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

Percentage Accurate: 97.5% → 98.8%

Time: 15.1s

Alternatives: 16

Speedup: 1.0×

• 33.5% 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: 98.8% 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 98.1%

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

   1. associate--l+ 98.1%

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

   2. fma-define 98.9%

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

   3. associate-/l* 98.9%

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

   4. fma-neg 98.9%

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

   5. distribute-neg-frac2 98.9%

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

   6. metadata-eval 98.9%

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

3. Simplified 98.9%

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

5. Final simplification 98.9%

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

Alternative 2: 97.9% 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 98.1%

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

   1. associate-+l- 98.1%

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

   2. *-commutative 98.1%

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

   3. associate-+l- 98.1%

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

   4. fma-define 98.5%

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

   5. *-commutative 98.5%

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

   6. associate-/l* 98.5%

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

   7. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{-118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(\frac{c}{a} - b \cdot 0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{+158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25))))
        (t_2 (+ c (* 0.0625 (* z t))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -4.1e+74)
     t_3
     (if (<= (* x y) -1.2e-219)
       t_1
       (if (<= (* x y) 3.4e-118)
         t_2
         (if (<= (* x y) 4.2e-11)
           (* a (- (/ c a) (* b 0.25)))
           (if (<= (* x y) 2.9e+158)
             t_2
             (if (<= (* x y) 5.8e+207) 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 + (b * (a * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -4.1e+74) {
		tmp = t_3;
	} else if ((x * y) <= -1.2e-219) {
		tmp = t_1;
	} else if ((x * y) <= 3.4e-118) {
		tmp = t_2;
	} else if ((x * y) <= 4.2e-11) {
		tmp = a * ((c / a) - (b * 0.25));
	} else if ((x * y) <= 2.9e+158) {
		tmp = t_2;
	} else if ((x * y) <= 5.8e+207) {
		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 + (b * (a * (-0.25d0)))
    t_2 = c + (0.0625d0 * (z * t))
    t_3 = c + (x * y)
    if ((x * y) <= (-4.1d+74)) then
        tmp = t_3
    else if ((x * y) <= (-1.2d-219)) then
        tmp = t_1
    else if ((x * y) <= 3.4d-118) then
        tmp = t_2
    else if ((x * y) <= 4.2d-11) then
        tmp = a * ((c / a) - (b * 0.25d0))
    else if ((x * y) <= 2.9d+158) then
        tmp = t_2
    else if ((x * y) <= 5.8d+207) 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 + (b * (a * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -4.1e+74) {
		tmp = t_3;
	} else if ((x * y) <= -1.2e-219) {
		tmp = t_1;
	} else if ((x * y) <= 3.4e-118) {
		tmp = t_2;
	} else if ((x * y) <= 4.2e-11) {
		tmp = a * ((c / a) - (b * 0.25));
	} else if ((x * y) <= 2.9e+158) {
		tmp = t_2;
	} else if ((x * y) <= 5.8e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (0.0625 * (z * t))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -4.1e+74:
		tmp = t_3
	elif (x * y) <= -1.2e-219:
		tmp = t_1
	elif (x * y) <= 3.4e-118:
		tmp = t_2
	elif (x * y) <= 4.2e-11:
		tmp = a * ((c / a) - (b * 0.25))
	elif (x * y) <= 2.9e+158:
		tmp = t_2
	elif (x * y) <= 5.8e+207:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_2 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -4.1e+74)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.2e-219)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.4e-118)
		tmp = t_2;
	elseif (Float64(x * y) <= 4.2e-11)
		tmp = Float64(a * Float64(Float64(c / a) - Float64(b * 0.25)));
	elseif (Float64(x * y) <= 2.9e+158)
		tmp = t_2;
	elseif (Float64(x * y) <= 5.8e+207)
		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 + (b * (a * -0.25));
	t_2 = c + (0.0625 * (z * t));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -4.1e+74)
		tmp = t_3;
	elseif ((x * y) <= -1.2e-219)
		tmp = t_1;
	elseif ((x * y) <= 3.4e-118)
		tmp = t_2;
	elseif ((x * y) <= 4.2e-11)
		tmp = a * ((c / a) - (b * 0.25));
	elseif ((x * y) <= 2.9e+158)
		tmp = t_2;
	elseif ((x * y) <= 5.8e+207)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.1e+74], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.2e-219], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.4e-118], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4.2e-11], N[(a * N[(N[(c / a), $MachinePrecision] - N[(b * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.9e+158], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5.8e+207], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.1e74 or 5.79999999999999994e207 < (*.f64 x y)

