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

Percentage Accurate: 97.5% → 98.9%

Time: 12.8s

Alternatives: 13

Speedup: 0.5×

• 33.2% 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: 97.5% 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: 98.9% 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 97.2%

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

   1. associate--l+ 97.2%

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

   2. fma-define 97.6%

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

   3. associate-/l* 97.6%

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

   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. Final simplification 98.8%

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

Alternative 2: 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 97.2%

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

   1. associate-+l- 97.2%

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

   2. *-commutative 97.2%

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

   3. associate-+l- 97.2%

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

   4. fma-define 97.6%

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

   5. *-commutative 97.6%

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

   6. associate-/l* 97.6%

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

   7. associate-/l* 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 3: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+40}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+19} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+144}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -1e+172)
     t_1
     (if (<= (* a b) -1e+40)
       (+ c (* x y))
       (if (or (<= (* a b) -2e+19) (not (<= (* a b) 4e+144)))
         t_1
         (+ c (* t (* z 0.0625))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -1e+172) {
		tmp = t_1;
	} else if ((a * b) <= -1e+40) {
		tmp = c + (x * y);
	} else if (((a * b) <= -2e+19) || !((a * b) <= 4e+144)) {
		tmp = t_1;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	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 = (x * y) - ((a * b) * 0.25d0)
    if ((a * b) <= (-1d+172)) then
        tmp = t_1
    else if ((a * b) <= (-1d+40)) then
        tmp = c + (x * y)
    else if (((a * b) <= (-2d+19)) .or. (.not. ((a * b) <= 4d+144))) then
        tmp = t_1
    else
        tmp = c + (t * (z * 0.0625d0))
    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 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -1e+172) {
		tmp = t_1;
	} else if ((a * b) <= -1e+40) {
		tmp = c + (x * y);
	} else if (((a * b) <= -2e+19) || !((a * b) <= 4e+144)) {
		tmp = t_1;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -1e+172:
		tmp = t_1
	elif (a * b) <= -1e+40:
		tmp = c + (x * y)
	elif ((a * b) <= -2e+19) or not ((a * b) <= 4e+144):
		tmp = t_1
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -1e+172)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e+40)
		tmp = Float64(c + Float64(x * y));
	elseif ((Float64(a * b) <= -2e+19) || !(Float64(a * b) <= 4e+144))
		tmp = t_1;
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -1e+172)
		tmp = t_1;
	elseif ((a * b) <= -1e+40)
		tmp = c + (x * y);
	elseif (((a * b) <= -2e+19) || ~(((a * b) <= 4e+144)))
		tmp = t_1;
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+172], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e+40], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+19], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4e+144]], $MachinePrecision]], t$95$1, N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.0000000000000001e172 or -1.00000000000000003e40 < (*.f64 a b) < -2e19 or 4.00000000000000009e144 < (*.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 89.7%

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

   4. Taylor expanded in c around 0 88.0%

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

   if -1.0000000000000001e172 < (*.f64 a b) < -1.00000000000000003e40

   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 inf 86.8%

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

   if -2e19 < (*.f64 a b) < 4.00000000000000009e144

   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 z around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*r* 67.3%

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

   5. Simplified 67.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+172}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+40}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+19} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY)
     (+ c t_1)
     (+ 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 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 + (y * (x + (0.0625 * ((z * t) / y))));
	}
	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 + (y * (x + (0.0625 * ((z * t) / y))));
	}
	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 + (y * (x + (0.0625 * ((z * t) / y))))
	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(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)
	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 + (y * (x + (0.0625 * ((z * t) / y))));
	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[(c + N[(y * N[(x + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $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 y around inf 14.3%

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

      1. associate-/l* 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in a around 0 57.1%

