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

Percentage Accurate: 97.7% → 99.0%

Time: 11.4s

Alternatives: 13

Speedup: 0.5×

• 32.2% 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: 97.7% 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: 99.0% 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 0.0%

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

   4. Taylor expanded in a around 0 83.3%

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

4. Final simplification 99.6%

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

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. *-commutative 97.6%

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

   3. associate-+l- 97.6%

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

   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* 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. Add Preprocessing

Alternative 3: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -2000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ c (* a (* b -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -1e+162)
     t_3
     (if (<= (* x y) -2000000000000.0)
       t_1
       (if (<= (* x y) -2e-291)
         t_2
         (if (<= (* x y) 2e-303)
           t_1
           (if (<= (* x y) 2e-21) t_2 (if (<= (* x y) 4e+39) t_1 t_3))))))))

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 = c + (a * (b * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+162) {
		tmp = t_3;
	} else if ((x * y) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -2e-291) {
		tmp = t_2;
	} else if ((x * y) <= 2e-303) {
		tmp = t_1;
	} else if ((x * y) <= 2e-21) {
		tmp = t_2;
	} else if ((x * y) <= 4e+39) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 + (t * (z * 0.0625d0))
    t_2 = c + (a * (b * (-0.25d0)))
    t_3 = c + (x * y)
    if ((x * y) <= (-1d+162)) then
        tmp = t_3
    else if ((x * y) <= (-2000000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-2d-291)) then
        tmp = t_2
    else if ((x * y) <= 2d-303) then
        tmp = t_1
    else if ((x * y) <= 2d-21) then
        tmp = t_2
    else if ((x * y) <= 4d+39) then
        tmp = t_1
    else
        tmp = t_3
    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 = c + (a * (b * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+162) {
		tmp = t_3;
	} else if ((x * y) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -2e-291) {
		tmp = t_2;
	} else if ((x * y) <= 2e-303) {
		tmp = t_1;
	} else if ((x * y) <= 2e-21) {
		tmp = t_2;
	} else if ((x * y) <= 4e+39) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (a * (b * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -1e+162:
		tmp = t_3
	elif (x * y) <= -2000000000000.0:
		tmp = t_1
	elif (x * y) <= -2e-291:
		tmp = t_2
	elif (x * y) <= 2e-303:
		tmp = t_1
	elif (x * y) <= 2e-21:
		tmp = t_2
	elif (x * y) <= 4e+39:
		tmp = t_1
	else:
		tmp = t_3
	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(c + Float64(a * Float64(b * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+162)
		tmp = t_3;
	elseif (Float64(x * y) <= -2000000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-291)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e-303)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-21)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e+39)
		tmp = t_1;
	else
		tmp = t_3;
	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 = c + (a * (b * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1e+162)
		tmp = t_3;
	elseif ((x * y) <= -2000000000000.0)
		tmp = t_1;
	elseif ((x * y) <= -2e-291)
		tmp = t_2;
	elseif ((x * y) <= 2e-303)
		tmp = t_1;
	elseif ((x * y) <= 2e-21)
		tmp = t_2;
	elseif ((x * y) <= 4e+39)
		tmp = t_1;
	else
		tmp = t_3;
	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[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+162], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2000000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-291], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e-303], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-21], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e+39], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999994e161 or 3.99999999999999976e39 < (*.f64 x y)

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 79.3%

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

   if -9.9999999999999994e161 < (*.f64 x y) < -2e12 or -1.99999999999999992e-291 < (*.f64 x y) < 1.99999999999999986e-303 or 1.99999999999999982e-21 < (*.f64 x y) < 3.99999999999999976e39

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 73.7%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*r* 73.7%

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

   5. Simplified 73.7%

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

   if -2e12 < (*.f64 x y) < -1.99999999999999992e-291 or 1.99999999999999986e-303 < (*.f64 x y) < 1.99999999999999982e-21

