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

Percentage Accurate: 97.8% → 97.8%

Time: 11.8s

Alternatives: 18

Speedup: 1.0×

• 32.9% 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: 97.8% 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: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. +-commutative N/A

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

   2. sub-neg N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

   6. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   10. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

   12. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

   13. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

   17. *-lowering-*.f64 97.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

3. Simplified 97.8%

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

   1. +-commutative N/A

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

   2. frac-2neg N/A

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

   3. distribute-frac-neg N/A

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

   4. unsub-neg N/A

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

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right), \color{blue}{\left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)}\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a \cdot b}}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   7. associate-/l* N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{t}{16}\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a} \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   8. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{1}{\frac{16}{t}}\right), \left(x \cdot y + c\right)\right), \left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   9. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{z}{\frac{16}{t}}\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a} \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{16}{t}\right)\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a} \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(x \cdot y + c\right)\right), \left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   12. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\left(x \cdot y\right), c\right)\right), \left(\frac{a \cdot \color{blue}{b}}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

   14. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \mathsf{/.f64}\left(\left(a \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(-4\right)\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(\color{blue}{-4}\right)\right)\right)\right) \]

   16. metadata-eval 98.1%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right) \]

6. Applied egg-rr 98.1%

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

Alternative 2: 41.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+64}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+150)
     (* a (/ b -4.0))
     (if (<= (* a b) -4e+84)
       c
       (if (<= (* a b) -5e-49)
         (* x y)
         (if (<= (* a b) -1e-163)
           t_1
           (if (<= (* a b) 1e+64)
             c
             (if (<= (* a b) 2e+107) t_1 (* (* a b) -0.25)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= -4e+84) {
		tmp = c;
	} else if ((a * b) <= -5e-49) {
		tmp = x * y;
	} else if ((a * b) <= -1e-163) {
		tmp = t_1;
	} else if ((a * b) <= 1e+64) {
		tmp = c;
	} else if ((a * b) <= 2e+107) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+150)) then
        tmp = a * (b / (-4.0d0))
    else if ((a * b) <= (-4d+84)) then
        tmp = c
    else if ((a * b) <= (-5d-49)) then
        tmp = x * y
    else if ((a * b) <= (-1d-163)) then
        tmp = t_1
    else if ((a * b) <= 1d+64) then
        tmp = c
    else if ((a * b) <= 2d+107) then
        tmp = t_1
    else
        tmp = (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 t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= -4e+84) {
		tmp = c;
	} else if ((a * b) <= -5e-49) {
		tmp = x * y;
	} else if ((a * b) <= -1e-163) {
		tmp = t_1;
	} else if ((a * b) <= 1e+64) {
		tmp = c;
	} else if ((a * b) <= 2e+107) {
		tmp = t_1;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+150:
		tmp = a * (b / -4.0)
	elif (a * b) <= -4e+84:
		tmp = c
	elif (a * b) <= -5e-49:
		tmp = x * y
	elif (a * b) <= -1e-163:
		tmp = t_1
	elif (a * b) <= 1e+64:
		tmp = c
	elif (a * b) <= 2e+107:
		tmp = t_1
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+150)
		tmp = Float64(a * Float64(b / -4.0));
	elseif (Float64(a * b) <= -4e+84)
		tmp = c;
	elseif (Float64(a * b) <= -5e-49)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -1e-163)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e+64)
		tmp = c;
	elseif (Float64(a * b) <= 2e+107)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) * -0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+150)
		tmp = a * (b / -4.0);
	elseif ((a * b) <= -4e+84)
		tmp = c;
	elseif ((a * b) <= -5e-49)
		tmp = x * y;
	elseif ((a * b) <= -1e-163)
		tmp = t_1;
	elseif ((a * b) <= 1e+64)
		tmp = c;
	elseif ((a * b) <= 2e+107)
		tmp = t_1;
	else
		tmp = (a * b) * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+150], N[(a * N[(b / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4e+84], c, If[LessEqual[N[(a * b), $MachinePrecision], -5e-49], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-163], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e+64], c, If[LessEqual[N[(a * b), $MachinePrecision], 2e+107], t$95$1, N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -5.00000000000000009e150

