.f64 x y) < 4.30000000000000033e-83 or 1.9e14 < (*.f64 x y) < 1e80

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 69.2%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]

   if -2.19999999999999987e81 < (*.f64 x y) < -4.40000000000000016e-4 or -4.4e-304 < (*.f64 x y) < 2.05000000000000011e-196 or 4.30000000000000033e-83 < (*.f64 x y) < 1.9e14 or 1e80 < (*.f64 x y) < 3.7999999999999999e119

   1. Initial program 95.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 77.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 77.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 77.0%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   4. Simplified 77.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+204}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -0.00044:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.05 \cdot 10^{-196}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-83}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+14}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 4: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + t_2\\ t_4 := x \cdot y + t_2\\ \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \cdot y \leq -5.3 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -7.8 \cdot 10^{-299}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.35 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 9.6 \cdot 10^{+79}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* 0.0625 (* z t)))
        (t_3 (+ c t_2))
        (t_4 (+ (* x y) t_2)))
   (if (<= (* x y) -1.55e+80)
     t_4
     (if (<= (* x y) -5.3e-5)
       t_1
       (if (<= (* x y) -7.8e-299)
         t_3
         (if (<= (* x y) 6.5e-202)
           t_1
           (if (<= (* x y) 2.35e-82)
             t_3
             (if (<= (* x y) 2.9e+21)
               t_1
               (if (<= (* x y) 9.6e+79)
                 t_4
                 (if (<= (* x y) 2.6e+123) t_1 (+ c (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = c + t_2;
	double t_4 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1.55e+80) {
		tmp = t_4;
	} else if ((x * y) <= -5.3e-5) {
		tmp = t_1;
	} else if ((x * y) <= -7.8e-299) {
		tmp = t_3;
	} else if ((x * y) <= 6.5e-202) {
		tmp = t_1;
	} else if ((x * y) <= 2.35e-82) {
		tmp = t_3;
	} else if ((x * y) <= 2.9e+21) {
		tmp = t_1;
	} else if ((x * y) <= 9.6e+79) {
		tmp = t_4;
	} else if ((x * y) <= 2.6e+123) {
		tmp = t_1;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = 0.0625d0 * (z * t)
    t_3 = c + t_2
    t_4 = (x * y) + t_2
    if ((x * y) <= (-1.55d+80)) then
        tmp = t_4
    else if ((x * y) <= (-5.3d-5)) then
        tmp = t_1
    else if ((x * y) <= (-7.8d-299)) then
        tmp = t_3
    else if ((x * y) <= 6.5d-202) then
        tmp = t_1
    else if ((x * y) <= 2.35d-82) then
        tmp = t_3
    else if ((x * y) <= 2.9d+21) then
        tmp = t_1
    else if ((x * y) <= 9.6d+79) then
        tmp = t_4
    else if ((x * y) <= 2.6d+123) then
        tmp = t_1
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = c + t_2;
	double t_4 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1.55e+80) {
		tmp = t_4;
	} else if ((x * y) <= -5.3e-5) {
		tmp = t_1;
	} else if ((x * y) <= -7.8e-299) {
		tmp = t_3;
	} else if ((x * y) <= 6.5e-202) {
		tmp = t_1;
	} else if ((x * y) <= 2.35e-82) {
		tmp = t_3;
	} else if ((x * y) <= 2.9e+21) {
		tmp = t_1;
	} else if ((x * y) <= 9.6e+79) {
		tmp = t_4;
	} else if ((x * y) <= 2.6e+123) {
		tmp = t_1;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = 0.0625 * (z * t)
	t_3 = c + t_2
	t_4 = (x * y) + t_2
	tmp = 0
	if (x * y) <= -1.55e+80:
		tmp = t_4
	elif (x * y) <= -5.3e-5:
		tmp = t_1
	elif (x * y) <= -7.8e-299:
		tmp = t_3
	elif (x * y) <= 6.5e-202:
		tmp = t_1
	elif (x * y) <= 2.35e-82:
		tmp = t_3
	elif (x * y) <= 2.9e+21:
		tmp = t_1
	elif (x * y) <= 9.6e+79:
		tmp = t_4
	elif (x * y) <= 2.6e+123:
		tmp = t_1
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(c + t_2)
	t_4 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(x * y) <= -1.55e+80)
		tmp = t_4;
	elseif (Float64(x * y) <= -5.3e-5)
		tmp = t_1;
	elseif (Float64(x * y) <= -7.8e-299)
		tmp = t_3;
	elseif (Float64(x * y) <= 6.5e-202)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.35e-82)
		tmp = t_3;
	elseif (Float64(x * y) <= 2.9e+21)
		tmp = t_1;
	elseif (Float64(x * y) <= 9.6e+79)
		tmp = t_4;
	elseif (Float64(x * y) <= 2.6e+123)
		tmp = t_1;
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = 0.0625 * (z * t);
	t_3 = c + t_2;
	t_4 = (x * y) + t_2;
	tmp = 0.0;
	if ((x * y) <= -1.55e+80)
		tmp = t_4;
	elseif ((x * y) <= -5.3e-5)
		tmp = t_1;
	elseif ((x * y) <= -7.8e-299)
		tmp = t_3;
	elseif ((x * y) <= 6.5e-202)
		tmp = t_1;
	elseif ((x * y) <= 2.35e-82)
		tmp = t_3;
	elseif ((x * y) <= 2.9e+21)
		tmp = t_1;
	elseif ((x * y) <= 9.6e+79)
		tmp = t_4;
	elseif ((x * y) <= 2.6e+123)
		tmp = t_1;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.55e+80], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], -5.3e-5], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -7.8e-299], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 6.5e-202], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.35e-82], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 2.9e+21], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 9.6e+79], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], 2.6e+123], t$95$1, N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.54999999999999994e80 or 2.9e21 < (*.f64 x y) < 9.59999999999999942e79