   1. Initial program 97.6%

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

   3. Taylor expanded in a around inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-*r* 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+162}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2000000000000:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-291}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-303}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-21}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+39}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ t_2 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2900000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))) (t_2 (* (* a b) -0.25)))
   (if (<= (* x y) -1.8e+155)
     (* x y)
     (if (<= (* x y) -2900000000.0)
       t_1
       (if (<= (* x y) -5.5e-298)
         t_2
         (if (<= (* x y) 1.4e-302)
           t_1
           (if (<= (* x y) 1.4e-19)
             t_2
             (if (<= (* x y) 6e+41) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double t_2 = (a * b) * -0.25;
	double tmp;
	if ((x * y) <= -1.8e+155) {
		tmp = x * y;
	} else if ((x * y) <= -2900000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-298) {
		tmp = t_2;
	} else if ((x * y) <= 1.4e-302) {
		tmp = t_1;
	} else if ((x * y) <= 1.4e-19) {
		tmp = t_2;
	} else if ((x * y) <= 6e+41) {
		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) :: t_2
    real(8) :: tmp
    t_1 = t * (z * 0.0625d0)
    t_2 = (a * b) * (-0.25d0)
    if ((x * y) <= (-1.8d+155)) then
        tmp = x * y
    else if ((x * y) <= (-2900000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-5.5d-298)) then
        tmp = t_2
    else if ((x * y) <= 1.4d-302) then
        tmp = t_1
    else if ((x * y) <= 1.4d-19) then
        tmp = t_2
    else if ((x * y) <= 6d+41) 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 = t * (z * 0.0625);
	double t_2 = (a * b) * -0.25;
	double tmp;
	if ((x * y) <= -1.8e+155) {
		tmp = x * y;
	} else if ((x * y) <= -2900000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-298) {
		tmp = t_2;
	} else if ((x * y) <= 1.4e-302) {
		tmp = t_1;
	} else if ((x * y) <= 1.4e-19) {
		tmp = t_2;
	} else if ((x * y) <= 6e+41) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	t_2 = (a * b) * -0.25
	tmp = 0
	if (x * y) <= -1.8e+155:
		tmp = x * y
	elif (x * y) <= -2900000000.0:
		tmp = t_1
	elif (x * y) <= -5.5e-298:
		tmp = t_2
	elif (x * y) <= 1.4e-302:
		tmp = t_1
	elif (x * y) <= 1.4e-19:
		tmp = t_2
	elif (x * y) <= 6e+41:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	t_2 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(x * y) <= -1.8e+155)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2900000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.5e-298)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.4e-302)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.4e-19)
		tmp = t_2;
	elseif (Float64(x * y) <= 6e+41)
		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 = t * (z * 0.0625);
	t_2 = (a * b) * -0.25;
	tmp = 0.0;
	if ((x * y) <= -1.8e+155)
		tmp = x * y;
	elseif ((x * y) <= -2900000000.0)
		tmp = t_1;
	elseif ((x * y) <= -5.5e-298)
		tmp = t_2;
	elseif ((x * y) <= 1.4e-302)
		tmp = t_1;
	elseif ((x * y) <= 1.4e-19)
		tmp = t_2;
	elseif ((x * y) <= 6e+41)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.8e+155], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2900000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-298], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.4e-302], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.4e-19], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 6e+41], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.80000000000000004e155 or 5.9999999999999997e41 < (*.f64 x y)

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 88.5%

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

   4. Taylor expanded in x around inf 71.8%

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

   if -1.80000000000000004e155 < (*.f64 x y) < -2.9e9 or -5.4999999999999996e-298 < (*.f64 x y) < 1.4e-302 or 1.40000000000000001e-19 < (*.f64 x y) < 5.9999999999999997e41

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*r* 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in t around inf 48.8%

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

      1. associate-*r* 48.8%

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

      2. *-commutative 48.8%

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

      3. associate-*r* 48.8%

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

   8. Simplified 48.8%

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

   if -2.9e9 < (*.f64 x y) < -5.4999999999999996e-298 or 1.4e-302 < (*.f64 x y) < 1.40000000000000001e-19

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 81.0%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. *-commutative 47.3%

