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

Percentage Accurate: 97.6% → 98.8%

Time: 14.5s

Alternatives: 15

Speedup: 0.5×

• 32.0% 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: 97.6% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(0.0625 \cdot \frac{z \cdot t}{b} + \frac{c}{b}\right) - a \cdot 0.25\right)\\ \end{array} \end{array} \]

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)
     (* b (- (+ (* 0.0625 (/ (* z t) b)) (/ c b)) (* a 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 = b * (((0.0625 * ((z * t) / b)) + (c / b)) - (a * 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 = b * (((0.0625 * ((z * t) / b)) + (c / b)) - (a * 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 = b * (((0.0625 * ((z * t) / b)) + (c / b)) - (a * 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(b * Float64(Float64(Float64(0.0625 * Float64(Float64(z * t) / b)) + Float64(c / b)) - Float64(a * 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 = b * (((0.0625 * ((z * t) / b)) + (c / b)) - (a * 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[(b * N[(N[(N[(0.0625 * N[(N[(z * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 62.5%

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

   4. Taylor expanded in b around inf 87.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(0.0625 \cdot \frac{t \cdot z}{b} + \frac{c}{b}\right) - 0.25 \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(0.0625 \cdot \frac{z \cdot t}{b} + \frac{c}{b}\right) - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate--l+ 96.8%

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

   2. fma-define 98.8%

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

   3. associate-/l* 98.8%

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

   4. fma-neg 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

Alternative 3: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-+l- 96.8%

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

   2. *-commutative 96.8%

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

   3. associate-+l- 96.8%

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

   4. fma-define 98.0%

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

   5. *-commutative 98.0%

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

   6. associate-/l* 98.0%

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

   7. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 4: 42.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -9.2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.1 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-221}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.22 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))))
   (if (<= (* x y) -9.2e+80)
     (* x y)
     (if (<= (* x y) -5.1e-65)
       t_1
       (if (<= (* x y) 1.9e-221)
         c
         (if (<= (* x y) 1.85e+26)
           (* a (* b -0.25))
           (if (<= (* x y) 1.22e+119) t_1 (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -9.2e+80) {
		tmp = x * y;
	} else if ((x * y) <= -5.1e-65) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e-221) {
		tmp = c;
	} else if ((x * y) <= 1.85e+26) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 1.22e+119) {
		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 = z * (t * 0.0625d0)
    if ((x * y) <= (-9.2d+80)) then
        tmp = x * y
    else if ((x * y) <= (-5.1d-65)) then
        tmp = t_1
    else if ((x * y) <= 1.9d-221) then
        tmp = c
    else if ((x * y) <= 1.85d+26) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 1.22d+119) 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 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -9.2e+80) {
		tmp = x * y;
	} else if ((x * y) <= -5.1e-65) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e-221) {
		tmp = c;
	} else if ((x * y) <= 1.85e+26) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 1.22e+119) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -9.2e+80:
		tmp = x * y
	elif (x * y) <= -5.1e-65:
		tmp = t_1
	elif (x * y) <= 1.9e-221:
		tmp = c
	elif (x * y) <= 1.85e+26:
		tmp = a * (b * -0.25)
	elif (x * y) <= 1.22e+119:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -9.2e+80)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.1e-65)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.9e-221)
		tmp = c;
	elseif (Float64(x * y) <= 1.85e+26)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 1.22e+119)
		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 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -9.2e+80)
		tmp = x * y;
	elseif ((x * y) <= -5.1e-65)
		tmp = t_1;
	elseif ((x * y) <= 1.9e-221)
		tmp = c;
	elseif ((x * y) <= 1.85e+26)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 1.22e+119)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9.2e+80], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.1e-65], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.9e-221], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.85e+26], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.22e+119], t$95$1, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.20000000000000016e80 or 1.2200000000000001e119 < (*.f64 x y)

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 83.9%

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

   4. Taylor expanded in x around inf 67.6%

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

   if -9.20000000000000016e80 < (*.f64 x y) < -5.10000000000000001e-65 or 1.84999999999999994e26 < (*.f64 x y) < 1.2200000000000001e119

