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

Percentage Accurate: 97.6% → 98.9%

Time: 12.8s

Alternatives: 12

Speedup: 0.1×

• 33.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate--l+ 98.5%

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

   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 99.3%

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

   5. distribute-neg-frac2 99.3%

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

   6. metadata-eval 99.3%

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

3. Simplified 99.3%

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

Alternative 2: 98.2% 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 98.5%

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

   1. associate-+l- 98.5%

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

   2. *-commutative 98.5%

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

   3. associate-+l- 98.5%

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

   4. fma-define 98.9%

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

   5. *-commutative 98.9%

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

   6. associate-/l* 98.9%

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

   7. associate-/l* 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -8.8e+58)
     t_1
     (if (<= (* x y) -1e-79)
       (* b (* a -0.25))
       (if (<= (* x y) 2.5e+16) (+ 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 = c + (x * y);
	double tmp;
	if ((x * y) <= -8.8e+58) {
		tmp = t_1;
	} else if ((x * y) <= -1e-79) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 2.5e+16) {
		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 = c + (x * y)
    if ((x * y) <= (-8.8d+58)) then
        tmp = t_1
    else if ((x * y) <= (-1d-79)) then
        tmp = b * (a * (-0.25d0))
    else if ((x * y) <= 2.5d+16) 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 = c + (x * y);
	double tmp;
	if ((x * y) <= -8.8e+58) {
		tmp = t_1;
	} else if ((x * y) <= -1e-79) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 2.5e+16) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -8.8e+58:
		tmp = t_1
	elif (x * y) <= -1e-79:
		tmp = b * (a * -0.25)
	elif (x * y) <= 2.5e+16:
		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(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -8.8e+58)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-79)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(x * y) <= 2.5e+16)
		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 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -8.8e+58)
		tmp = t_1;
	elseif ((x * y) <= -1e-79)
		tmp = b * (a * -0.25);
	elseif ((x * y) <= 2.5e+16)
		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[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.8e+58], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-79], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+16], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.8000000000000003e58 or 2.5e16 < (*.f64 x y)

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 83.3%

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

   4. Taylor expanded in t around 0 71.0%

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

   if -8.8000000000000003e58 < (*.f64 x y) < -1e-79

   1. Initial program 96.8%

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

      1. associate--l+ 96.8%

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

      2. fma-define 96.8%

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

      3. associate-/l* 96.8%

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

      4. fma-neg 100.0%

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

      5. distribute-neg-frac2 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*r* 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in c around inf 66.8%

      \[\leadsto \color{blue}{c \cdot \left(1 + -0.25 \cdot \frac{a \cdot b}{c}\right)} \]

   9. Taylor expanded in c around 0 57.2%

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

       1. associate-*r* 57.2%

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

       2. *-commutative 57.2%

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

       3. *-commutative 57.2%

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

   11. Simplified 57.2%

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

   if -1e-79 < (*.f64 x y) < 2.5e16

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0 70.2%

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

   4. Taylor expanded in t around inf 66.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+58}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+15}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-43}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= a -6.8e+108)
     t_1
     (if (<= a -5.8e+15)
       c
       (if (<= a -2.5e-246) (* t (* z 0.0625)) (if (<= a 9e-43) c t_1))))))