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 82.1%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{-4}\right), \color{blue}{a}\right) \]

      7. /-lowering-/.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, -4\right), a\right) \]

   9. Applied egg-rr 84.2%

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

   if -5.00000000000000009e150 < (*.f64 a b) < -4.00000000000000023e84 or -9.99999999999999923e-164 < (*.f64 a b) < 1.00000000000000002e64

   1. Initial program 98.6%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   6. Step-by-step derivation

   7. Simplified 45.6%

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

   if -4.00000000000000023e84 < (*.f64 a b) < -4.9999999999999999e-49

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 59.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 59.4%

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

   if -4.9999999999999999e-49 < (*.f64 a b) < -9.99999999999999923e-164 or 1.00000000000000002e64 < (*.f64 a b) < 1.9999999999999999e107

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{16}, \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 72.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 72.6%

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

   if 1.9999999999999999e107 < (*.f64 a b)

   1. Initial program 94.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 94.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 94.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 69.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-163}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+64}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+107}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 3 \cdot 10^{+65}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) -0.25)))
   (if (<= (* a b) -6.5e+148)
     t_2
     (if (<= (* a b) -1.65e+83)
       c
       (if (<= (* a b) -1.55e-49)
         (* x y)
         (if (<= (* a b) -1.5e-175)
           t_1
           (if (<= (* a b) 3e+65) c (if (<= (* a b) 2.6e+111) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -6.5e+148) {
		tmp = t_2;
	} else if ((a * b) <= -1.65e+83) {
		tmp = c;
	} else if ((a * b) <= -1.55e-49) {
		tmp = x * y;
	} else if ((a * b) <= -1.5e-175) {
		tmp = t_1;
	} else if ((a * b) <= 3e+65) {
		tmp = c;
	} else if ((a * b) <= 2.6e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (a * b) * (-0.25d0)
    if ((a * b) <= (-6.5d+148)) then
        tmp = t_2
    else if ((a * b) <= (-1.65d+83)) then
        tmp = c
    else if ((a * b) <= (-1.55d-49)) then
        tmp = x * y
    else if ((a * b) <= (-1.5d-175)) then
        tmp = t_1
    else if ((a * b) <= 3d+65) then
        tmp = c
    else if ((a * b) <= 2.6d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -6.5e+148) {
		tmp = t_2;
	} else if ((a * b) <= -1.65e+83) {
		tmp = c;
	} else if ((a * b) <= -1.55e-49) {
		tmp = x * y;
	} else if ((a * b) <= -1.5e-175) {
		tmp = t_1;
	} else if ((a * b) <= 3e+65) {
		tmp = c;
	} else if ((a * b) <= 2.6e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -6.5e+148:
		tmp = t_2
	elif (a * b) <= -1.65e+83:
		tmp = c
	elif (a * b) <= -1.55e-49:
		tmp = x * y
	elif (a * b) <= -1.5e-175:
		tmp = t_1
	elif (a * b) <= 3e+65:
		tmp = c
	elif (a * b) <= 2.6e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -6.5e+148)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.65e+83)
		tmp = c;
	elseif (Float64(a * b) <= -1.55e-49)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -1.5e-175)
		tmp = t_1;
	elseif (Float64(a * b) <= 3e+65)
		tmp = c;
	elseif (Float64(a * b) <= 2.6e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -6.5e+148)
		tmp = t_2;
	elseif ((a * b) <= -1.65e+83)
		tmp = c;
	elseif ((a * b) <= -1.55e-49)
		tmp = x * y;
	elseif ((a * b) <= -1.5e-175)
		tmp = t_1;
	elseif ((a * b) <= 3e+65)
		tmp = c;
	elseif ((a * b) <= 2.6e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -6.5e+148], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.65e+83], c, If[LessEqual[N[(a * b), $MachinePrecision], -1.55e-49], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.5e-175], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3e+65], c, If[LessEqual[N[(a * b), $MachinePrecision], 2.6e+111], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -6.49999999999999947e148 or 2.5999999999999999e111 < (*.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. Step-by-step derivation