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 88.0%

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

   4. Taylor expanded in z around inf 75.5%

      \[\leadsto \color{blue}{z \cdot \left(\left(0.0625 \cdot t + \frac{c}{z}\right) - 0.25 \cdot \frac{a \cdot b}{z}\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 75.5%

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

      2. associate-*r/ 75.5%

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

      3. div-sub 75.6%

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

      4. cancel-sign-sub-inv 75.6%

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

      5. metadata-eval 75.6%

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

      6. *-commutative 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in t around inf 49.8%

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

   if -5.10000000000000001e-65 < (*.f64 x y) < 1.9e-221

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 47.1%

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

   if 1.9e-221 < (*.f64 x y) < 1.84999999999999994e26

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.1%

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

   4. Taylor expanded in a around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*r* 46.6%

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

   6. Simplified 46.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.1 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-221}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.22 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := x \cdot \left(y - 0.25 \cdot \frac{a \cdot b}{x}\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (* x (- y (* 0.25 (/ (* a b) x))))))
   (if (<= (* x y) -5e+68)
     t_2
     (if (<= (* x y) 1e-261)
       t_1
       (if (<= (* x y) 2e+26)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 1e+119) 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 + (t * (z * 0.0625));
	double t_2 = x * (y - (0.25 * ((a * b) / x)));
	double tmp;
	if ((x * y) <= -5e+68) {
		tmp = t_2;
	} else if ((x * y) <= 1e-261) {
		tmp = t_1;
	} else if ((x * y) <= 2e+26) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+119) {
		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 + (t * (z * 0.0625d0))
    t_2 = x * (y - (0.25d0 * ((a * b) / x)))
    if ((x * y) <= (-5d+68)) then
        tmp = t_2
    else if ((x * y) <= 1d-261) then
        tmp = t_1
    else if ((x * y) <= 2d+26) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1d+119) 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 + (t * (z * 0.0625));
	double t_2 = x * (y - (0.25 * ((a * b) / x)));
	double tmp;
	if ((x * y) <= -5e+68) {
		tmp = t_2;
	} else if ((x * y) <= 1e-261) {
		tmp = t_1;
	} else if ((x * y) <= 2e+26) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = x * (y - (0.25 * ((a * b) / x)))
	tmp = 0
	if (x * y) <= -5e+68:
		tmp = t_2
	elif (x * y) <= 1e-261:
		tmp = t_1
	elif (x * y) <= 2e+26:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1e+119:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(x * Float64(y - Float64(0.25 * Float64(Float64(a * b) / x))))
	tmp = 0.0
	if (Float64(x * y) <= -5e+68)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e-261)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1e+119)
		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 + (t * (z * 0.0625));
	t_2 = x * (y - (0.25 * ((a * b) / x)));
	tmp = 0.0;
	if ((x * y) <= -5e+68)
		tmp = t_2;
	elseif ((x * y) <= 1e-261)
		tmp = t_1;
	elseif ((x * y) <= 2e+26)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1e+119)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y - N[(0.25 * N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+68], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e-261], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+119], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000004e68 or 9.99999999999999944e118 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 78.4%

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

   4. Taylor expanded in t around 0 69.3%

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

   5. Taylor expanded in x around inf 84.5%

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

   6. Taylor expanded in c around 0 79.8%

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

   if -5.0000000000000004e68 < (*.f64 x y) < 9.99999999999999984e-262 or 2.0000000000000001e26 < (*.f64 x y) < 9.99999999999999944e118