   1. Initial program 94.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 94.9%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 85.3%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{0.0625 \cdot \left(t \cdot z\right) + c}\right) \]

      2. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c\right) \]

      3. associate-*r* 85.3%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(z \cdot 0.0625\right)} + c\right) \]

      4. fma-def 85.3%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(t, z \cdot 0.0625, c\right)}\right) \]

      5. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(t, \color{blue}{0.0625 \cdot z}, c\right)\right) \]

   6. Simplified 85.3%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(t, 0.0625 \cdot z, c\right)}\right) \]

   7. Taylor expanded in c around 0 77.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]

   if -1.54999999999999994e80 < (*.f64 x y) < -5.3000000000000001e-5 or -7.7999999999999997e-299 < (*.f64 x y) < 6.49999999999999956e-202 or 2.35e-82 < (*.f64 x y) < 2.9e21 or 9.59999999999999942e79 < (*.f64 x y) < 2.59999999999999985e123

   1. Initial program 95.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 77.2%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 77.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   4. Simplified 77.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if -5.3000000000000001e-5 < (*.f64 x y) < -7.7999999999999997e-299 or 6.49999999999999956e-202 < (*.f64 x y) < 2.35e-82

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]

   if 2.59999999999999985e123 < (*.f64 x y)

   1. Initial program 88.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 89.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -5.3 \cdot 10^{-5}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -7.8 \cdot 10^{-299}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{-202}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.35 \cdot 10^{-82}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 9.6 \cdot 10^{+79}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+123}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 5: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (- (+ c (* x y)) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 54.5%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 6: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+90}:\\ \;\;\;\;c + t_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 10^{-92}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot y + t_1\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -2e+143)
     t_2
     (if (<= (* a b) -2e+90)
       (+ c t_1)
       (if (<= (* a b) -1e+49)
         t_2
         (if (<= (* a b) 1e-92)
           (+ c (* x y))
           (if (<= (* a b) 5e+84)
             (+ (* x y) t_1)
             (+ c (* a (* b -0.25))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -2e+143) {
		tmp = t_2;
	} else if ((a * b) <= -2e+90) {
		tmp = c + t_1;
	} else if ((a * b) <= -1e+49) {
		tmp = t_2;
	} else if ((a * b) <= 1e-92) {
		tmp = c + (x * y);
	} else if ((a * b) <= 5e+84) {
		tmp = (x * y) + t_1;
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (x * y) - ((a * b) * 0.25d0)
    if ((a * b) <= (-2d+143)) then
        tmp = t_2
    else if ((a * b) <= (-2d+90)) then
        tmp = c + t_1
    else if ((a * b) <= (-1d+49)) then
        tmp = t_2
    else if ((a * b) <= 1d-92) then
        tmp = c + (x * y)
    else if ((a * b) <= 5d+84) then
        tmp = (x * y) + t_1
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -2e+143) {
		tmp = t_2;
	} else if ((a * b) <= -2e+90) {
		tmp = c + t_1;
	} else if ((a * b) <= -1e+49) {
		tmp = t_2;
	} else if ((a * b) <= 1e-92) {
		tmp = c + (x * y);
	} else if ((a * b) <= 5e+84) {
		tmp = (x * y) + t_1;
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -2e+143:
		tmp = t_2
	elif (a * b) <= -2e+90:
		tmp = c + t_1
	elif (a * b) <= -1e+49:
		tmp = t_2
	elif (a * b) <= 1e-92:
		tmp = c + (x * y)
	elif (a * b) <= 5e+84:
		tmp = (x * y) + t_1
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -2e+143)
		tmp = t_2;
	elseif (Float64(a * b) <= -2e+90)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= -1e+49)
		tmp = t_2;
	elseif (Float64(a * b) <= 1e-92)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 5e+84)
		tmp = Float64(Float64(x * y) + t_1);