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 (a <= -6.8e+108) {
		tmp = t_1;
	} else if (a <= -5.8e+15) {
		tmp = c;
	} else if (a <= -2.5e-246) {
		tmp = t * (z * 0.0625);
	} else if (a <= 9e-43) {
		tmp = 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 = b * (a * (-0.25d0))
    if (a <= (-6.8d+108)) then
        tmp = t_1
    else if (a <= (-5.8d+15)) then
        tmp = c
    else if (a <= (-2.5d-246)) then
        tmp = t * (z * 0.0625d0)
    else if (a <= 9d-43) then
        tmp = 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 = b * (a * -0.25);
	double tmp;
	if (a <= -6.8e+108) {
		tmp = t_1;
	} else if (a <= -5.8e+15) {
		tmp = c;
	} else if (a <= -2.5e-246) {
		tmp = t * (z * 0.0625);
	} else if (a <= 9e-43) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if a <= -6.8e+108:
		tmp = t_1
	elif a <= -5.8e+15:
		tmp = c
	elif a <= -2.5e-246:
		tmp = t * (z * 0.0625)
	elif a <= 9e-43:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (a <= -6.8e+108)
		tmp = t_1;
	elseif (a <= -5.8e+15)
		tmp = c;
	elseif (a <= -2.5e-246)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (a <= 9e-43)
		tmp = c;
	else
		tmp = t_1;
	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 (a <= -6.8e+108)
		tmp = t_1;
	elseif (a <= -5.8e+15)
		tmp = c;
	elseif (a <= -2.5e-246)
		tmp = t * (z * 0.0625);
	elseif (a <= 9e-43)
		tmp = c;
	else
		tmp = t_1;
	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[a, -6.8e+108], t$95$1, If[LessEqual[a, -5.8e+15], c, If[LessEqual[a, -2.5e-246], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-43], c, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.79999999999999992e108 or 9.0000000000000005e-43 < a

   1. Initial program 97.4%

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

      1. associate--l+ 97.4%

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

      2. fma-define 98.3%

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

      3. associate-/l* 98.3%

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

      4. fma-neg 99.1%

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

      5. distribute-neg-frac2 99.1%

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

      6. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in a around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*r* 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(1 + -0.25 \cdot \frac{a \cdot b}{c}\right)} \]

   9. Taylor expanded in c around 0 51.5%

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

       1. associate-*r* 51.5%

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

       2. *-commutative 51.5%

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

       3. *-commutative 51.5%

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

   11. Simplified 51.5%

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

   if -6.79999999999999992e108 < a < -5.8e15 or -2.4999999999999998e-246 < a < 9.0000000000000005e-43

   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 30.5%

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

   if -5.8e15 < a < -2.4999999999999998e-246

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 82.5%

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

   4. Taylor expanded in t around inf 53.2%

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

   5. Taylor expanded in c around 0 34.2%

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

      1. associate-*r* 50.2%

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

      2. *-commutative 50.2%

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

      3. associate-*r* 50.2%

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

   7. Simplified 34.2%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+15}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-43}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-43} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e-43) (not (<= (* a b) 2e-32)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e-43) || !((a * b) <= 2e-32)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d-43)) .or. (.not. ((a * b) <= 2d-32))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e-43) || !((a * b) <= 2e-32)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e-43) or not ((a * b) <= 2e-32):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e-43) || !(Float64(a * b) <= 2e-32))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e-43) || ~(((a * b) <= 2e-32)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e-43], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e-32]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.00000000000000019e-43 or 2.00000000000000011e-32 < (*.f64 a b)

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 87.6%

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

   if -5.00000000000000019e-43 < (*.f64 a b) < 2.00000000000000011e-32

   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 0 100.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-43} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+223} \lor \neg \left(a \cdot b \leq 10^{+141}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+223) (not (<= (* a b) 1e+141)))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+223) || !((a * b) <= 1e+141)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+223)) .or. (.not. ((a * b) <= 1d+141))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+223) || !((a * b) <= 1e+141)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+223) or not ((a * b) <= 1e+141):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+223) || !(Float64(a * b) <= 1e+141))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+223) || ~(((a * b) <= 1e+141)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+223], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+141]], $MachinePrecision]], N[(c + N[(a * N[(b * -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 (*.f64 a b) < -4.99999999999999985e223 or 1.00000000000000002e141 < (*.f64 a b)

   1. Initial program 93.9%

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

      1. associate--l+ 93.9%

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

      2. fma-define 95.5%

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

      3. associate-/l* 95.5%

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

      4. fma-neg 97.1%

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

      5. distribute-neg-frac2 97.1%

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

      6. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in a around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*r* 87.5%