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 71.2%

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

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

      3. associate-*r* 71.2%

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

   5. Simplified 71.2%

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

   if 9.99999999999999984e-262 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*r* 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y - 0.25 \cdot \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-261}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+119}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - 0.25 \cdot \frac{a \cdot b}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* x y) -5e+68)
     t_2
     (if (<= (* x y) 1e-261)
       t_1
       (if (<= (* x y) 2e+26)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 1e+119) 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 + (t * (z * 0.0625));
	double t_2 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -5e+68) {
		tmp = t_2;
	} else if ((x * y) <= 1e-261) {
		tmp = t_1;
	} else if ((x * y) <= 2e+26) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+119) {
		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 + (t * (z * 0.0625d0))
    t_2 = (x * y) - ((a * b) * 0.25d0)
    if ((x * y) <= (-5d+68)) then
        tmp = t_2
    else if ((x * y) <= 1d-261) then
        tmp = t_1
    else if ((x * y) <= 2d+26) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1d+119) 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 + (t * (z * 0.0625));
	double t_2 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -5e+68) {
		tmp = t_2;
	} else if ((x * y) <= 1e-261) {
		tmp = t_1;
	} else if ((x * y) <= 2e+26) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (x * y) <= -5e+68:
		tmp = t_2
	elif (x * y) <= 1e-261:
		tmp = t_1
	elif (x * y) <= 2e+26:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1e+119:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(x * y) <= -5e+68)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e-261)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1e+119)
		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 + (t * (z * 0.0625));
	t_2 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((x * y) <= -5e+68)
		tmp = t_2;
	elseif ((x * y) <= 1e-261)
		tmp = t_1;
	elseif ((x * y) <= 2e+26)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1e+119)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+68], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e-261], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+119], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000004e68 or 9.99999999999999944e118 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 83.3%

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

   4. Taylor expanded in c around 0 78.7%

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

   if -5.0000000000000004e68 < (*.f64 x y) < 9.99999999999999984e-262 or 2.0000000000000001e26 < (*.f64 x y) < 9.99999999999999944e118

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 71.2%

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

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

      3. associate-*r* 71.2%

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

   5. Simplified 71.2%

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

   if 9.99999999999999984e-262 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*r* 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 10^{-261}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+119}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))))
   (if (<= (* x y) -1e+81)
     (+ c (* x y))
     (if (<= (* x y) 1e-261)
       t_1
       (if (<= (* x y) 2e+26)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 1e+119) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double tmp;
	if ((x * y) <= -1e+81) {
		tmp = c + (x * y);
	} else if ((x * y) <= 1e-261) {
		tmp = t_1;
	} else if ((x * y) <= 2e+26) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+119) {
		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 = c + (t * (z * 0.0625d0))
    if ((x * y) <= (-1d+81)) then
        tmp = c + (x * y)
    else if ((x * y) <= 1d-261) then
        tmp = t_1
    else if ((x * y) <= 2d+26) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1d+119) 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 = c + (t * (z * 0.0625));
	double tmp;
	if ((x * y) <= -1e+81) {
		tmp = c + (x * y);
	} else if ((x * y) <= 1e-261) {
		tmp = t_1;
	} else if ((x * y) <= 2e+26) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 1e+119) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	tmp = 0
	if (x * y) <= -1e+81:
		tmp = c + (x * y)
	elif (x * y) <= 1e-261:
		tmp = t_1
	elif (x * y) <= 2e+26:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 1e+119:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+81)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= 1e-261)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1e+119)
		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 = c + (t * (z * 0.0625));
	tmp = 0.0;
	if ((x * y) <= -1e+81)
		tmp = c + (x * y);
	elseif ((x * y) <= 1e-261)
		tmp = t_1;
	elseif ((x * y) <= 2e+26)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 1e+119)
		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[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+81], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-261], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+119], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999921e80

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 74.1%

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

   if -9.99999999999999921e80 < (*.f64 x y) < 9.99999999999999984e-262 or 2.0000000000000001e26 < (*.f64 x y) < 9.99999999999999944e118

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 70.3%

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

      1. associate-*r* 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r* 70.3%

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

   5. Simplified 70.3%

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

   if 9.99999999999999984e-262 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*r* 78.6%

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

   5. Simplified 78.6%

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

   if 9.99999999999999944e118 < (*.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. Add Preprocessing