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

   6. Simplified 47.3%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2900000000:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-298}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ t_2 := t \cdot \left(z \cdot 0.0625 + \frac{c}{t}\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-15}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25)))
        (t_2 (* t (+ (* z 0.0625) (/ c t)))))
   (if (<= t -5.6e-34)
     t_2
     (if (<= t 2.7e-110)
       t_1
       (if (<= t 6.6e-15)
         (+ c (* x y))
         (if (<= t 7.4e+49)
           t_1
           (if (<= t 2.3e+81)
             (+ c (* t (* z 0.0625)))
             (if (<= t 1.5e+170) t_1 t_2))))))))

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 t_2 = t * ((z * 0.0625) + (c / t));
	double tmp;
	if (t <= -5.6e-34) {
		tmp = t_2;
	} else if (t <= 2.7e-110) {
		tmp = t_1;
	} else if (t <= 6.6e-15) {
		tmp = c + (x * y);
	} else if (t <= 7.4e+49) {
		tmp = t_1;
	} else if (t <= 2.3e+81) {
		tmp = c + (t * (z * 0.0625));
	} else if (t <= 1.5e+170) {
		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 = (x * y) - ((a * b) * 0.25d0)
    t_2 = t * ((z * 0.0625d0) + (c / t))
    if (t <= (-5.6d-34)) then
        tmp = t_2
    else if (t <= 2.7d-110) then
        tmp = t_1
    else if (t <= 6.6d-15) then
        tmp = c + (x * y)
    else if (t <= 7.4d+49) then
        tmp = t_1
    else if (t <= 2.3d+81) then
        tmp = c + (t * (z * 0.0625d0))
    else if (t <= 1.5d+170) 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 = (x * y) - ((a * b) * 0.25);
	double t_2 = t * ((z * 0.0625) + (c / t));
	double tmp;
	if (t <= -5.6e-34) {
		tmp = t_2;
	} else if (t <= 2.7e-110) {
		tmp = t_1;
	} else if (t <= 6.6e-15) {
		tmp = c + (x * y);
	} else if (t <= 7.4e+49) {
		tmp = t_1;
	} else if (t <= 2.3e+81) {
		tmp = c + (t * (z * 0.0625));
	} else if (t <= 1.5e+170) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	t_2 = t * ((z * 0.0625) + (c / t))
	tmp = 0
	if t <= -5.6e-34:
		tmp = t_2
	elif t <= 2.7e-110:
		tmp = t_1
	elif t <= 6.6e-15:
		tmp = c + (x * y)
	elif t <= 7.4e+49:
		tmp = t_1
	elif t <= 2.3e+81:
		tmp = c + (t * (z * 0.0625))
	elif t <= 1.5e+170:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	t_2 = Float64(t * Float64(Float64(z * 0.0625) + Float64(c / t)))
	tmp = 0.0
	if (t <= -5.6e-34)
		tmp = t_2;
	elseif (t <= 2.7e-110)
		tmp = t_1;
	elseif (t <= 6.6e-15)
		tmp = Float64(c + Float64(x * y));
	elseif (t <= 7.4e+49)
		tmp = t_1;
	elseif (t <= 2.3e+81)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (t <= 1.5e+170)
		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 = (x * y) - ((a * b) * 0.25);
	t_2 = t * ((z * 0.0625) + (c / t));
	tmp = 0.0;
	if (t <= -5.6e-34)
		tmp = t_2;
	elseif (t <= 2.7e-110)
		tmp = t_1;
	elseif (t <= 6.6e-15)
		tmp = c + (x * y);
	elseif (t <= 7.4e+49)
		tmp = t_1;
	elseif (t <= 2.3e+81)
		tmp = c + (t * (z * 0.0625));
	elseif (t <= 1.5e+170)
		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[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z * 0.0625), $MachinePrecision] + N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e-34], t$95$2, If[LessEqual[t, 2.7e-110], t$95$1, If[LessEqual[t, 6.6e-15], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e+49], t$95$1, If[LessEqual[t, 2.3e+81], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+170], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.59999999999999994e-34 or 1.49999999999999998e170 < t

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. associate-*r* 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*r* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around inf 66.1%