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 95.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 95.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 74.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 74.6%

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

   if -6.49999999999999947e148 < (*.f64 a b) < -1.64999999999999992e83 or -1.5e-175 < (*.f64 a b) < 3.0000000000000002e65

   1. Initial program 98.6%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   6. Step-by-step derivation

   7. Simplified 45.6%

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

   if -1.64999999999999992e83 < (*.f64 a b) < -1.55e-49

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 59.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 59.4%

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

   if -1.55e-49 < (*.f64 a b) < -1.5e-175 or 3.0000000000000002e65 < (*.f64 a b) < 2.5999999999999999e111

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{16}, \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 72.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 72.6%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{-175}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 3 \cdot 10^{+65}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+82}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{-178}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{+61}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -8.2e+147)
     t_1
     (if (<= (* a b) -5e+82)
       c
       (if (<= (* a b) -2.1e-178) (* x y) (if (<= (* a b) 1.16e+61) c t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -8.2e+147) {
		tmp = t_1;
	} else if ((a * b) <= -5e+82) {
		tmp = c;
	} else if ((a * b) <= -2.1e-178) {
		tmp = x * y;
	} else if ((a * b) <= 1.16e+61) {
		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 = (a * b) * (-0.25d0)
    if ((a * b) <= (-8.2d+147)) then
        tmp = t_1
    else if ((a * b) <= (-5d+82)) then
        tmp = c
    else if ((a * b) <= (-2.1d-178)) then
        tmp = x * y
    else if ((a * b) <= 1.16d+61) 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 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -8.2e+147) {
		tmp = t_1;
	} else if ((a * b) <= -5e+82) {
		tmp = c;
	} else if ((a * b) <= -2.1e-178) {
		tmp = x * y;
	} else if ((a * b) <= 1.16e+61) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -8.2e+147:
		tmp = t_1
	elif (a * b) <= -5e+82:
		tmp = c
	elif (a * b) <= -2.1e-178:
		tmp = x * y
	elif (a * b) <= 1.16e+61:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -8.2e+147)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e+82)
		tmp = c;
	elseif (Float64(a * b) <= -2.1e-178)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.16e+61)
		tmp = c;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -8.2e+147)
		tmp = t_1;
	elseif ((a * b) <= -5e+82)
		tmp = c;
	elseif ((a * b) <= -2.1e-178)
		tmp = x * y;
	elseif ((a * b) <= 1.16e+61)
		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[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -8.2e+147], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e+82], c, If[LessEqual[N[(a * b), $MachinePrecision], -2.1e-178], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.16e+61], c, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.19999999999999932e147 or 1.16e61 < (*.f64 a b)

   1. Initial program 96.1%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 96.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 96.1%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 68.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 68.9%

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

   if -8.19999999999999932e147 < (*.f64 a b) < -5.00000000000000015e82 or -2.1e-178 < (*.f64 a b) < 1.16e61

   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. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.5%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   6. Step-by-step derivation