   3. Taylor expanded in z around 0 82.8%

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

   4. Taylor expanded in x around inf 69.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 10^{-261}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+119}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+101}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-220}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* x y) -8.8e+101)
     (* x y)
     (if (<= (* x y) -3.5e-67)
       t_1
       (if (<= (* x y) 1.9e-220) c (if (<= (* x y) 4e+34) 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 ((x * y) <= -8.8e+101) {
		tmp = x * y;
	} else if ((x * y) <= -3.5e-67) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e-220) {
		tmp = c;
	} else if ((x * y) <= 4e+34) {
		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 ((x * y) <= (-8.8d+101)) then
        tmp = x * y
    else if ((x * y) <= (-3.5d-67)) then
        tmp = t_1
    else if ((x * y) <= 1.9d-220) then
        tmp = c
    else if ((x * y) <= 4d+34) 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 ((x * y) <= -8.8e+101) {
		tmp = x * y;
	} else if ((x * y) <= -3.5e-67) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e-220) {
		tmp = c;
	} else if ((x * y) <= 4e+34) {
		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 (x * y) <= -8.8e+101:
		tmp = x * y
	elif (x * y) <= -3.5e-67:
		tmp = t_1
	elif (x * y) <= 1.9e-220:
		tmp = c
	elif (x * y) <= 4e+34:
		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 (Float64(x * y) <= -8.8e+101)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.5e-67)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.9e-220)
		tmp = c;
	elseif (Float64(x * y) <= 4e+34)
		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 ((x * y) <= -8.8e+101)
		tmp = x * y;
	elseif ((x * y) <= -3.5e-67)
		tmp = t_1;
	elseif ((x * y) <= 1.9e-220)
		tmp = c;
	elseif ((x * y) <= 4e+34)
		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[N[(x * y), $MachinePrecision], -8.8e+101], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.5e-67], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.9e-220], c, If[LessEqual[N[(x * y), $MachinePrecision], 4e+34], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.8000000000000003e101 or 3.99999999999999978e34 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 79.7%

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

   4. Taylor expanded in x around inf 60.5%

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

   if -8.8000000000000003e101 < (*.f64 x y) < -3.5e-67 or 1.90000000000000004e-220 < (*.f64 x y) < 3.99999999999999978e34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 65.3%

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

   4. Taylor expanded in a around inf 41.1%

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

      1. *-commutative 41.1%

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

      2. associate-*r* 41.1%

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

   6. Simplified 41.1%

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

   if -3.5e-67 < (*.f64 x y) < 1.90000000000000004e-220

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 47.1%

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

Alternative 9: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+28}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -1e+81)
     t_1
     (if (<= (* x y) -2e-41)
       (* z (* t 0.0625))
       (if (<= (* x y) 1e+28) (+ c (* a (* b -0.25))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+81) {
		tmp = t_1;
	} else if ((x * y) <= -2e-41) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 1e+28) {
		tmp = c + (a * (b * -0.25));
	} 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 = c + (x * y)
    if ((x * y) <= (-1d+81)) then
        tmp = t_1
    else if ((x * y) <= (-2d-41)) then
        tmp = z * (t * 0.0625d0)
    else if ((x * y) <= 1d+28) then
        tmp = c + (a * (b * (-0.25d0)))
    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 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+81) {
		tmp = t_1;
	} else if ((x * y) <= -2e-41) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 1e+28) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -1e+81:
		tmp = t_1
	elif (x * y) <= -2e-41:
		tmp = z * (t * 0.0625)
	elif (x * y) <= 1e+28:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+81)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-41)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (Float64(x * y) <= 1e+28)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1e+81)
		tmp = t_1;
	elseif ((x * y) <= -2e-41)
		tmp = z * (t * 0.0625);
	elseif ((x * y) <= 1e+28)
		tmp = c + (a * (b * -0.25));
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+81], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+28], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999921e80 or 9.99999999999999958e27 < (*.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 67.6%

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

   if -9.99999999999999921e80 < (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around inf 96.1%

      \[\leadsto \color{blue}{z \cdot \left(\left(0.0625 \cdot t + \frac{c}{z}\right) - 0.25 \cdot \frac{a \cdot b}{z}\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 96.1%

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

      2. associate-*r/ 96.1%

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

      3. div-sub 96.1%

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

      4. cancel-sign-sub-inv 96.1%

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

      5. metadata-eval 96.1%

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

      6. *-commutative 96.1%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in t around inf 66.2%