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

   if -5.59999999999999994e-34 < t < 2.6999999999999998e-110 or 6.6e-15 < t < 7.40000000000000036e49 or 2.2999999999999999e81 < t < 1.49999999999999998e170

   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 0 88.0%

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

   4. Taylor expanded in c around 0 71.4%

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

   if 2.6999999999999998e-110 < t < 6.6e-15

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 73.5%

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

   if 7.40000000000000036e49 < t < 2.2999999999999999e81

   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 inf 88.5%

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

      1. associate-*r* 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.5%

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

   5. Simplified 88.5%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + \frac{c}{t}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-110}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-15}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+170}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + \frac{c}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.5 \cdot 10^{+118} \lor \neg \left(a \cdot b \leq 2.3 \cdot 10^{+89}\right) \land \left(a \cdot b \leq 1.22 \cdot 10^{+123} \lor \neg \left(a \cdot b \leq 6.2 \cdot 10^{+165}\right)\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -6.5e+118)
         (and (not (<= (* a b) 2.3e+89))
              (or (<= (* a b) 1.22e+123) (not (<= (* a b) 6.2e+165)))))
   (* (* a b) -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 (((a * b) <= -6.5e+118) || (!((a * b) <= 2.3e+89) && (((a * b) <= 1.22e+123) || !((a * b) <= 6.2e+165)))) {
		tmp = (a * b) * -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 (((a * b) <= (-6.5d+118)) .or. (.not. ((a * b) <= 2.3d+89)) .and. ((a * b) <= 1.22d+123) .or. (.not. ((a * b) <= 6.2d+165))) then
        tmp = (a * b) * (-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 (((a * b) <= -6.5e+118) || (!((a * b) <= 2.3e+89) && (((a * b) <= 1.22e+123) || !((a * b) <= 6.2e+165)))) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -6.5e+118) or (not ((a * b) <= 2.3e+89) and (((a * b) <= 1.22e+123) or not ((a * b) <= 6.2e+165))):
		tmp = (a * b) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -6.5e+118) || (!(Float64(a * b) <= 2.3e+89) && ((Float64(a * b) <= 1.22e+123) || !(Float64(a * b) <= 6.2e+165))))
		tmp = Float64(Float64(a * b) * -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 (((a * b) <= -6.5e+118) || (~(((a * b) <= 2.3e+89)) && (((a * b) <= 1.22e+123) || ~(((a * b) <= 6.2e+165)))))
		tmp = (a * b) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -6.5e+118], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.3e+89]], $MachinePrecision], Or[LessEqual[N[(a * b), $MachinePrecision], 1.22e+123], N[Not[LessEqual[N[(a * b), $MachinePrecision], 6.2e+165]], $MachinePrecision]]]], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -6.5e118 or 2.2999999999999999e89 < (*.f64 a b) < 1.22e123 or 6.2000000000000003e165 < (*.f64 a b)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 84.2%

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

   4. Taylor expanded in a around inf 72.9%

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

      1. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   if -6.5e118 < (*.f64 a b) < 2.2999999999999999e89 or 1.22e123 < (*.f64 a b) < 6.2000000000000003e165

   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 x around inf 63.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.5 \cdot 10^{+118} \lor \neg \left(a \cdot b \leq 2.3 \cdot 10^{+89}\right) \land \left(a \cdot b \leq 1.22 \cdot 10^{+123} \lor \neg \left(a \cdot b \leq 6.2 \cdot 10^{+165}\right)\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-21}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -1e+162)
     t_2
     (if (<= (* x y) -1e+36)
       t_1
       (if (<= (* x y) 2e-21)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 4e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+162) {
		tmp = t_2;
	} else if ((x * y) <= -1e+36) {
		tmp = t_1;
	} else if ((x * y) <= 2e-21) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 4e+39) {
		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 = t * (z * 0.0625d0)
    t_2 = c + (x * y)
    if ((x * y) <= (-1d+162)) then
        tmp = t_2
    else if ((x * y) <= (-1d+36)) then
        tmp = t_1
    else if ((x * y) <= 2d-21) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 4d+39) 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 = t * (z * 0.0625);
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1e+162) {
		tmp = t_2;
	} else if ((x * y) <= -1e+36) {
		tmp = t_1;
	} else if ((x * y) <= 2e-21) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 4e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -1e+162:
		tmp = t_2
	elif (x * y) <= -1e+36:
		tmp = t_1
	elif (x * y) <= 2e-21:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 4e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+162)
		tmp = t_2;
	elseif (Float64(x * y) <= -1e+36)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-21)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 4e+39)
		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 = t * (z * 0.0625);
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1e+162)
		tmp = t_2;
	elseif ((x * y) <= -1e+36)
		tmp = t_1;
	elseif ((x * y) <= 2e-21)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 4e+39)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+162], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1e+36], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-21], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999994e161 or 3.99999999999999976e39 < (*.f64 x y)