   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 a around 0 83.7%

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

   4. Taylor expanded in t around 0 76.6%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   if -4.1e74 < (*.f64 x y) < -1.20000000000000007e-219 or 2.90000000000000024e158 < (*.f64 x y) < 5.79999999999999994e207

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

      3. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -1.20000000000000007e-219 < (*.f64 x y) < 3.39999999999999991e-118 or 4.1999999999999997e-11 < (*.f64 x y) < 2.90000000000000024e158

   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 83.0%

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

   4. Taylor expanded in x around 0 73.5%

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

   if 3.39999999999999991e-118 < (*.f64 x y) < 4.1999999999999997e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 94.6%

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

   4. Taylor expanded in c around inf 63.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+74}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-219}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{-118}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(\frac{c}{a} - b \cdot 0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{+158}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+207}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -6.4 \cdot 10^{+69}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-297}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2.3 \cdot 10^{-241}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.55 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* z (* t 0.0625))))
   (if (<= (* x y) -6.4e+69)
     (* x y)
     (if (<= (* x y) -5.2e-220)
       t_1
       (if (<= (* x y) 2e-297)
         t_2
         (if (<= (* x y) 2.3e-241)
           c
           (if (<= (* x y) 2.55e+157)
             t_2
             (if (<= (* x y) 3.8e+207) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -6.4e+69) {
		tmp = x * y;
	} else if ((x * y) <= -5.2e-220) {
		tmp = t_1;
	} else if ((x * y) <= 2e-297) {
		tmp = t_2;
	} else if ((x * y) <= 2.3e-241) {
		tmp = c;
	} else if ((x * y) <= 2.55e+157) {
		tmp = t_2;
	} else if ((x * y) <= 3.8e+207) {
		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 = b * (a * (-0.25d0))
    t_2 = z * (t * 0.0625d0)
    if ((x * y) <= (-6.4d+69)) then
        tmp = x * y
    else if ((x * y) <= (-5.2d-220)) then
        tmp = t_1
    else if ((x * y) <= 2d-297) then
        tmp = t_2
    else if ((x * y) <= 2.3d-241) then
        tmp = c
    else if ((x * y) <= 2.55d+157) then
        tmp = t_2
    else if ((x * y) <= 3.8d+207) 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 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -6.4e+69) {
		tmp = x * y;
	} else if ((x * y) <= -5.2e-220) {
		tmp = t_1;
	} else if ((x * y) <= 2e-297) {
		tmp = t_2;
	} else if ((x * y) <= 2.3e-241) {
		tmp = c;
	} else if ((x * y) <= 2.55e+157) {
		tmp = t_2;
	} else if ((x * y) <= 3.8e+207) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -6.4e+69:
		tmp = x * y
	elif (x * y) <= -5.2e-220:
		tmp = t_1
	elif (x * y) <= 2e-297:
		tmp = t_2
	elif (x * y) <= 2.3e-241:
		tmp = c
	elif (x * y) <= 2.55e+157:
		tmp = t_2
	elif (x * y) <= 3.8e+207:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -6.4e+69)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.2e-220)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-297)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.3e-241)
		tmp = c;
	elseif (Float64(x * y) <= 2.55e+157)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.8e+207)
		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 = b * (a * -0.25);
	t_2 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -6.4e+69)
		tmp = x * y;
	elseif ((x * y) <= -5.2e-220)
		tmp = t_1;
	elseif ((x * y) <= 2e-297)
		tmp = t_2;
	elseif ((x * y) <= 2.3e-241)
		tmp = c;
	elseif ((x * y) <= 2.55e+157)
		tmp = t_2;
	elseif ((x * y) <= 3.8e+207)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.4e+69], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.2e-220], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-297], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.3e-241], c, If[LessEqual[N[(x * y), $MachinePrecision], 2.55e+157], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+207], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -6.3999999999999997e69 or 3.79999999999999986e207 < (*.f64 x y)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 93.4%

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

   4. Taylor expanded in a around 0 84.3%

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

   5. Taylor expanded in x around inf 70.0%

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

   if -6.3999999999999997e69 < (*.f64 x y) < -5.2e-220 or 2.55e157 < (*.f64 x y) < 3.79999999999999986e207