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

   7. Simplified 87.5%

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

   if -4.99999999999999985e223 < (*.f64 a b) < 1.00000000000000002e141

   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 87.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+223} \lor \neg \left(a \cdot b \leq 10^{+141}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+223}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+132}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+223)
   (+ c (* a (* b -0.25)))
   (if (<= (* a b) 1e+132)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (* t (* z 0.0625)) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+223) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 1e+132) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (t * (z * 0.0625)) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-5d+223)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 1d+132) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (t * (z * 0.0625d0)) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+223) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 1e+132) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (t * (z * 0.0625)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+223:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 1e+132:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (t * (z * 0.0625)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+223)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 1e+132)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(t * Float64(z * 0.0625)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+223)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 1e+132)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (t * (z * 0.0625)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+223], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+132], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.99999999999999985e223

   1. Initial program 90.9%

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

      1. associate--l+ 90.9%

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

      2. fma-define 90.9%

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

      3. associate-/l* 90.9%

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

      4. fma-neg 95.5%

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

      5. distribute-neg-frac2 95.5%

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

      6. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around inf 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*r* 91.2%

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

   7. Simplified 91.2%

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

   if -4.99999999999999985e223 < (*.f64 a b) < 9.99999999999999991e131

   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 87.0%

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

   if 9.99999999999999991e131 < (*.f64 a b)

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 90.8%

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

   4. Taylor expanded in c around 0 88.5%

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

      1. associate-*r* 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.5%

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

   6. Simplified 88.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+223}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+132}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-43} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e-43) (not (<= (* a b) 2e-32)))
   (+ c (* a (* b -0.25)))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e-43) || !((a * b) <= 2e-32)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d-43)) .or. (.not. ((a * b) <= 2d-32))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e-43) || !((a * b) <= 2e-32)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e-43) or not ((a * b) <= 2e-32):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e-43) || !(Float64(a * b) <= 2e-32))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e-43) || ~(((a * b) <= 2e-32)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e-43], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e-32]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.00000000000000019e-43 or 2.00000000000000011e-32 < (*.f64 a b)

   1. Initial program 97.4%

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

      1. associate--l+ 97.4%

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

      2. fma-define 98.1%

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

      3. associate-/l* 98.1%

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

      4. fma-neg 98.8%

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

      5. distribute-neg-frac2 98.8%

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

      6. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in a around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*r* 69.5%

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

   7. Simplified 69.5%

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

   if -5.00000000000000019e-43 < (*.f64 a b) < 2.00000000000000011e-32

   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 0 100.0%

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

   4. Taylor expanded in t around inf 67.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-43} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c + \left(x \cdot y + \left(0.0625 \cdot \left(z \cdot t\right) - \frac{a}{\frac{4}{b}}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (+ (* x y) (- (* 0.0625 (* z t)) (/ a (/ 4.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((x * y) + ((0.0625 * (z * t)) - (a / (4.0 / 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 = c + ((x * y) + ((0.0625d0 * (z * t)) - (a / (4.0d0 / b))))
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) + ((0.0625 * (z * t)) - (a / (4.0 / b))));
}

Python

def code(x, y, z, t, a, b, c):
	return c + ((x * y) + ((0.0625 * (z * t)) - (a / (4.0 / b))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(x * y) + Float64(Float64(0.0625 * Float64(z * t)) - Float64(a / Float64(4.0 / b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + ((x * y) + ((0.0625 * (z * t)) - (a / (4.0 / b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a / N[(4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

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

   1. clear-num 98.4%

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

   2. inv-pow 98.4%

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

   3. *-commutative 98.4%

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

   4. associate-/r* 98.7%

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

4. Applied egg-rr 98.7%

   \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \color{blue}{{\left(\frac{\frac{4}{b}}{a}\right)}^{-1}}\right) + c \]
5. Step-by-step derivation

   1. unpow-1 98.7%

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

6. Simplified 98.7%

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

   1. associate--l+ 98.7%

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

   2. div-inv 98.7%

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

   3. metadata-eval 98.7%

      \[\leadsto \left(x \cdot y + \left(\left(z \cdot t\right) \cdot \color{blue}{0.0625} - \frac{1}{\frac{\frac{4}{b}}{a}}\right)\right) + c \]

   4. *-commutative 98.7%

      \[\leadsto \left(x \cdot y + \left(\color{blue}{0.0625 \cdot \left(z \cdot t\right)} - \frac{1}{\frac{\frac{4}{b}}{a}}\right)\right) + c \]

