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

Percentage Accurate: 97.5% → 97.5%

Time: 2.3s

Alternatives: 10

Speedup: 1.0×

• 32.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 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]

Derivation

1. Initial program 99.2%

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

Alternative 2: 87.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;z \cdot t \leq -2.25 \cdot 10^{-82}:\\ \;\;\;\;t\_2 + c\\ \mathbf{elif}\;z \cdot t \leq 1.4 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot y + c\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)) (t_2 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= (* z t) -2.25e-82)
     (+ t_2 c)
     (if (<= (* z t) 1.4e+75) (- (+ (* x y) c) t_1) (- 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) / 4.0;
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -2.25e-82) {
		tmp = t_2 + c;
	} else if ((z * t) <= 1.4e+75) {
		tmp = ((x * y) + c) - t_1;
	} 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) / 4.0d0
    t_2 = (x * y) + ((z * t) / 16.0d0)
    if ((z * t) <= (-2.25d-82)) then
        tmp = t_2 + c
    else if ((z * t) <= 1.4d+75) then
        tmp = ((x * y) + c) - t_1
    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) / 4.0;
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -2.25e-82) {
		tmp = t_2 + c;
	} else if ((z * t) <= 1.4e+75) {
		tmp = ((x * y) + c) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	t_2 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if (z * t) <= -2.25e-82:
		tmp = t_2 + c
	elif (z * t) <= 1.4e+75:
		tmp = ((x * y) + c) - t_1
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (Float64(z * t) <= -2.25e-82)
		tmp = Float64(t_2 + c);
	elseif (Float64(z * t) <= 1.4e+75)
		tmp = Float64(Float64(Float64(x * y) + c) - t_1);
	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) / 4.0;
	t_2 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if ((z * t) <= -2.25e-82)
		tmp = t_2 + c;
	elseif ((z * t) <= 1.4e+75)
		tmp = ((x * y) + c) - t_1;
	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] / 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2.25e-82], N[(t$95$2 + c), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1.4e+75], N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.2499999999999999e-82

   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 x around 0

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

   5. Applied rewrites 88.9%

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

   if -2.2499999999999999e-82 < (*.f64 z t) < 1.40000000000000006e75

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.3%

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

   if 1.40000000000000006e75 < (*.f64 z t)

   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 0

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

   5. Applied rewrites 92.9%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;z \cdot t \leq -2.25 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 1.55 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y - \frac{a \cdot b}{4}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= (* z t) -2.25e-82)
     t_1
     (if (<= (* z t) 1.55e-8)
       (- (* x y) (/ (* a b) 4.0))
       (if (<= (* z t) 2e+75) (+ (* x y) c) t_1)))))

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);
	double tmp;
	if ((z * t) <= -2.25e-82) {
		tmp = t_1;
	} else if ((z * t) <= 1.55e-8) {
		tmp = (x * y) - ((a * b) / 4.0);
	} else if ((z * t) <= 2e+75) {
		tmp = (x * y) + c;
	} 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) + ((z * t) / 16.0d0)
    if ((z * t) <= (-2.25d-82)) then
        tmp = t_1
    else if ((z * t) <= 1.55d-8) then
        tmp = (x * y) - ((a * b) / 4.0d0)
    else if ((z * t) <= 2d+75) then
        tmp = (x * y) + c
    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) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -2.25e-82) {
		tmp = t_1;
	} else if ((z * t) <= 1.55e-8) {
		tmp = (x * y) - ((a * b) / 4.0);
	} else if ((z * t) <= 2e+75) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if (z * t) <= -2.25e-82:
		tmp = t_1
	elif (z * t) <= 1.55e-8:
		tmp = (x * y) - ((a * b) / 4.0)
	elif (z * t) <= 2e+75:
		tmp = (x * y) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (Float64(z * t) <= -2.25e-82)
		tmp = t_1;
	elseif (Float64(z * t) <= 1.55e-8)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) / 4.0));
	elseif (Float64(z * t) <= 2e+75)
		tmp = Float64(Float64(x * y) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if ((z * t) <= -2.25e-82)
		tmp = t_1;
	elseif ((z * t) <= 1.55e-8)
		tmp = (x * y) - ((a * b) / 4.0);
	elseif ((z * t) <= 2e+75)
		tmp = (x * y) + c;
	else
		tmp = t_1;
	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[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2.25e-82], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1.55e-8], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+75], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.2499999999999999e-82 or 1.99999999999999985e75 < (*.f64 z t)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 78.1%