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

4. Final simplification 98.8%

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

Alternative 5: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := t \cdot \left(z \cdot 0.0625 + \frac{c}{t}\right)\\ t_3 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (* t (+ (* z 0.0625) (/ c t))))
        (t_3 (+ c (* b (* a -0.25)))))
   (if (<= t -3e-35)
     t_2
     (if (<= t 5.8e-189)
       t_1
       (if (<= t 2.3e-54)
         t_3
         (if (<= t 8.2e-30) t_1 (if (<= t 5e+130) 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 + (x * y);
	double t_2 = t * ((z * 0.0625) + (c / t));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (t <= -3e-35) {
		tmp = t_2;
	} else if (t <= 5.8e-189) {
		tmp = t_1;
	} else if (t <= 2.3e-54) {
		tmp = t_3;
	} else if (t <= 8.2e-30) {
		tmp = t_1;
	} else if (t <= 5e+130) {
		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 + (x * y)
    t_2 = t * ((z * 0.0625d0) + (c / t))
    t_3 = c + (b * (a * (-0.25d0)))
    if (t <= (-3d-35)) then
        tmp = t_2
    else if (t <= 5.8d-189) then
        tmp = t_1
    else if (t <= 2.3d-54) then
        tmp = t_3
    else if (t <= 8.2d-30) then
        tmp = t_1
    else if (t <= 5d+130) 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 + (x * y);
	double t_2 = t * ((z * 0.0625) + (c / t));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (t <= -3e-35) {
		tmp = t_2;
	} else if (t <= 5.8e-189) {
		tmp = t_1;
	} else if (t <= 2.3e-54) {
		tmp = t_3;
	} else if (t <= 8.2e-30) {
		tmp = t_1;
	} else if (t <= 5e+130) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = t * ((z * 0.0625) + (c / t))
	t_3 = c + (b * (a * -0.25))
	tmp = 0
	if t <= -3e-35:
		tmp = t_2
	elif t <= 5.8e-189:
		tmp = t_1
	elif t <= 2.3e-54:
		tmp = t_3
	elif t <= 8.2e-30:
		tmp = t_1
	elif t <= 5e+130:
		tmp = t_3
	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(t * Float64(Float64(z * 0.0625) + Float64(c / t)))
	t_3 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (t <= -3e-35)
		tmp = t_2;
	elseif (t <= 5.8e-189)
		tmp = t_1;
	elseif (t <= 2.3e-54)
		tmp = t_3;
	elseif (t <= 8.2e-30)
		tmp = t_1;
	elseif (t <= 5e+130)
		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 + (x * y);
	t_2 = t * ((z * 0.0625) + (c / t));
	t_3 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (t <= -3e-35)
		tmp = t_2;
	elseif (t <= 5.8e-189)
		tmp = t_1;
	elseif (t <= 2.3e-54)
		tmp = t_3;
	elseif (t <= 8.2e-30)
		tmp = t_1;
	elseif (t <= 5e+130)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z * 0.0625), $MachinePrecision] + N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e-35], t$95$2, If[LessEqual[t, 5.8e-189], t$95$1, If[LessEqual[t, 2.3e-54], t$95$3, If[LessEqual[t, 8.2e-30], t$95$1, If[LessEqual[t, 5e+130], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.99999999999999989e-35 or 4.9999999999999996e130 < t

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 62.7%

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

      1. associate-*r* 62.7%

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

      2. *-commutative 62.7%

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

      3. associate-*r* 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in t around inf 62.7%

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

   if -2.99999999999999989e-35 < t < 5.8e-189 or 2.2999999999999999e-54 < t < 8.2000000000000007e-30

   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 inf 59.7%

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

   if 5.8e-189 < t < 2.2999999999999999e-54 or 8.2000000000000007e-30 < t < 4.9999999999999996e130

   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 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   5. Simplified 66.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + \frac{c}{t}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-189}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-30}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+130}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + \frac{c}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_3 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-54}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+130}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* t (* z 0.0625))))
        (t_3 (+ c (* b (* a -0.25)))))
   (if (<= t -2e-34)
     t_2
     (if (<= t 2.1e-188)
       t_1
       (if (<= t 2.8e-54)
         t_3
         (if (<= t 2.3e-30) t_1 (if (<= t 6.2e+130) 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 + (x * y);
	double t_2 = c + (t * (z * 0.0625));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (t <= -2e-34) {
		tmp = t_2;
	} else if (t <= 2.1e-188) {
		tmp = t_1;
	} else if (t <= 2.8e-54) {
		tmp = t_3;
	} else if (t <= 2.3e-30) {
		tmp = t_1;
	} else if (t <= 6.2e+130) {
		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 + (x * y)
    t_2 = c + (t * (z * 0.0625d0))
    t_3 = c + (b * (a * (-0.25d0)))
    if (t <= (-2d-34)) then
        tmp = t_2
    else if (t <= 2.1d-188) then
        tmp = t_1
    else if (t <= 2.8d-54) then
        tmp = t_3
    else if (t <= 2.3d-30) then
        tmp = t_1
    else if (t <= 6.2d+130) 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 + (x * y);
	double t_2 = c + (t * (z * 0.0625));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (t <= -2e-34) {
		tmp = t_2;
	} else if (t <= 2.1e-188) {
		tmp = t_1;
	} else if (t <= 2.8e-54) {
		tmp = t_3;
	} else if (t <= 2.3e-30) {
		tmp = t_1;
	} else if (t <= 6.2e+130) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (t * (z * 0.0625))
	t_3 = c + (b * (a * -0.25))
	tmp = 0
	if t <= -2e-34:
		tmp = t_2
	elif t <= 2.1e-188:
		tmp = t_1
	elif t <= 2.8e-54:
		tmp = t_3
	elif t <= 2.3e-30:
		tmp = t_1
	elif t <= 6.2e+130:
		tmp = t_3
	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(c + Float64(t * Float64(z * 0.0625)))
	t_3 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (t <= -2e-34)
		tmp = t_2;
	elseif (t <= 2.1e-188)
		tmp = t_1;
	elseif (t <= 2.8e-54)
		tmp = t_3;
	elseif (t <= 2.3e-30)
		tmp = t_1;
	elseif (t <= 6.2e+130)
		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 + (x * y);
	t_2 = c + (t * (z * 0.0625));
	t_3 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (t <= -2e-34)
		tmp = t_2;
	elseif (t <= 2.1e-188)
		tmp = t_1;
	elseif (t <= 2.8e-54)
		tmp = t_3;
	elseif (t <= 2.3e-30)
		tmp = t_1;
	elseif (t <= 6.2e+130)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-34], t$95$2, If[LessEqual[t, 2.1e-188], t$95$1, If[LessEqual[t, 2.8e-54], t$95$3, If[LessEqual[t, 2.3e-30], t$95$1, If[LessEqual[t, 6.2e+130], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999986e-34 or 6.1999999999999999e130 < t