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

   if -2.00000000000000001e-41 < (*.f64 x y) < 9.99999999999999958e27

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-*r* 72.0%

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

   5. Simplified 72.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+28}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot \left(y + \frac{a \cdot \left(b \cdot -0.25\right)}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1e+81)
   (+ c (* x (+ y (/ (* a (* b -0.25)) x))))
   (if (<= (* x y) 2e+26)
     (- (+ c (* 0.0625 (* z t))) (* (* a b) 0.25))
     (+ c (* y (+ x (* 0.0625 (/ (* z t) y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1e+81) {
		tmp = c + (x * (y + ((a * (b * -0.25)) / x)));
	} else if ((x * y) <= 2e+26) {
		tmp = (c + (0.0625 * (z * t))) - ((a * b) * 0.25);
	} else {
		tmp = c + (y * (x + (0.0625 * ((z * t) / 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 ((x * y) <= (-1d+81)) then
        tmp = c + (x * (y + ((a * (b * (-0.25d0))) / x)))
    else if ((x * y) <= 2d+26) then
        tmp = (c + (0.0625d0 * (z * t))) - ((a * b) * 0.25d0)
    else
        tmp = c + (y * (x + (0.0625d0 * ((z * t) / 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 ((x * y) <= -1e+81) {
		tmp = c + (x * (y + ((a * (b * -0.25)) / x)));
	} else if ((x * y) <= 2e+26) {
		tmp = (c + (0.0625 * (z * t))) - ((a * b) * 0.25);
	} else {
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1e+81:
		tmp = c + (x * (y + ((a * (b * -0.25)) / x)))
	elif (x * y) <= 2e+26:
		tmp = (c + (0.0625 * (z * t))) - ((a * b) * 0.25)
	else:
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1e+81)
		tmp = Float64(c + Float64(x * Float64(y + Float64(Float64(a * Float64(b * -0.25)) / x))));
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(y * Float64(x + Float64(0.0625 * Float64(Float64(z * t) / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -1e+81)
		tmp = c + (x * (y + ((a * (b * -0.25)) / x)));
	elseif ((x * y) <= 2e+26)
		tmp = (c + (0.0625 * (z * t))) - ((a * b) * 0.25);
	else
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+81], N[(c + N[(x * N[(y + N[(N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(y * N[(x + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999921e80

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 79.0%

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

   4. Taylor expanded in t around 0 69.2%

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

   5. Taylor expanded in x around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r* 84.7%

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

   7. Simplified 84.7%

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

   if -9.99999999999999921e80 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.2%

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

   if 2.0000000000000001e26 < (*.f64 x y)

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 94.9%

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

   4. Taylor expanded in a around 0 84.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot \left(y + \frac{a \cdot \left(b \cdot -0.25\right)}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+112} \lor \neg \left(a \cdot b \leq 10^{+15}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+112) (not (<= (* a b) 1e+15)))
   (- (+ 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) <= -5e+112) || !((a * b) <= 1e+15)) {
		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) <= (-5d+112)) .or. (.not. ((a * b) <= 1d+15))) 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) <= -5e+112) || !((a * b) <= 1e+15)) {
		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) <= -5e+112) or not ((a * b) <= 1e+15):
		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) <= -5e+112) || !(Float64(a * b) <= 1e+15))
		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) <= -5e+112) || ~(((a * b) <= 1e+15)))
		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], -5e+112], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+15]], $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) < -5e112 or 1e15 < (*.f64 a b)

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 81.7%

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

   if -5e112 < (*.f64 a b) < 1e15

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0 95.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+112} \lor \neg \left(a \cdot b \leq 10^{+15}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+255}:\\ \;\;\;\;x \cdot \left(y - 0.25 \cdot \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+184}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -1e+255)
   (* x (- y (* 0.25 (/ (* a b) x))))
   (if (<= (* a b) 5e+184)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (* x y) (* (* 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) <= -1e+255) {
		tmp = x * (y - (0.25 * ((a * b) / x)));
	} else if ((a * b) <= 5e+184) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((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) <= (-1d+255)) then
        tmp = x * (y - (0.25d0 * ((a * b) / x)))
    else if ((a * b) <= 5d+184) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (x * y) - ((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) <= -1e+255) {
		tmp = x * (y - (0.25 * ((a * b) / x)));
	} else if ((a * b) <= 5e+184) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -1e+255:
		tmp = x * (y - (0.25 * ((a * b) / x)))
	elif (a * b) <= 5e+184:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -1e+255)
		tmp = Float64(x * Float64(y - Float64(0.25 * Float64(Float64(a * b) / x))));
	elseif (Float64(a * b) <= 5e+184)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(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)
	tmp = 0.0;
	if ((a * b) <= -1e+255)
		tmp = x * (y - (0.25 * ((a * b) / x)));
	elseif ((a * b) <= 5e+184)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+255], N[(x * N[(y - N[(0.25 * N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+184], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999988e254