      \[\leadsto x \cdot y + \color{blue}{\frac{z \cdot t}{16}} \]

   if -2.2499999999999999e-82 < (*.f64 z t) < 1.55e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.4%

      \[\leadsto x \cdot y - \frac{\color{blue}{a \cdot b}}{4} \]

   if 1.55e-8 < (*.f64 z t) < 1.99999999999999985e75

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 70.3%

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

Alternative 4: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) + c\\ \mathbf{if}\;z \cdot t \leq -2.25 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2.55 \cdot 10^{+31}:\\ \;\;\;\;\left(x \cdot y + c\right) - \frac{a \cdot b}{4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (+ (* x y) (/ (* z t) 16.0)) c)))
   (if (<= (* z t) -2.25e-82)
     t_1
     (if (<= (* z t) 2.55e+31) (- (+ (* x y) c) (/ (* a b) 4.0)) t_1))))

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)) + c;
	double tmp;
	if ((z * t) <= -2.25e-82) {
		tmp = t_1;
	} else if ((z * t) <= 2.55e+31) {
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	} 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) + ((z * t) / 16.0d0)) + c
    if ((z * t) <= (-2.25d-82)) then
        tmp = t_1
    else if ((z * t) <= 2.55d+31) then
        tmp = ((x * y) + c) - ((a * b) / 4.0d0)
    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) + ((z * t) / 16.0)) + c;
	double tmp;
	if ((z * t) <= -2.25e-82) {
		tmp = t_1;
	} else if ((z * t) <= 2.55e+31) {
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) + c
	tmp = 0
	if (z * t) <= -2.25e-82:
		tmp = t_1
	elif (z * t) <= 2.55e+31:
		tmp = ((x * y) + c) - ((a * b) / 4.0)
	else:
		tmp = t_1
	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)) + c)
	tmp = 0.0
	if (Float64(z * t) <= -2.25e-82)
		tmp = t_1;
	elseif (Float64(z * t) <= 2.55e+31)
		tmp = Float64(Float64(Float64(x * y) + c) - Float64(Float64(a * b) / 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) + c;
	tmp = 0.0;
	if ((z * t) <= -2.25e-82)
		tmp = t_1;
	elseif ((z * t) <= 2.55e+31)
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	else
		tmp = t_1;
	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] + c), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2.25e-82], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2.55e+31], N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.2499999999999999e-82 or 2.5499999999999998e31 < (*.f64 z t)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.3%

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

   if -2.2499999999999999e-82 < (*.f64 z t) < 2.5499999999999998e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.4%

      \[\leadsto \left(x \cdot y + c\right) - \frac{\color{blue}{a \cdot b}}{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;z \cdot t \leq -3.7 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 3.8 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot y + c\right) - \frac{a \cdot b}{4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= (* z t) -3.7e+211)
     t_1
     (if (<= (* z t) 3.8e+77) (- (+ (* x y) c) (/ (* a b) 4.0)) t_1))))

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);
	double tmp;
	if ((z * t) <= -3.7e+211) {
		tmp = t_1;
	} else if ((z * t) <= 3.8e+77) {
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	} 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) + ((z * t) / 16.0d0)
    if ((z * t) <= (-3.7d+211)) then
        tmp = t_1
    else if ((z * t) <= 3.8d+77) then
        tmp = ((x * y) + c) - ((a * b) / 4.0d0)
    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) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -3.7e+211) {
		tmp = t_1;
	} else if ((z * t) <= 3.8e+77) {
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if (z * t) <= -3.7e+211:
		tmp = t_1
	elif (z * t) <= 3.8e+77:
		tmp = ((x * y) + c) - ((a * b) / 4.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (Float64(z * t) <= -3.7e+211)
		tmp = t_1;
	elseif (Float64(z * t) <= 3.8e+77)
		tmp = Float64(Float64(Float64(x * y) + c) - Float64(Float64(a * b) / 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if ((z * t) <= -3.7e+211)
		tmp = t_1;
	elseif ((z * t) <= 3.8e+77)
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	else
		tmp = t_1;
	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[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -3.7e+211], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 3.8e+77], N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -3.7000000000000001e211 or 3.8000000000000001e77 < (*.f64 z t)