   5. *-commutative 98.7%

      \[\leadsto \left(x \cdot y + \left(0.0625 \cdot \color{blue}{\left(t \cdot z\right)} - \frac{1}{\frac{\frac{4}{b}}{a}}\right)\right) + c \]

   6. clear-num 98.8%

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

8. Applied egg-rr 98.8%

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

9. Final simplification 98.8%

   \[\leadsto c + \left(x \cdot y + \left(0.0625 \cdot \left(z \cdot t\right) - \frac{a}{\frac{4}{b}}\right)\right) \]
10. Add Preprocessing

Alternative 10: 55.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+111} \lor \neg \left(a \leq 4 \cdot 10^{+65}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -2.4e+111) (not (<= a 4e+65))) (* b (* a -0.25)) (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.4e+111) || !(a <= 4e+65)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-2.4d+111)) .or. (.not. (a <= 4d+65))) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.4e+111) || !(a <= 4e+65)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -2.4e+111) or not (a <= 4e+65):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -2.4e+111) || !(a <= 4e+65))
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -2.4e+111) || ~((a <= 4e+65)))
		tmp = b * (a * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -2.4e+111], N[Not[LessEqual[a, 4e+65]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.40000000000000006e111 or 4e65 < a

   1. Initial program 96.6%

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

      1. associate--l+ 96.6%

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

      2. fma-define 97.8%

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

      3. associate-/l* 97.8%

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

      4. fma-neg 98.9%

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

      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. Taylor expanded in a around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*r* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in c around inf 61.0%

      \[\leadsto \color{blue}{c \cdot \left(1 + -0.25 \cdot \frac{a \cdot b}{c}\right)} \]

   9. Taylor expanded in c around 0 58.3%

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

       1. associate-*r* 58.3%

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

       2. *-commutative 58.3%

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

       3. *-commutative 58.3%

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

   11. Simplified 58.3%

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

   if -2.40000000000000006e111 < a < 4e65

   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 84.4%

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

   4. Taylor expanded in t around 0 55.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+111} \lor \neg \left(a \leq 4 \cdot 10^{+65}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.55e-13) c (if (<= c 6.2e+85) (* b (* a -0.25)) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.55e-13) {
		tmp = c;
	} else if (c <= 6.2e+85) {
		tmp = b * (a * -0.25);
	} 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 <= (-1.55d-13)) then
        tmp = c
    else if (c <= 6.2d+85) then
        tmp = b * (a * (-0.25d0))
    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 <= -1.55e-13) {
		tmp = c;
	} else if (c <= 6.2e+85) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.55e-13:
		tmp = c
	elif c <= 6.2e+85:
		tmp = b * (a * -0.25)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.55e-13)
		tmp = c;
	elseif (c <= 6.2e+85)
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -1.55e-13)
		tmp = c;
	elseif (c <= 6.2e+85)
		tmp = b * (a * -0.25);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.55e-13], c, If[LessEqual[c, 6.2e+85], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -1.55e-13 or 6.20000000000000023e85 < c

   1. Initial program 99.0%

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

   3. Taylor expanded in c around inf 44.0%

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

   if -1.55e-13 < c < 6.20000000000000023e85

   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 98.1%

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

      3. associate-/l* 98.1%

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

      4. fma-neg 98.8%

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

      5. distribute-neg-frac2 98.8%

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

      6. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in a around inf 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-*r* 45.2%

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

   7. Simplified 45.2%

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

   8. Taylor expanded in c around inf 34.7%

      \[\leadsto \color{blue}{c \cdot \left(1 + -0.25 \cdot \frac{a \cdot b}{c}\right)} \]

   9. Taylor expanded in c around 0 41.3%

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

       1. associate-*r* 41.8%

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

       2. *-commutative 41.8%

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

       3. *-commutative 41.8%

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

   11. Simplified 41.8%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 22.0% 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 98.5%

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

3. Taylor expanded in c around inf 21.5%

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

Reproduce

herbie shell --seed 2024145 
(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))