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 65.5%

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

      1. associate-*r* 65.5%

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

      2. *-commutative 65.5%

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

      3. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in b around inf 62.1%

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

   7. Taylor expanded in a around inf 51.2%

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

   if -5.2e-220 < (*.f64 x y) < 2.00000000000000008e-297 or 2.2999999999999999e-241 < (*.f64 x y) < 2.55e157

   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 x around inf 84.3%

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

   4. Taylor expanded in a around 0 69.5%

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

   5. Taylor expanded in t around inf 48.5%

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

      1. associate-*r* 48.5%

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

   7. Simplified 48.5%

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

   if 2.00000000000000008e-297 < (*.f64 x y) < 2.2999999999999999e-241

   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 61.9%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.4 \cdot 10^{+69}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-297}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.3 \cdot 10^{-241}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.55 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -3 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-219}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t))))
        (t_2 (* b (* a -0.25)))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -3e+85)
     t_3
     (if (<= (* x y) -2.45e-179)
       t_1
       (if (<= (* x y) -1.2e-219)
         t_2
         (if (<= (* x y) 1.75e+178)
           t_1
           (if (<= (* x y) 3.8e+207) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double t_2 = b * (a * -0.25);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -3e+85) {
		tmp = t_3;
	} else if ((x * y) <= -2.45e-179) {
		tmp = t_1;
	} else if ((x * y) <= -1.2e-219) {
		tmp = t_2;
	} else if ((x * y) <= 1.75e+178) {
		tmp = t_1;
	} else if ((x * y) <= 3.8e+207) {
		tmp = t_2;
	} 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 + (0.0625d0 * (z * t))
    t_2 = b * (a * (-0.25d0))
    t_3 = c + (x * y)
    if ((x * y) <= (-3d+85)) then
        tmp = t_3
    else if ((x * y) <= (-2.45d-179)) then
        tmp = t_1
    else if ((x * y) <= (-1.2d-219)) then
        tmp = t_2
    else if ((x * y) <= 1.75d+178) then
        tmp = t_1
    else if ((x * y) <= 3.8d+207) then
        tmp = t_2
    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 + (0.0625 * (z * t));
	double t_2 = b * (a * -0.25);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -3e+85) {
		tmp = t_3;
	} else if ((x * y) <= -2.45e-179) {
		tmp = t_1;
	} else if ((x * y) <= -1.2e-219) {
		tmp = t_2;
	} else if ((x * y) <= 1.75e+178) {
		tmp = t_1;
	} else if ((x * y) <= 3.8e+207) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (z * t))
	t_2 = b * (a * -0.25)
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -3e+85:
		tmp = t_3
	elif (x * y) <= -2.45e-179:
		tmp = t_1
	elif (x * y) <= -1.2e-219:
		tmp = t_2
	elif (x * y) <= 1.75e+178:
		tmp = t_1
	elif (x * y) <= 3.8e+207:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_2 = Float64(b * Float64(a * -0.25))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3e+85)
		tmp = t_3;
	elseif (Float64(x * y) <= -2.45e-179)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.2e-219)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.75e+178)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.8e+207)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (0.0625 * (z * t));
	t_2 = b * (a * -0.25);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -3e+85)
		tmp = t_3;
	elseif ((x * y) <= -2.45e-179)
		tmp = t_1;
	elseif ((x * y) <= -1.2e-219)
		tmp = t_2;
	elseif ((x * y) <= 1.75e+178)
		tmp = t_1;
	elseif ((x * y) <= 3.8e+207)
		tmp = t_2;
	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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3e+85], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2.45e-179], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.2e-219], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.75e+178], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+207], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3e85 or 3.79999999999999986e207 < (*.f64 x y)

   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 a around 0 83.7%

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

   4. Taylor expanded in t around 0 76.6%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   if -3e85 < (*.f64 x y) < -2.45e-179 or -1.20000000000000007e-219 < (*.f64 x y) < 1.75e178

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0 75.5%

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

   4. Taylor expanded in x around 0 65.6%

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

   if -2.45e-179 < (*.f64 x y) < -1.20000000000000007e-219 or 1.75e178 < (*.f64 x y) < 3.79999999999999986e207

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 91.8%

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

      1. associate-*r* 91.8%

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

      2. *-commutative 91.8%

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

      3. *-commutative 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in b around inf 91.8%