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -2e+143)
		tmp = t_2;
	elseif ((a * b) <= -2e+90)
		tmp = c + t_1;
	elseif ((a * b) <= -1e+49)
		tmp = t_2;
	elseif ((a * b) <= 1e-92)
		tmp = c + (x * y);
	elseif ((a * b) <= 5e+84)
		tmp = (x * y) + t_1;
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+143], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2e+90], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e+49], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1e-92], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+84], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -2e143 or -1.99999999999999993e90 < (*.f64 a b) < -9.99999999999999946e48

   1. Initial program 91.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 80.2%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 74.5%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2e143 < (*.f64 a b) < -1.99999999999999993e90

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]

   if -9.99999999999999946e48 < (*.f64 a b) < 9.99999999999999988e-93

   1. Initial program 98.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 72.1%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if 9.99999999999999988e-93 < (*.f64 a b) < 5.0000000000000001e84

   1. Initial program 97.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 97.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 97.6%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 97.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 97.5%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 97.5%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 85.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 85.8%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{0.0625 \cdot \left(t \cdot z\right) + c}\right) \]

      2. *-commutative 85.8%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c\right) \]

      3. associate-*r* 85.8%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(z \cdot 0.0625\right)} + c\right) \]

      4. fma-def 85.8%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(t, z \cdot 0.0625, c\right)}\right) \]

      5. *-commutative 85.8%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(t, \color{blue}{0.0625 \cdot z}, c\right)\right) \]

   6. Simplified 85.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(t, 0.0625 \cdot z, c\right)}\right) \]

   7. Taylor expanded in c around 0 76.6%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]

   if 5.0000000000000001e84 < (*.f64 a b)

   1. Initial program 89.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 82.7%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 82.7%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 82.7%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   4. Simplified 82.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+90}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{-92}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 7: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right) + \left(c + \frac{a}{\frac{-4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) 5e+293)
   (+ (+ (* x y) (* t (* z 0.0625))) (+ c (/ a (/ -4.0 b))))
   (* a (* b -0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= 5e+293) {
		tmp = ((x * y) + (t * (z * 0.0625))) + (c + (a / (-4.0 / b)));
	} else {
		tmp = a * (b * -0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= 5d+293) then
        tmp = ((x * y) + (t * (z * 0.0625d0))) + (c + (a / ((-4.0d0) / b)))
    else
        tmp = a * (b * (-0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= 5e+293) {
		tmp = ((x * y) + (t * (z * 0.0625))) + (c + (a / (-4.0 / b)));
	} else {
		tmp = a * (b * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= 5e+293:
		tmp = ((x * y) + (t * (z * 0.0625))) + (c + (a / (-4.0 / b)))
	else:
		tmp = a * (b * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= 5e+293)
		tmp = Float64(Float64(Float64(x * y) + Float64(t * Float64(z * 0.0625))) + Float64(c + Float64(a / Float64(-4.0 / b))));
	else
		tmp = Float64(a * Float64(b * -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= 5e+293)
		tmp = ((x * y) + (t * (z * 0.0625))) + (c + (a / (-4.0 / b)));
	else
		tmp = a * (b * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], 5e+293], N[(N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < 5.00000000000000033e293