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 62.7%

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

      1. associate-*r* 62.7%

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

      2. *-commutative 62.7%

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

      3. associate-*r* 62.7%

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

   5. Simplified 62.7%

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

   if -1.99999999999999986e-34 < t < 2.0999999999999999e-188 or 2.8000000000000002e-54 < t < 2.29999999999999984e-30

   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 inf 59.7%

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

   if 2.0999999999999999e-188 < t < 2.8000000000000002e-54 or 2.29999999999999984e-30 < t < 6.1999999999999999e130

   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 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   5. Simplified 66.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-34}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-188}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-54}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+130}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+178} \lor \neg \left(x \cdot y \leq 100000000000\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -1e+178) (not (<= (* x y) 100000000000.0)))
     (- (+ c (* x y)) t_1)
     (- (+ c (* 0.0625 (* z t))) 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 (((x * y) <= -1e+178) || !((x * y) <= 100000000000.0)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (z * t))) - 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 (((x * y) <= (-1d+178)) .or. (.not. ((x * y) <= 100000000000.0d0))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + (0.0625d0 * (z * t))) - 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 (((x * y) <= -1e+178) || !((x * y) <= 100000000000.0)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -1e+178) or not ((x * y) <= 100000000000.0):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + (0.0625 * (z * t))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+178) || !(Float64(x * y) <= 100000000000.0))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - 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 (((x * y) <= -1e+178) || ~(((x * y) <= 100000000000.0)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + (0.0625 * (z * t))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+178], N[Not[LessEqual[N[(x * y), $MachinePrecision], 100000000000.0]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.0000000000000001e178 or 1e11 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 89.1%

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

   if -1.0000000000000001e178 < (*.f64 x y) < 1e11

   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 95.4%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+178} \lor \neg \left(x \cdot y \leq 100000000000\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+172} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+172) (not (<= (* a b) 4e+144)))
   (- (* 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) <= -1e+172) || !((a * b) <= 4e+144)) {
		tmp = (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) <= (-1d+172)) .or. (.not. ((a * b) <= 4d+144))) then
        tmp = (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) <= -1e+172) || !((a * b) <= 4e+144)) {
		tmp = (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) <= -1e+172) or not ((a * b) <= 4e+144):
		tmp = (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) <= -1e+172) || !(Float64(a * b) <= 4e+144))
		tmp = Float64(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) <= -1e+172) || ~(((a * b) <= 4e+144)))
		tmp = (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], -1e+172], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4e+144]], $MachinePrecision]], N[(N[(x * y), $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) < -1.0000000000000001e172 or 4.00000000000000009e144 < (*.f64 a b)