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

   7. Taylor expanded in a around inf 91.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3 \cdot 10^{+85}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{-179}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+190}:\\ \;\;\;\;a \cdot \left(\frac{c}{a} - b \cdot 0.25\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-213}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-151}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (+ y (* 0.0625 (/ (* z t) x))))))
   (if (<= x -3.4e+208)
     t_1
     (if (<= x -9e+190)
       (* a (- (/ c a) (* b 0.25)))
       (if (<= x -6.8e-16)
         t_1
         (if (<= x -2.8e-213)
           (+ c (* b (* a -0.25)))
           (if (<= x 7.5e-151) (+ 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 = x * (y + (0.0625 * ((z * t) / x)));
	double tmp;
	if (x <= -3.4e+208) {
		tmp = t_1;
	} else if (x <= -9e+190) {
		tmp = a * ((c / a) - (b * 0.25));
	} else if (x <= -6.8e-16) {
		tmp = t_1;
	} else if (x <= -2.8e-213) {
		tmp = c + (b * (a * -0.25));
	} else if (x <= 7.5e-151) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y + (0.0625d0 * ((z * t) / x)))
    if (x <= (-3.4d+208)) then
        tmp = t_1
    else if (x <= (-9d+190)) then
        tmp = a * ((c / a) - (b * 0.25d0))
    else if (x <= (-6.8d-16)) then
        tmp = t_1
    else if (x <= (-2.8d-213)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (x <= 7.5d-151) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (y + (0.0625 * ((z * t) / x)));
	double tmp;
	if (x <= -3.4e+208) {
		tmp = t_1;
	} else if (x <= -9e+190) {
		tmp = a * ((c / a) - (b * 0.25));
	} else if (x <= -6.8e-16) {
		tmp = t_1;
	} else if (x <= -2.8e-213) {
		tmp = c + (b * (a * -0.25));
	} else if (x <= 7.5e-151) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x * (y + (0.0625 * ((z * t) / x)))
	tmp = 0
	if x <= -3.4e+208:
		tmp = t_1
	elif x <= -9e+190:
		tmp = a * ((c / a) - (b * 0.25))
	elif x <= -6.8e-16:
		tmp = t_1
	elif x <= -2.8e-213:
		tmp = c + (b * (a * -0.25))
	elif x <= 7.5e-151:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(y + Float64(0.0625 * Float64(Float64(z * t) / x))))
	tmp = 0.0
	if (x <= -3.4e+208)
		tmp = t_1;
	elseif (x <= -9e+190)
		tmp = Float64(a * Float64(Float64(c / a) - Float64(b * 0.25)));
	elseif (x <= -6.8e-16)
		tmp = t_1;
	elseif (x <= -2.8e-213)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (x <= 7.5e-151)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x * (y + (0.0625 * ((z * t) / x)));
	tmp = 0.0;
	if (x <= -3.4e+208)
		tmp = t_1;
	elseif (x <= -9e+190)
		tmp = a * ((c / a) - (b * 0.25));
	elseif (x <= -6.8e-16)
		tmp = t_1;
	elseif (x <= -2.8e-213)
		tmp = c + (b * (a * -0.25));
	elseif (x <= 7.5e-151)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(y + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+208], t$95$1, If[LessEqual[x, -9e+190], N[(a * N[(N[(c / a), $MachinePrecision] - N[(b * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e-16], t$95$1, If[LessEqual[x, -2.8e-213], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-151], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.3999999999999998e208 or -8.9999999999999999e190 < x < -6.8e-16 or 7.5000000000000004e-151 < x

   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 x around inf 96.0%

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

   4. Taylor expanded in a around 0 76.5%

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

   5. Taylor expanded in c around 0 61.8%

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

   if -3.3999999999999998e208 < x < -8.9999999999999999e190

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf 75.0%

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

   4. Taylor expanded in c around inf 75.6%

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

   if -6.8e-16 < x < -2.8e-213

   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 62.4%

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

      1. associate-*r* 62.4%

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

      2. *-commutative 62.4%

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

      3. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   if -2.8e-213 < x < 7.5000000000000004e-151