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 97.5%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 97.5%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 97.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 97.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 97.9%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 97.9%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 97.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 97.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 97.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 97.8%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 97.4%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 97.4%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 97.4%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 97.4%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 97.4%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   if 5.00000000000000033e293 < (*.f64 a b)

   1. Initial program 68.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 68.8%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 68.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 75.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 75.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 75.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 75.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 75.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 75.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 75.0%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 68.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 68.8%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 68.8%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 68.8%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 68.8%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in a around inf 93.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 93.8%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 93.8%

         \[\leadsto \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      3. associate-*r* 93.8%

         \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   8. Simplified 93.8%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right) + \left(c + \frac{a}{\frac{-4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 8: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+110}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+45) (not (<= (* a b) 5e+110)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+45) || !((a * b) <= 5e+110)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-2d+45)) .or. (.not. ((a * b) <= 5d+110))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+45) || !((a * b) <= 5e+110)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2e+45) or not ((a * b) <= 5e+110):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2e+45) || !(Float64(a * b) <= 5e+110))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2e+45) || ~(((a * b) <= 5e+110)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+45], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+110]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.9999999999999999e45 or 4.99999999999999978e110 < (*.f64 a b)

   1. Initial program 91.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 82.4%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.9999999999999999e45 < (*.f64 a b) < 4.99999999999999978e110

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 92.9%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+110}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+143)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 5e+110)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ c (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+143) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+110) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2d+143)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 5d+110) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+143) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+110) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+143:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 5e+110:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+143)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 5e+110)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+143)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 5e+110)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+143], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+110], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2e143

   1. Initial program 89.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 77.6%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 70.7%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2e143 < (*.f64 a b) < 4.99999999999999978e110

   1. Initial program 98.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 91.2%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 4.99999999999999978e110 < (*.f64 a b)

   1. Initial program 88.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 83.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 83.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 83.8%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   4. Simplified 83.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 10: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -1e+144)
     (- t_1 (* (* a b) 0.25))
     (if (<= (* a b) 5e+110) (+ c (+ (* x y) t_1)) (+ c (* a (* b -0.25)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+144) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+110) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-1d+144)) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else if ((a * b) <= 5d+110) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+144) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+110) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -1e+144:
		tmp = t_1 - ((a * b) * 0.25)
	elif (a * b) <= 5e+110:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1e+144)
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 5e+110)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -1e+144)
		tmp = t_1 - ((a * b) * 0.25);
	elseif ((a * b) <= 5e+110)
		tmp = c + ((x * y) + t_1);
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+144], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+110], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000002e144

   1. Initial program 88.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   3. Taylor expanded in c around 0 70.8%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.00000000000000002e144 < (*.f64 a b) < 4.99999999999999978e110

   1. Initial program 98.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 91.2%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 4.99999999999999978e110 < (*.f64 a b)

   1. Initial program 88.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 83.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 83.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 83.8%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   4. Simplified 83.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+144}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 11: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+144}:\\ \;\;\;\;c + \left(t_1 - t_2\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* a b) -1e+144)
     (+ c (- t_1 t_2))
     (if (<= (* a b) 5e+110) (+ c (+ (* x y) t_1)) (- (+ c (* x y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -1e+144) {
		tmp = c + (t_1 - t_2);
	} else if ((a * b) <= 5e+110) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (a * b) * 0.25d0
    if ((a * b) <= (-1d+144)) then
        tmp = c + (t_1 - t_2)
    else if ((a * b) <= 5d+110) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + (x * y)) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -1e+144) {
		tmp = c + (t_1 - t_2);
	} else if ((a * b) <= 5e+110) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	tmp = 0
	if (a * b) <= -1e+144:
		tmp = c + (t_1 - t_2)
	elif (a * b) <= 5e+110:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + (x * y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -1e+144)
		tmp = Float64(c + Float64(t_1 - t_2));
	elseif (Float64(a * b) <= 5e+110)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -1e+144)
		tmp = c + (t_1 - t_2);
	elseif ((a * b) <= 5e+110)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + (x * y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+144], N[(c + N[(t$95$1 - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+110], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000002e144