   1. Initial program 88.4%

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

   3. Taylor expanded in z around inf 85.1%

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

   4. Taylor expanded in t around 0 85.1%

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

   5. Taylor expanded in x around inf 81.3%

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

   6. Taylor expanded in c around 0 85.2%

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

   if -9.99999999999999988e254 < (*.f64 a b) < 4.9999999999999999e184

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 88.3%

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

   if 4.9999999999999999e184 < (*.f64 a b)

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in c around 0 85.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+255}:\\ \;\;\;\;x \cdot \left(y - 0.25 \cdot \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+184}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+156}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= b -9e-25)
     t_1
     (if (<= b 5.2e+156)
       (+ c (* x y))
       (if (<= b 3.7e+226) (* z (* t 0.0625)) 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 <= -9e-25) {
		tmp = t_1;
	} else if (b <= 5.2e+156) {
		tmp = c + (x * y);
	} else if (b <= 3.7e+226) {
		tmp = z * (t * 0.0625);
	} 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 <= (-9d-25)) then
        tmp = t_1
    else if (b <= 5.2d+156) then
        tmp = c + (x * y)
    else if (b <= 3.7d+226) then
        tmp = z * (t * 0.0625d0)
    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 <= -9e-25) {
		tmp = t_1;
	} else if (b <= 5.2e+156) {
		tmp = c + (x * y);
	} else if (b <= 3.7e+226) {
		tmp = z * (t * 0.0625);
	} 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 <= -9e-25:
		tmp = t_1
	elif b <= 5.2e+156:
		tmp = c + (x * y)
	elif b <= 3.7e+226:
		tmp = z * (t * 0.0625)
	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 <= -9e-25)
		tmp = t_1;
	elseif (b <= 5.2e+156)
		tmp = Float64(c + Float64(x * y));
	elseif (b <= 3.7e+226)
		tmp = Float64(z * Float64(t * 0.0625));
	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 <= -9e-25)
		tmp = t_1;
	elseif (b <= 5.2e+156)
		tmp = c + (x * y);
	elseif (b <= 3.7e+226)
		tmp = z * (t * 0.0625);
	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, -9e-25], t$95$1, If[LessEqual[b, 5.2e+156], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+226], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.0000000000000002e-25 or 3.69999999999999982e226 < b

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 81.2%

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

   4. Taylor expanded in a around inf 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-*r* 42.5%

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

   6. Simplified 42.5%

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

   if -9.0000000000000002e-25 < b < 5.20000000000000037e156

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 60.8%

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

   if 5.20000000000000037e156 < b < 3.69999999999999982e226

   1. Initial program 84.2%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in z around inf 74.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(0.0625 \cdot t + \frac{c}{z}\right) - 0.25 \cdot \frac{a \cdot b}{z}\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 74.9%

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

      2. associate-*r/ 74.9%

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

      3. div-sub 74.9%

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

      4. cancel-sign-sub-inv 74.9%

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

      5. metadata-eval 74.9%

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

      6. *-commutative 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in t around inf 49.2%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+156}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.36 \cdot 10^{+45} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.36e+45) (not (<= (* x y) 2.9e+48))) (* 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) <= -1.36e+45) || !((x * y) <= 2.9e+48)) {
		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) <= (-1.36d+45)) .or. (.not. ((x * y) <= 2.9d+48))) 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) <= -1.36e+45) || !((x * y) <= 2.9e+48)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.36e+45) or not ((x * y) <= 2.9e+48):
		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) <= -1.36e+45) || !(Float64(x * y) <= 2.9e+48))
		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) <= -1.36e+45) || ~(((x * y) <= 2.9e+48)))
		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], -1.36e+45], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+48]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.36e45 or 2.8999999999999999e48 < (*.f64 x y)

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 78.0%

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

   4. Taylor expanded in x around inf 56.1%

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

   if -1.36e45 < (*.f64 x y) < 2.8999999999999999e48

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 36.7%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.36 \cdot 10^{+45} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.9% 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 96.8%

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

3. Taylor expanded in c around inf 24.2%

   \[\leadsto \color{blue}{c} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024135 
(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))