   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 0 82.6%

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

   4. Taylor expanded in x around 0 76.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+190}:\\ \;\;\;\;a \cdot \left(\frac{c}{a} - b \cdot 0.25\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-213}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-151}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.26 \cdot 10^{+159}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -1.6e+81)
     t_2
     (if (<= (* x y) -7.5e-220)
       t_1
       (if (<= (* x y) 1.26e+159)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 3.8e+207) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.6e+81) {
		tmp = t_2;
	} else if ((x * y) <= -7.5e-220) {
		tmp = t_1;
	} else if ((x * y) <= 1.26e+159) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 3.8e+207) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-1.6d+81)) then
        tmp = t_2
    else if ((x * y) <= (-7.5d-220)) then
        tmp = t_1
    else if ((x * y) <= 1.26d+159) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 3.8d+207) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.6e+81) {
		tmp = t_2;
	} else if ((x * y) <= -7.5e-220) {
		tmp = t_1;
	} else if ((x * y) <= 1.26e+159) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 3.8e+207) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.6e+81:
		tmp = t_2
	elif (x * y) <= -7.5e-220:
		tmp = t_1
	elif (x * y) <= 1.26e+159:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 3.8e+207:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.6e+81)
		tmp = t_2;
	elseif (Float64(x * y) <= -7.5e-220)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.26e+159)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 3.8e+207)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.6e+81)
		tmp = t_2;
	elseif ((x * y) <= -7.5e-220)
		tmp = t_1;
	elseif ((x * y) <= 1.26e+159)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 3.8e+207)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.6e+81], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -7.5e-220], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.26e+159], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+207], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.6e81 or 3.79999999999999986e207 < (*.f64 x y)

   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 a around 0 83.7%

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

   4. Taylor expanded in t around 0 76.6%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   if -1.6e81 < (*.f64 x y) < -7.5000000000000002e-220 or 1.2599999999999999e159 < (*.f64 x y) < 3.79999999999999986e207

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

      3. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -7.5000000000000002e-220 < (*.f64 x y) < 1.2599999999999999e159

   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 79.3%

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

   4. Taylor expanded in x around 0 69.2%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{-220}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.26 \cdot 10^{+159}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-138}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= (* x y) -1.75e+61)
     (* x y)
     (if (<= (* x y) -1.55e-257)
       t_1
       (if (<= (* x y) 4.3e-138) c (if (<= (* x y) 3.8e+207) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -1.75e+61) {
		tmp = x * y;
	} else if ((x * y) <= -1.55e-257) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e-138) {
		tmp = c;
	} else if ((x * y) <= 3.8e+207) {
		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 = b * (a * (-0.25d0))
    if ((x * y) <= (-1.75d+61)) then
        tmp = x * y
    else if ((x * y) <= (-1.55d-257)) then
        tmp = t_1
    else if ((x * y) <= 4.3d-138) then
        tmp = c
    else if ((x * y) <= 3.8d+207) 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 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -1.75e+61) {
		tmp = x * y;
	} else if ((x * y) <= -1.55e-257) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e-138) {
		tmp = c;
	} else if ((x * y) <= 3.8e+207) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if (x * y) <= -1.75e+61:
		tmp = x * y
	elif (x * y) <= -1.55e-257:
		tmp = t_1
	elif (x * y) <= 4.3e-138:
		tmp = c
	elif (x * y) <= 3.8e+207:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -1.75e+61)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.55e-257)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.3e-138)
		tmp = c;
	elseif (Float64(x * y) <= 3.8e+207)
		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 = b * (a * -0.25);
	tmp = 0.0;
	if ((x * y) <= -1.75e+61)
		tmp = x * y;
	elseif ((x * y) <= -1.55e-257)
		tmp = t_1;
	elseif ((x * y) <= 4.3e-138)
		tmp = c;
	elseif ((x * y) <= 3.8e+207)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.75e+61], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.55e-257], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.3e-138], c, If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+207], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.75000000000000009e61 or 3.79999999999999986e207 < (*.f64 x y)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 93.4%

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

   4. Taylor expanded in a around 0 84.3%

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

   5. Taylor expanded in x around inf 70.0%

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

   if -1.75000000000000009e61 < (*.f64 x y) < -1.55000000000000004e-257 or 4.3e-138 < (*.f64 x y) < 3.79999999999999986e207

   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 inf 50.7%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