   1. Initial program 88.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   if -1.00000000000000002e144 < (*.f64 a b) < 4.99999999999999978e110

   1. Initial program 98.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 91.2%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 4.99999999999999978e110 < (*.f64 a b)

   1. Initial program 88.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 87.9%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+144}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-243}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= y -2.2e-88)
     (* x y)
     (if (<= y -1.7e-243)
       c
       (if (<= y 1.12e-187)
         (* z (* t 0.0625))
         (if (<= y 5.8e-88)
           t_1
           (if (<= y 2.6e-49) c (if (<= y 8e-36) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (y <= -2.2e-88) {
		tmp = x * y;
	} else if (y <= -1.7e-243) {
		tmp = c;
	} else if (y <= 1.12e-187) {
		tmp = z * (t * 0.0625);
	} else if (y <= 5.8e-88) {
		tmp = t_1;
	} else if (y <= 2.6e-49) {
		tmp = c;
	} else if (y <= 8e-36) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    if (y <= (-2.2d-88)) then
        tmp = x * y
    else if (y <= (-1.7d-243)) then
        tmp = c
    else if (y <= 1.12d-187) then
        tmp = z * (t * 0.0625d0)
    else if (y <= 5.8d-88) then
        tmp = t_1
    else if (y <= 2.6d-49) then
        tmp = c
    else if (y <= 8d-36) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (y <= -2.2e-88) {
		tmp = x * y;
	} else if (y <= -1.7e-243) {
		tmp = c;
	} else if (y <= 1.12e-187) {
		tmp = z * (t * 0.0625);
	} else if (y <= 5.8e-88) {
		tmp = t_1;
	} else if (y <= 2.6e-49) {
		tmp = c;
	} else if (y <= 8e-36) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if y <= -2.2e-88:
		tmp = x * y
	elif y <= -1.7e-243:
		tmp = c
	elif y <= 1.12e-187:
		tmp = z * (t * 0.0625)
	elif y <= 5.8e-88:
		tmp = t_1
	elif y <= 2.6e-49:
		tmp = c
	elif y <= 8e-36:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (y <= -2.2e-88)
		tmp = Float64(x * y);
	elseif (y <= -1.7e-243)
		tmp = c;
	elseif (y <= 1.12e-187)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (y <= 5.8e-88)
		tmp = t_1;
	elseif (y <= 2.6e-49)
		tmp = c;
	elseif (y <= 8e-36)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if (y <= -2.2e-88)
		tmp = x * y;
	elseif (y <= -1.7e-243)
		tmp = c;
	elseif (y <= 1.12e-187)
		tmp = z * (t * 0.0625);
	elseif (y <= 5.8e-88)
		tmp = t_1;
	elseif (y <= 2.6e-49)
		tmp = c;
	elseif (y <= 8e-36)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-88], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.7e-243], c, If[LessEqual[y, 1.12e-187], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-88], t$95$1, If[LessEqual[y, 2.6e-49], c, If[LessEqual[y, 8e-36], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.20000000000000005e-88 or 7.9999999999999995e-36 < y

   1. Initial program 94.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 94.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 94.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 96.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 96.1%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 94.5%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 94.5%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 94.5%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 94.5%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 94.5%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in x around inf 48.0%

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

   if -2.20000000000000005e-88 < y < -1.69999999999999998e-243 or 5.8000000000000003e-88 < y < 2.59999999999999995e-49

   1. Initial program 98.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 46.6%

      \[\leadsto \color{blue}{c} \]

   if -1.69999999999999998e-243 < y < 1.12e-187

   1. Initial program 97.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 97.8%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 97.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 97.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 97.8%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 97.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 97.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 97.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 97.6%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 97.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 97.6%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 97.6%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 97.6%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in t around inf 35.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.4%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} \]

      2. *-commutative 35.4%

         \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} \]

   8. Simplified 35.4%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} \]

   if 1.12e-187 < y < 5.8000000000000003e-88 or 2.59999999999999995e-49 < y < 7.9999999999999995e-36