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 79.3%

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

   if -9.9999999999999994e161 < (*.f64 x y) < -1.00000000000000004e36 or 1.99999999999999982e-21 < (*.f64 x y) < 3.99999999999999976e39

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 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%

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

   6. Taylor expanded in t around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-*r* 63.3%

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

   8. Simplified 63.3%

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

   if -1.00000000000000004e36 < (*.f64 x y) < 1.99999999999999982e-21

   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 a around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-*r* 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+162}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-21}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+155}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))))
   (if (<= (* x y) -1.05e+155)
     (* x y)
     (if (<= (* x y) -5.6e-219)
       t_1
       (if (<= (* x y) 1.8e-30) c (if (<= (* x y) 4.6e+40) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double tmp;
	if ((x * y) <= -1.05e+155) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e-219) {
		tmp = t_1;
	} else if ((x * y) <= 1.8e-30) {
		tmp = c;
	} else if ((x * y) <= 4.6e+40) {
		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 = t * (z * 0.0625d0)
    if ((x * y) <= (-1.05d+155)) then
        tmp = x * y
    else if ((x * y) <= (-5.6d-219)) then
        tmp = t_1
    else if ((x * y) <= 1.8d-30) then
        tmp = c
    else if ((x * y) <= 4.6d+40) 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 = t * (z * 0.0625);
	double tmp;
	if ((x * y) <= -1.05e+155) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e-219) {
		tmp = t_1;
	} else if ((x * y) <= 1.8e-30) {
		tmp = c;
	} else if ((x * y) <= 4.6e+40) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	tmp = 0
	if (x * y) <= -1.05e+155:
		tmp = x * y
	elif (x * y) <= -5.6e-219:
		tmp = t_1
	elif (x * y) <= 1.8e-30:
		tmp = c
	elif (x * y) <= 4.6e+40:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -1.05e+155)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.6e-219)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.8e-30)
		tmp = c;
	elseif (Float64(x * y) <= 4.6e+40)
		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 = t * (z * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -1.05e+155)
		tmp = x * y;
	elseif ((x * y) <= -5.6e-219)
		tmp = t_1;
	elseif ((x * y) <= 1.8e-30)
		tmp = c;
	elseif ((x * y) <= 4.6e+40)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.05e+155], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.6e-219], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.8e-30], c, If[LessEqual[N[(x * y), $MachinePrecision], 4.6e+40], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.05e155 or 4.59999999999999987e40 < (*.f64 x y)

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 88.5%

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

   4. Taylor expanded in x around inf 71.8%

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

   if -1.05e155 < (*.f64 x y) < -5.5999999999999998e-219 or 1.8000000000000002e-30 < (*.f64 x y) < 4.59999999999999987e40

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 59.0%

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

      1. associate-*r* 59.0%

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

      2. *-commutative 59.0%

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

      3. associate-*r* 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in t around inf 43.6%