      3. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in b around inf 49.2%

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

   7. Taylor expanded in a around inf 38.9%

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

   if -1.55000000000000004e-257 < (*.f64 x y) < 4.3e-138

   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 40.7%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-138}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+72} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+70}\right):\\ \;\;\;\;\left(c + t\_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* a b) -1e+72) (not (<= (* a b) 5e+70)))
     (- (+ c t_1) (* (* a b) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -1e+72) || !((a * b) <= 5e+70)) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + 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 = 0.0625d0 * (z * t)
    if (((a * b) <= (-1d+72)) .or. (.not. ((a * b) <= 5d+70))) then
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + 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 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -1e+72) || !((a * b) <= 5e+70)) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((a * b) <= -1e+72) or not ((a * b) <= 5e+70):
		tmp = (c + t_1) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -1e+72) || !(Float64(a * b) <= 5e+70))
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((a * b) <= -1e+72) || ~(((a * b) <= 5e+70)))
		tmp = (c + t_1) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+72], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+70]], $MachinePrecision]], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.99999999999999944e71 or 5.0000000000000002e70 < (*.f64 a b)

   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 x around 0 87.4%

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

   if -9.99999999999999944e71 < (*.f64 a b) < 5.0000000000000002e70

   1. Initial program 98.7%

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

   3. Taylor expanded in a around 0 94.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+72} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+70}\right):\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* z (* t 0.0625))))
   (if (<= z -3e+93)
     t_2
     (if (<= z -6.8e-152)
       t_1
       (if (<= z -7e-175) (* b (* a -0.25)) (if (<= z 1.56e-111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if (z <= -3e+93) {
		tmp = t_2;
	} else if (z <= -6.8e-152) {
		tmp = t_1;
	} else if (z <= -7e-175) {
		tmp = b * (a * -0.25);
	} else if (z <= 1.56e-111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = z * (t * 0.0625d0)
    if (z <= (-3d+93)) then
        tmp = t_2
    else if (z <= (-6.8d-152)) then
        tmp = t_1
    else if (z <= (-7d-175)) then
        tmp = b * (a * (-0.25d0))
    else if (z <= 1.56d-111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if (z <= -3e+93) {
		tmp = t_2;
	} else if (z <= -6.8e-152) {
		tmp = t_1;
	} else if (z <= -7e-175) {
		tmp = b * (a * -0.25);
	} else if (z <= 1.56e-111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = z * (t * 0.0625)
	tmp = 0
	if z <= -3e+93:
		tmp = t_2
	elif z <= -6.8e-152:
		tmp = t_1
	elif z <= -7e-175:
		tmp = b * (a * -0.25)
	elif z <= 1.56e-111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (z <= -3e+93)
		tmp = t_2;
	elseif (z <= -6.8e-152)
		tmp = t_1;
	elseif (z <= -7e-175)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (z <= 1.56e-111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = z * (t * 0.0625);
	tmp = 0.0;
	if (z <= -3e+93)
		tmp = t_2;
	elseif (z <= -6.8e-152)
		tmp = t_1;
	elseif (z <= -7e-175)
		tmp = b * (a * -0.25);
	elseif (z <= 1.56e-111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+93], t$95$2, If[LessEqual[z, -6.8e-152], t$95$1, If[LessEqual[z, -7e-175], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e-111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999978e93 or 1.56e-111 < z

   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 x around inf 85.1%

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

   4. Taylor expanded in a around 0 68.8%

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

   5. Taylor expanded in t around inf 49.7%

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

      1. associate-*r* 49.7%

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

   7. Simplified 49.7%

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

   if -2.99999999999999978e93 < z < -6.79999999999999968e-152 or -6.99999999999999997e-175 < z < 1.56e-111

   1. Initial program 99.1%

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

   3. Taylor expanded in a around 0 74.5%

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

   4. Taylor expanded in t around 0 61.0%

      \[\leadsto \color{blue}{c + x \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 61.0%

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

   6. Simplified 61.0%

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

   if -6.79999999999999968e-152 < z < -6.99999999999999997e-175

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 88.3%

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

      1. associate-*r* 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in b around inf 88.3%

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

   7. Taylor expanded in a around inf 76.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-152}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-111}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+236} \lor \neg \left(a \cdot b \leq 10^{+135}\right):\\ \;\;\;\;t\_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* a b) -5e+236) (not (<= (* a b) 1e+135)))
     (- t_1 (* (* a b) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -5e+236) || !((a * b) <= 1e+135)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + 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 = 0.0625d0 * (z * t)
    if (((a * b) <= (-5d+236)) .or. (.not. ((a * b) <= 1d+135))) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + 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 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -5e+236) || !((a * b) <= 1e+135)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((a * b) <= -5e+236) or not ((a * b) <= 1e+135):
		tmp = t_1 - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -5e+236) || !(Float64(a * b) <= 1e+135))
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((a * b) <= -5e+236) || ~(((a * b) <= 1e+135)))
		tmp = t_1 - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+236], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+135]], $MachinePrecision]], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.9999999999999997e236 or 9.99999999999999962e134 < (*.f64 a b)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 91.2%