   1. Initial program 92.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 92.9%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 92.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 92.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 92.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 92.9%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 92.9%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 92.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 92.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 92.8%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 92.8%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 92.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 92.8%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 92.8%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 92.8%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 92.8%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in a around inf 45.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 45.3%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 45.3%

         \[\leadsto \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      3. associate-*r* 45.3%

         \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-243}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 13: 38.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-305}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-164}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= b -1.95e-57)
     t_1
     (if (<= b -7e-305)
       (* x y)
       (if (<= b 8.2e-164) c (if (<= b 3.7e+98) (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (b <= -1.95e-57) {
		tmp = t_1;
	} else if (b <= -7e-305) {
		tmp = x * y;
	} else if (b <= 8.2e-164) {
		tmp = c;
	} else if (b <= 3.7e+98) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    if (b <= (-1.95d-57)) then
        tmp = t_1
    else if (b <= (-7d-305)) then
        tmp = x * y
    else if (b <= 8.2d-164) then
        tmp = c
    else if (b <= 3.7d+98) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (b <= -1.95e-57) {
		tmp = t_1;
	} else if (b <= -7e-305) {
		tmp = x * y;
	} else if (b <= 8.2e-164) {
		tmp = c;
	} else if (b <= 3.7e+98) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if b <= -1.95e-57:
		tmp = t_1
	elif b <= -7e-305:
		tmp = x * y
	elif b <= 8.2e-164:
		tmp = c
	elif b <= 3.7e+98:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (b <= -1.95e-57)
		tmp = t_1;
	elseif (b <= -7e-305)
		tmp = Float64(x * y);
	elseif (b <= 8.2e-164)
		tmp = c;
	elseif (b <= 3.7e+98)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if (b <= -1.95e-57)
		tmp = t_1;
	elseif (b <= -7e-305)
		tmp = x * y;
	elseif (b <= 8.2e-164)
		tmp = c;
	elseif (b <= 3.7e+98)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.95e-57], t$95$1, If[LessEqual[b, -7e-305], N[(x * y), $MachinePrecision], If[LessEqual[b, 8.2e-164], c, If[LessEqual[b, 3.7e+98], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.95000000000000003e-57 or 3.6999999999999999e98 < b

   1. Initial program 91.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 91.9%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 91.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 93.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 93.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 93.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 93.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 93.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 93.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 93.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 91.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 91.8%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 91.8%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 91.8%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 91.8%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in a around inf 43.7%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 43.7%

         \[\leadsto \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      3. associate-*r* 43.7%

         \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   8. Simplified 43.7%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   if -1.95000000000000003e-57 < b < -6.9999999999999996e-305 or 8.1999999999999996e-164 < b < 3.6999999999999999e98

   1. Initial program 98.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 98.1%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 98.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 98.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 98.1%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 98.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 98.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 98.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 98.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 98.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 98.1%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 98.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 98.1%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 98.1%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 98.1%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in x around inf 34.7%

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

   if -6.9999999999999996e-305 < b < 8.1999999999999996e-164

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 38.3%

      \[\leadsto \color{blue}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-305}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-164}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 14: 53.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* z (* t 0.0625))))
   (if (<= t -3.8e+24)
     t_2
     (if (<= t 4.4e-213)
       t_1
       (if (<= t 8.6e-175) (* a (* b -0.25)) (if (<= t 1.15e+163) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if (t <= -3.8e+24) {
		tmp = t_2;
	} else if (t <= 4.4e-213) {
		tmp = t_1;
	} else if (t <= 8.6e-175) {
		tmp = a * (b * -0.25);
	} else if (t <= 1.15e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = z * (t * 0.0625d0)
    if (t <= (-3.8d+24)) then
        tmp = t_2
    else if (t <= 4.4d-213) then
        tmp = t_1
    else if (t <= 8.6d-175) then
        tmp = a * (b * (-0.25d0))
    else if (t <= 1.15d+163) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if (t <= -3.8e+24) {
		tmp = t_2;
	} else if (t <= 4.4e-213) {
		tmp = t_1;
	} else if (t <= 8.6e-175) {
		tmp = a * (b * -0.25);
	} else if (t <= 1.15e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = z * (t * 0.0625)
	tmp = 0
	if t <= -3.8e+24:
		tmp = t_2
	elif t <= 4.4e-213:
		tmp = t_1
	elif t <= 8.6e-175:
		tmp = a * (b * -0.25)
	elif t <= 1.15e+163:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (t <= -3.8e+24)
		tmp = t_2;
	elseif (t <= 4.4e-213)
		tmp = t_1;
	elseif (t <= 8.6e-175)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (t <= 1.15e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = z * (t * 0.0625);
	tmp = 0.0;
	if (t <= -3.8e+24)
		tmp = t_2;
	elseif (t <= 4.4e-213)
		tmp = t_1;
	elseif (t <= 8.6e-175)
		tmp = a * (b * -0.25);
	elseif (t <= 1.15e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+24], t$95$2, If[LessEqual[t, 4.4e-213], t$95$1, If[LessEqual[t, 8.6e-175], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+163], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000015e24 or 1.15000000000000001e163 < t