   7. Simplified 46.1%

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

   if -5.00000000000000015e82 < (*.f64 a b) < -2.1e-178

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 46.7%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 46.7%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{+147}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+82}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{-178}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{+61}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+126}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) -4.0)))
   (if (<= (* a b) -4e+84)
     (+ c t_1)
     (if (<= (* a b) -1e-176)
       (+ (* x y) (* 0.0625 (* z t)))
       (if (<= (* a b) 4e+126) (+ c (* t (* z 0.0625))) (+ (* x y) 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 tmp;
	if ((a * b) <= -4e+84) {
		tmp = c + t_1;
	} else if ((a * b) <= -1e-176) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 4e+126) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / (-4.0d0)
    if ((a * b) <= (-4d+84)) then
        tmp = c + t_1
    else if ((a * b) <= (-1d-176)) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else if ((a * b) <= 4d+126) then
        tmp = c + (t * (z * 0.0625d0))
    else
        tmp = (x * y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -4e+84) {
		tmp = c + t_1;
	} else if ((a * b) <= -1e-176) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 4e+126) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / -4.0
	tmp = 0
	if (a * b) <= -4e+84:
		tmp = c + t_1
	elif (a * b) <= -1e-176:
		tmp = (x * y) + (0.0625 * (z * t))
	elif (a * b) <= 4e+126:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / -4.0)
	tmp = 0.0
	if (Float64(a * b) <= -4e+84)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= -1e-176)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 4e+126)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / -4.0;
	tmp = 0.0;
	if ((a * b) <= -4e+84)
		tmp = c + t_1;
	elseif ((a * b) <= -1e-176)
		tmp = (x * y) + (0.0625 * (z * t));
	elseif ((a * b) <= 4e+126)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = (x * y) + 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]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+84], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-176], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4e+126], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.00000000000000023e84

   1. Initial program 98.6%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{c}\right) \]
   6. Step-by-step derivation

   7. Simplified 79.2%

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

   if -4.00000000000000023e84 < (*.f64 a b) < -1e-176

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 95.5%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{1}{16}} \cdot \left(t \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{16}, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      5. *-lowering-*.f64 85.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 85.0%

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

   if -1e-176 < (*.f64 a b) < 3.9999999999999997e126

   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. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.5%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 94.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 94.4%

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

   8. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \color{blue}{c}\right) \]
   9. Step-by-step derivation

   10. Simplified 71.2%

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

       1. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(z \cdot t\right)\right), c\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{1}{16} \cdot z\right) \cdot t\right), c\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{16} \cdot z\right), t\right), c\right) \]

       4. *-lowering-*.f64 71.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, z\right), t\right), c\right) \]

   12. Applied egg-rr 71.9%

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

   if 3.9999999999999997e126 < (*.f64 a b)

   1. Initial program 93.8%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 82.3%

      \[\leadsto \frac{a \cdot b}{-4} + \color{blue}{x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+126}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+107}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (/ (* a b) -4.0))))
   (if (<= (* a b) -4e+84)
     t_1
     (if (<= (* a b) -1e-176)
       (+ (* x y) (* 0.0625 (* z t)))
       (if (<= (* a b) 2e+107) (+ c (* t (* z 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4e+84) {
		tmp = t_1;
	} else if ((a * b) <= -1e-176) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 2e+107) {
		tmp = c + (t * (z * 0.0625));
	} 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 + ((a * b) / (-4.0d0))
    if ((a * b) <= (-4d+84)) then
        tmp = t_1
    else if ((a * b) <= (-1d-176)) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else if ((a * b) <= 2d+107) then
        tmp = c + (t * (z * 0.0625d0))
    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 + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4e+84) {
		tmp = t_1;
	} else if ((a * b) <= -1e-176) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 2e+107) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -4e+84:
		tmp = t_1
	elif (a * b) <= -1e-176:
		tmp = (x * y) + (0.0625 * (z * t))
	elif (a * b) <= 2e+107:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -4e+84)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e-176)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 2e+107)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -4e+84)
		tmp = t_1;
	elseif ((a * b) <= -1e-176)
		tmp = (x * y) + (0.0625 * (z * t));
	elseif ((a * b) <= 2e+107)
		tmp = c + (t * (z * 0.0625));
	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[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+84], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e-176], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+107], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.00000000000000023e84 or 1.9999999999999999e107 < (*.f64 a b)

   1. Initial program 96.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 96.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 96.4%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{c}\right) \]
   6. Step-by-step derivation