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

   4. Taylor expanded in z around inf 83.0%

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

   5. Taylor expanded in c around 0 90.2%

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

   if -4.9999999999999997e236 < (*.f64 a b) < 9.99999999999999962e134

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 90.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+236} \lor \neg \left(a \cdot b \leq 10^{+135}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+135}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

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) -2e+151)
     (- (+ c (* x y)) t_1)
     (if (<= (* a b) 1e+135) (+ c (+ (* x y) t_2)) (- 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) <= -2e+151) {
		tmp = (c + (x * y)) - t_1;
	} else if ((a * b) <= 1e+135) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = 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) <= (-2d+151)) then
        tmp = (c + (x * y)) - t_1
    else if ((a * b) <= 1d+135) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = 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) <= -2e+151) {
		tmp = (c + (x * y)) - t_1;
	} else if ((a * b) <= 1e+135) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = 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) <= -2e+151:
		tmp = (c + (x * y)) - t_1
	elif (a * b) <= 1e+135:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = 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) <= -2e+151)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(a * b) <= 1e+135)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(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) <= -2e+151)
		tmp = (c + (x * y)) - t_1;
	elseif ((a * b) <= 1e+135)
		tmp = c + ((x * y) + t_2);
	else
		tmp = 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], -2e+151], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+135], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000003e151

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 89.0%

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

   if -2.00000000000000003e151 < (*.f64 a b) < 9.99999999999999962e134

   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 a around 0 92.5%

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

   if 9.99999999999999962e134 < (*.f64 a b)

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0 89.3%

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

   4. Taylor expanded in z around inf 83.3%

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

   5. Taylor expanded in c around 0 89.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+135}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+157} \lor \neg \left(a \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -6.6e+157) (not (<= a 8e+36)))
   (+ c (* b (* a -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 <= -6.6e+157) || !(a <= 8e+36)) {
		tmp = c + (b * (a * -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 <= (-6.6d+157)) .or. (.not. (a <= 8d+36))) then
        tmp = c + (b * (a * (-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 <= -6.6e+157) || !(a <= 8e+36)) {
		tmp = c + (b * (a * -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 <= -6.6e+157) or not (a <= 8e+36):
		tmp = c + (b * (a * -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 ((a <= -6.6e+157) || !(a <= 8e+36))
		tmp = Float64(c + Float64(b * Float64(a * -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 <= -6.6e+157) || ~((a <= 8e+36)))
		tmp = c + (b * (a * -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[a, -6.6e+157], N[Not[LessEqual[a, 8e+36]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $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 a < -6.6000000000000003e157 or 8.00000000000000034e36 < a

   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 a around inf 58.3%

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

      1. associate-*r* 59.2%

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

      2. *-commutative 59.2%

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

      3. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if -6.6000000000000003e157 < a < 8.00000000000000034e36

   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 a around 0 84.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+157} \lor \neg \left(a \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

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 + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

3. Final simplification 98.1%

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

Alternative 15: 37.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+137}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.55e+69) c (if (<= c 4.5e+137) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.55e+69) {
		tmp = c;
	} else if (c <= 4.5e+137) {
		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 (c <= (-2.55d+69)) then
        tmp = c
    else if (c <= 4.5d+137) 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 (c <= -2.55e+69) {
		tmp = c;
	} else if (c <= 4.5e+137) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.55e+69:
		tmp = c
	elif c <= 4.5e+137:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.55e+69)
		tmp = c;
	elseif (c <= 4.5e+137)
		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 (c <= -2.55e+69)
		tmp = c;
	elseif (c <= 4.5e+137)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.55e+69], c, If[LessEqual[c, 4.5e+137], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -2.54999999999999999e69 or 4.5000000000000001e137 < c

   1. Initial program 98.7%

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

   3. Taylor expanded in c around inf 43.9%

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

   if -2.54999999999999999e69 < c < 4.5000000000000001e137

   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 x around inf 89.0%

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

   4. Taylor expanded in a around 0 66.9%

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

   5. Taylor expanded in x around inf 37.8%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+137}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.6% 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 98.1%

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

3. Taylor expanded in c around inf 18.5%

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

4. Final simplification 18.5%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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))