   1. Initial program 89.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 89.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 89.4%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 91.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 91.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 91.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 91.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 91.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 91.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 91.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 91.7%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 89.3%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 89.3%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 89.3%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 89.3%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 89.3%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in t around inf 56.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 56.1%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} \]

      2. *-commutative 56.1%

         \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} \]

   8. Simplified 56.1%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} \]

   if -3.80000000000000015e24 < t < 4.40000000000000019e-213 or 8.59999999999999996e-175 < t < 1.15000000000000001e163

   1. Initial program 98.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 62.7%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if 4.40000000000000019e-213 < t < 8.59999999999999996e-175

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 100.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 100.0%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 100.0%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 100.0%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in a around inf 26.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 26.0%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 26.0%

         \[\leadsto \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      3. associate-*r* 26.0%

         \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   8. Simplified 26.0%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-213}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+163}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]

Alternative 15: 41.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+118}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.75e+80) (not (<= (* x y) 7.5e+118))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.75e+80) || !((x * y) <= 7.5e+118)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.75d+80)) .or. (.not. ((x * y) <= 7.5d+118))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.75e+80) || !((x * y) <= 7.5e+118)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.75e+80) or not ((x * y) <= 7.5e+118):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.75e+80) || !(Float64(x * y) <= 7.5e+118))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.75e+80) || ~(((x * y) <= 7.5e+118)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.75e+80], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.5e+118]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.74999999999999997e80 or 7.50000000000000003e118 < (*.f64 x y)

   1. Initial program 91.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. sub-neg 91.1%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

      2. associate-+l+ 91.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

      3. fma-def 93.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      4. associate-*l/ 93.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

      5. distribute-frac-neg 93.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

      6. distribute-rgt-neg-out 93.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

      7. associate-/l* 93.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

      8. neg-mul-1 93.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

      9. associate-/r* 93.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

      10. metadata-eval 93.7%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 91.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      2. *-commutative 91.1%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{z}{16}}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      3. div-inv 91.1%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      4. metadata-eval 91.1%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   5. Applied egg-rr 91.1%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

   6. Taylor expanded in x around inf 72.0%

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

   if -1.74999999999999997e80 < (*.f64 x y) < 7.50000000000000003e118

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 30.0%

      \[\leadsto \color{blue}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+118}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 16: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+51} \lor \neg \left(z \leq 38000000\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.3e+51) (not (<= z 38000000.0)))
   (+ c (* 0.0625 (* z t)))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.3e+51) || !(z <= 38000000.0)) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.3d+51)) .or. (.not. (z <= 38000000.0d0))) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.3e+51) || !(z <= 38000000.0)) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.3e+51) or not (z <= 38000000.0):
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.3e+51) || !(z <= 38000000.0))
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.3e+51) || ~((z <= 38000000.0)))
		tmp = c + (0.0625 * (z * t));
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.3e+51], N[Not[LessEqual[z, 38000000.0]], $MachinePrecision]], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e51 or 3.8e7 < z

   1. Initial program 91.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]

   if -1.3000000000000001e51 < z < 3.8e7

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 64.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+51} \lor \neg \left(z \leq 38000000\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 17: 22.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 95.7%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Taylor expanded in c around inf 24.0%

   \[\leadsto \color{blue}{c} \]

3. Final simplification 24.0%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))