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

      1. associate-*r* 43.6%

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

      2. *-commutative 43.6%

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

      3. associate-*r* 43.6%

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

   8. Simplified 43.6%

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

   if -5.5999999999999998e-219 < (*.f64 x y) < 1.8000000000000002e-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 c around inf 37.2%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+155}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+124}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+33}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -1e+124)
     (- (+ c (* x y)) t_1)
     (if (<= (* a b) 5e+33) (+ c (+ (* x y) t_2)) (- (+ c t_2) 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+124) {
		tmp = (c + (x * y)) - t_1;
	} else if ((a * b) <= 5e+33) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-1d+124)) then
        tmp = (c + (x * y)) - t_1
    else if ((a * b) <= 5d+33) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + t_2) - 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+124) {
		tmp = (c + (x * y)) - t_1;
	} else if ((a * b) <= 5e+33) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -1e+124:
		tmp = (c + (x * y)) - t_1
	elif (a * b) <= 5e+33:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1e+124)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(a * b) <= 5e+33)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -1e+124)
		tmp = (c + (x * y)) - t_1;
	elseif ((a * b) <= 5e+33)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + t_2) - 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]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+124], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+33], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999948e123

   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 0 87.9%

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

   if -9.99999999999999948e123 < (*.f64 a b) < 4.99999999999999973e33

   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 94.4%

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

   if 4.99999999999999973e33 < (*.f64 a b)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 84.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+124}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+33}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+124} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+77}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+124) (not (<= (* a b) 2e+77)))
   (- (+ 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) <= -1e+124) || !((a * b) <= 2e+77)) {
		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) <= (-1d+124)) .or. (.not. ((a * b) <= 2d+77))) 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) <= -1e+124) || !((a * b) <= 2e+77)) {
		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) <= -1e+124) or not ((a * b) <= 2e+77):
		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) <= -1e+124) || !(Float64(a * b) <= 2e+77))
		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) <= -1e+124) || ~(((a * b) <= 2e+77)))
		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], -1e+124], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+77]], $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) < -9.99999999999999948e123 or 1.99999999999999997e77 < (*.f64 a b)

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 83.7%

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

   if -9.99999999999999948e123 < (*.f64 a b) < 1.99999999999999997e77

   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 93.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+124} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+77}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+124} \lor \neg \left(a \cdot b \leq 10^{+165}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+124) (not (<= (* a b) 1e+165)))
   (- (* 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+124) || !((a * b) <= 1e+165)) {
		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+124)) .or. (.not. ((a * b) <= 1d+165))) 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+124) || !((a * b) <= 1e+165)) {
		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+124) or not ((a * b) <= 1e+165):
		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+124) || !(Float64(a * b) <= 1e+165))
		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+124) || ~(((a * b) <= 1e+165)))
		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+124], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+165]], $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) < -9.99999999999999948e123 or 9.99999999999999899e164 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 87.0%

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

   4. Taylor expanded in c around 0 83.2%

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

   if -9.99999999999999948e123 < (*.f64 a b) < 9.99999999999999899e164

   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 91.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+124} \lor \neg \left(a \cdot b \leq 10^{+165}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+68} \lor \neg \left(x \cdot y \leq 2.5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.25e+68) (not (<= (* x y) 2.5e-25))) (* 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) <= -2.25e+68) || !((x * y) <= 2.5e-25)) {
		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) <= (-2.25d+68)) .or. (.not. ((x * y) <= 2.5d-25))) 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) <= -2.25e+68) || !((x * y) <= 2.5e-25)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.25e+68) or not ((x * y) <= 2.5e-25):
		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) <= -2.25e+68) || !(Float64(x * y) <= 2.5e-25))
		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) <= -2.25e+68) || ~(((x * y) <= 2.5e-25)))
		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], -2.25e+68], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.5e-25]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.2500000000000002e68 or 2.49999999999999981e-25 < (*.f64 x y)

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 76.4%

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

   4. Taylor expanded in x around inf 56.8%

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

   if -2.2500000000000002e68 < (*.f64 x y) < 2.49999999999999981e-25

   1. Initial program 97.8%

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

   3. Taylor expanded in c around inf 32.5%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+68} \lor \neg \left(x \cdot y \leq 2.5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 22.5% 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 97.6%

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

3. Taylor expanded in c around inf 21.2%

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

Reproduce

herbie shell --seed 2024085 
(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))