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 88.0%

      \[\leadsto x \cdot y + \color{blue}{\frac{z \cdot t}{16}} \]

   if -3.7000000000000001e211 < (*.f64 z t) < 3.8000000000000001e77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 90.8%

      \[\leadsto \left(x \cdot y + c\right) - \frac{\color{blue}{a \cdot b}}{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;z \cdot t \leq -1.12 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= (* z t) -1.12e-111) t_1 (if (<= (* z t) 2e+75) (+ (* x y) c) t_1))))

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);
	double tmp;
	if ((z * t) <= -1.12e-111) {
		tmp = t_1;
	} else if ((z * t) <= 2e+75) {
		tmp = (x * y) + c;
	} 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) + ((z * t) / 16.0d0)
    if ((z * t) <= (-1.12d-111)) then
        tmp = t_1
    else if ((z * t) <= 2d+75) then
        tmp = (x * y) + c
    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) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -1.12e-111) {
		tmp = t_1;
	} else if ((z * t) <= 2e+75) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if (z * t) <= -1.12e-111:
		tmp = t_1
	elif (z * t) <= 2e+75:
		tmp = (x * y) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (Float64(z * t) <= -1.12e-111)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e+75)
		tmp = Float64(Float64(x * y) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if ((z * t) <= -1.12e-111)
		tmp = t_1;
	elseif ((z * t) <= 2e+75)
		tmp = (x * y) + c;
	else
		tmp = t_1;
	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[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1.12e-111], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e+75], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.12000000000000009e-111 or 1.99999999999999985e75 < (*.f64 z t)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.7%

      \[\leadsto x \cdot y + \color{blue}{\frac{z \cdot t}{16}} \]

   if -1.12000000000000009e-111 < (*.f64 z t) < 1.99999999999999985e75

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 61.2%

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

Alternative 7: 39.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.06 \cdot 10^{-32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0.0092:\\ \;\;\;\;a \cdot b + c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1.06e-32)
   (* x y)
   (if (<= (* x y) 0.0092) (+ (* a b) c) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1.06e-32) {
		tmp = x * y;
	} else if ((x * y) <= 0.0092) {
		tmp = (a * b) + c;
	} 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) :: tmp
    if ((x * y) <= (-1.06d-32)) then
        tmp = x * y
    else if ((x * y) <= 0.0092d0) then
        tmp = (a * b) + c
    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 tmp;
	if ((x * y) <= -1.06e-32) {
		tmp = x * y;
	} else if ((x * y) <= 0.0092) {
		tmp = (a * b) + c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1.06e-32:
		tmp = x * y
	elif (x * y) <= 0.0092:
		tmp = (a * b) + c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1.06e-32)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 0.0092)
		tmp = Float64(Float64(a * b) + c);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -1.06e-32)
		tmp = x * y;
	elseif ((x * y) <= 0.0092)
		tmp = (a * b) + c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.06e-32], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0092], N[(N[(a * b), $MachinePrecision] + c), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.05999999999999994e-32 or 0.0091999999999999998 < (*.f64 x y)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 59.4%

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

   if -1.05999999999999994e-32 < (*.f64 x y) < 0.0091999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \color{blue}{\left(t \cdot z\right)} + c \]

   8. Applied rewrites 9.3%

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

   9. Taylor expanded in x around -inf

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

   11. Applied rewrites 30.1%

       \[\leadsto a \cdot \color{blue}{b} + c \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 48.4% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ x \cdot y + c \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 49.9%

   \[\leadsto \color{blue}{x \cdot y} + c \]
6. Add Preprocessing

Alternative 9: 28.1% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ x \cdot y \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x * y)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * y), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 79.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 31.1%

   \[\leadsto x \cdot \color{blue}{y} \]
9. Add Preprocessing

Alternative 10: 2.7% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

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 = a * b
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c)
	return Float64(a * b)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 79.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 73.3%

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

9. Taylor expanded in x around inf

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

11. Applied rewrites 2.1%

    \[\leadsto \frac{a \cdot b}{4} - \frac{\color{blue}{a \cdot b}}{4} \]

12. Taylor expanded in y around inf

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

14. Applied rewrites 2.2%

    \[\leadsto \color{blue}{a \cdot b} \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  :pre (TRUE)
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))