   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 90.0%

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

   4. Taylor expanded in c around 0 88.1%

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

   if -1.0000000000000001e172 < (*.f64 a b) < 4.00000000000000009e144

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 93.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+172} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+30} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+116}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+30) (not (<= (* a b) 5e+116)))
   (- (+ 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+30) || !((a * b) <= 5e+116)) {
		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+30)) .or. (.not. ((a * b) <= 5d+116))) 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+30) || !((a * b) <= 5e+116)) {
		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+30) or not ((a * b) <= 5e+116):
		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+30) || !(Float64(a * b) <= 5e+116))
		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+30) || ~(((a * b) <= 5e+116)))
		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+30], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+116]], $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) < -2e30 or 5.00000000000000025e116 < (*.f64 a b)

   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 0 90.2%

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

   if -2e30 < (*.f64 a b) < 5.00000000000000025e116

   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 94.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+30} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+116}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{-77} \lor \neg \left(b \leq 1.65 \cdot 10^{+95}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -6.1e-77) (not (<= b 1.65e+95)))
   (+ c (* b (* a -0.25)))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -6.1e-77) || !(b <= 1.65e+95)) {
		tmp = c + (b * (a * -0.25));
	} 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 ((b <= (-6.1d-77)) .or. (.not. (b <= 1.65d+95))) then
        tmp = c + (b * (a * (-0.25d0)))
    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 ((b <= -6.1e-77) || !(b <= 1.65e+95)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -6.1e-77) or not (b <= 1.65e+95):
		tmp = c + (b * (a * -0.25))
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -6.1e-77) || !(b <= 1.65e+95))
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	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 ((b <= -6.1e-77) || ~((b <= 1.65e+95)))
		tmp = c + (b * (a * -0.25));
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -6.1e-77], N[Not[LessEqual[b, 1.65e+95]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.1000000000000002e-77 or 1.6499999999999999e95 < b

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-*r* 68.5%

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

   5. Simplified 68.5%

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

   if -6.1000000000000002e-77 < b < 1.6499999999999999e95

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 60.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{-77} \lor \neg \left(b \leq 1.65 \cdot 10^{+95}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-14} \lor \neg \left(t \leq 4.5 \cdot 10^{+57}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.15e-14) (not (<= t 4.5e+57))) (* t (* z 0.0625)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.15e-14) || !(t <= 4.5e+57)) {
		tmp = t * (z * 0.0625);
	} 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 ((t <= (-2.15d-14)) .or. (.not. (t <= 4.5d+57))) then
        tmp = t * (z * 0.0625d0)
    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 ((t <= -2.15e-14) || !(t <= 4.5e+57)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.15e-14) or not (t <= 4.5e+57):
		tmp = t * (z * 0.0625)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.15e-14) || !(t <= 4.5e+57))
		tmp = Float64(t * Float64(z * 0.0625));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.15e-14) || ~((t <= 4.5e+57)))
		tmp = t * (z * 0.0625);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.15e-14], N[Not[LessEqual[t, 4.5e+57]], $MachinePrecision]], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if t < -2.14999999999999999e-14 or 4.49999999999999996e57 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-*r* 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in t around inf 58.2%

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

   7. Taylor expanded in t around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-*l* 42.3%

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

      3. *-commutative 42.3%

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

   9. Simplified 42.3%

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

   if -2.14999999999999999e-14 < t < 4.49999999999999996e57

   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 25.3%

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

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-14} \lor \neg \left(t \leq 4.5 \cdot 10^{+57}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+56} \lor \neg \left(t \leq 6.8 \cdot 10^{+122}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.5e+56) (not (<= t 6.8e+122)))
   (* t (* z 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.5e+56) || !(t <= 6.8e+122)) {
		tmp = t * (z * 0.0625);
	} 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 ((t <= (-1.5d+56)) .or. (.not. (t <= 6.8d+122))) then
        tmp = t * (z * 0.0625d0)
    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 ((t <= -1.5e+56) || !(t <= 6.8e+122)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.5e+56) or not (t <= 6.8e+122):
		tmp = t * (z * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.5e+56) || !(t <= 6.8e+122))
		tmp = Float64(t * Float64(z * 0.0625));
	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 ((t <= -1.5e+56) || ~((t <= 6.8e+122)))
		tmp = t * (z * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.5e+56], N[Not[LessEqual[t, 6.8e+122]], $MachinePrecision]], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000003e56 or 6.8e122 < t

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 61.2%

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

      1. associate-*r* 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in t around inf 61.2%

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

   7. Taylor expanded in t around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-*l* 51.3%

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

      3. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if -1.50000000000000003e56 < t < 6.8e122

   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 inf 55.9%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+56} \lor \neg \left(t \leq 6.8 \cdot 10^{+122}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 21.8% 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 97.2%

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

3. Taylor expanded in c around inf 21.4%

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

4. Final simplification 21.4%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(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))