   7. Simplified 79.0%

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

   if -4.00000000000000023e84 < (*.f64 a b) < -1e-176

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 95.5%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{1}{16}} \cdot \left(t \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{16}, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      5. *-lowering-*.f64 85.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 85.0%

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

   if -1e-176 < (*.f64 a b) < 1.9999999999999999e107

   1. Initial program 98.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 95.1%

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

   8. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \color{blue}{c}\right) \]
   9. Step-by-step derivation

   10. Simplified 71.5%

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

       1. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(z \cdot t\right)\right), c\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{1}{16} \cdot z\right) \cdot t\right), c\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{16} \cdot z\right), t\right), c\right) \]

       4. *-lowering-*.f64 72.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, z\right), t\right), c\right) \]

   12. Applied egg-rr 72.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+107}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+107}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (/ (* a b) -4.0))))
   (if (<= (* a b) -5e+146)
     t_1
     (if (<= (* a b) -5e-49)
       (+ (* x y) c)
       (if (<= (* a b) 2e+107) (+ c (* t (* z 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -5e+146) {
		tmp = t_1;
	} else if ((a * b) <= -5e-49) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 2e+107) {
		tmp = c + (t * (z * 0.0625));
	} 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 + ((a * b) / (-4.0d0))
    if ((a * b) <= (-5d+146)) then
        tmp = t_1
    else if ((a * b) <= (-5d-49)) then
        tmp = (x * y) + c
    else if ((a * b) <= 2d+107) then
        tmp = c + (t * (z * 0.0625d0))
    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 + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -5e+146) {
		tmp = t_1;
	} else if ((a * b) <= -5e-49) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 2e+107) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -5e+146:
		tmp = t_1
	elif (a * b) <= -5e-49:
		tmp = (x * y) + c
	elif (a * b) <= 2e+107:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -5e+146)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e-49)
		tmp = Float64(Float64(x * y) + c);
	elseif (Float64(a * b) <= 2e+107)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -5e+146)
		tmp = t_1;
	elseif ((a * b) <= -5e-49)
		tmp = (x * y) + c;
	elseif ((a * b) <= 2e+107)
		tmp = c + (t * (z * 0.0625));
	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[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+146], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e-49], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+107], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e146 or 1.9999999999999999e107 < (*.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. Step-by-step derivation

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 95.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 95.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{c}\right) \]
   6. Step-by-step derivation

   7. Simplified 82.6%

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

   if -4.9999999999999999e146 < (*.f64 a b) < -4.9999999999999999e-49

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 89.4%

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

   8. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 70.6%

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

   if -4.9999999999999999e-49 < (*.f64 a b) < 1.9999999999999999e107

   1. Initial program 98.6%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.6%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 95.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 95.7%

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

   8. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \color{blue}{c}\right) \]
   9. Step-by-step derivation

   10. Simplified 72.6%

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

       1. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(z \cdot t\right)\right), c\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{1}{16} \cdot z\right) \cdot t\right), c\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{16} \cdot z\right), t\right), c\right) \]

       4. *-lowering-*.f64 73.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, z\right), t\right), c\right) \]

   12. Applied egg-rr 73.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+146}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+107}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+150)
   (* a (/ b -4.0))
   (if (<= (* a b) -5e-49)
     (+ (* x y) c)
     (if (<= (* a b) 5e+136) (+ c (* 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+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= -5e-49) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 5e+136) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (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+150)) then
        tmp = a * (b / (-4.0d0))
    else if ((a * b) <= (-5d-49)) then
        tmp = (x * y) + c
    else if ((a * b) <= 5d+136) then
        tmp = c + (t * (z * 0.0625d0))
    else
        tmp = (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+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= -5e-49) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 5e+136) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+150:
		tmp = a * (b / -4.0)
	elif (a * b) <= -5e-49:
		tmp = (x * y) + c
	elif (a * b) <= 5e+136:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+150)
		tmp = Float64(a * Float64(b / -4.0));
	elseif (Float64(a * b) <= -5e-49)
		tmp = Float64(Float64(x * y) + c);
	elseif (Float64(a * b) <= 5e+136)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = 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+150)
		tmp = a * (b / -4.0);
	elseif ((a * b) <= -5e-49)
		tmp = (x * y) + c;
	elseif ((a * b) <= 5e+136)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = (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+150], N[(a * N[(b / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-49], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+136], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.00000000000000009e150

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 82.1%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{-4}\right), \color{blue}{a}\right) \]

      7. /-lowering-/.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, -4\right), a\right) \]

   9. Applied egg-rr 84.2%

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

   if -5.00000000000000009e150 < (*.f64 a b) < -4.9999999999999999e-49

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 89.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 89.1%

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

   8. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 70.8%

         \[\leadsto \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 70.8%

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

   if -4.9999999999999999e-49 < (*.f64 a b) < 5.0000000000000002e136

   1. Initial program 98.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 94.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 94.4%

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

   8. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \color{blue}{c}\right) \]
   9. Step-by-step derivation

   10. Simplified 71.7%

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

       1. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(z \cdot t\right)\right), c\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{1}{16} \cdot z\right) \cdot t\right), c\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{16} \cdot z\right), t\right), c\right) \]

       4. *-lowering-*.f64 72.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, z\right), t\right), c\right) \]

   12. Applied egg-rr 72.3%

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

   if 5.0000000000000002e136 < (*.f64 a b)

   1. Initial program 93.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 73.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+150)
   (* a (/ b -4.0))
   (if (<= (* a b) -5e-49)
     (+ (* x y) c)
     (if (<= (* a b) 5e+136) (+ c (* 0.0625 (* z t))) (* (* 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+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= -5e-49) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 5e+136) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (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+150)) then
        tmp = a * (b / (-4.0d0))
    else if ((a * b) <= (-5d-49)) then
        tmp = (x * y) + c
    else if ((a * b) <= 5d+136) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = (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+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= -5e-49) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 5e+136) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+150:
		tmp = a * (b / -4.0)
	elif (a * b) <= -5e-49:
		tmp = (x * y) + c
	elif (a * b) <= 5e+136:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+150)
		tmp = Float64(a * Float64(b / -4.0));
	elseif (Float64(a * b) <= -5e-49)
		tmp = Float64(Float64(x * y) + c);
	elseif (Float64(a * b) <= 5e+136)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = 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+150)
		tmp = a * (b / -4.0);
	elseif ((a * b) <= -5e-49)
		tmp = (x * y) + c;
	elseif ((a * b) <= 5e+136)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = (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+150], N[(a * N[(b / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-49], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+136], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.00000000000000009e150

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 82.1%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{-4}\right), \color{blue}{a}\right) \]

      7. /-lowering-/.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, -4\right), a\right) \]

   9. Applied egg-rr 84.2%

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

   if -5.00000000000000009e150 < (*.f64 a b) < -4.9999999999999999e-49

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 89.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 89.1%

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

   8. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 70.8%

         \[\leadsto \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 70.8%

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

   if -4.9999999999999999e-49 < (*.f64 a b) < 5.0000000000000002e136

   1. Initial program 98.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 98.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 98.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 94.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 94.4%

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

   8. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \color{blue}{c}\right) \]
   9. Step-by-step derivation

   10. Simplified 71.7%

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

   if 5.0000000000000002e136 < (*.f64 a b)

   1. Initial program 93.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 73.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\frac{0.0625 \cdot \left(z \cdot t\right)}{b} + a \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+202}:\\ \;\;\;\;\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (+ (/ (* 0.0625 (* z t)) b) (* a -0.25)))))
   (if (<= (* a b) -5e+150)
     t_1
     (if (<= (* a b) 1e+202) (+ (/ z (/ 16.0 t)) (+ (* 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 = b * (((0.0625 * (z * t)) / b) + (a * -0.25));
	double tmp;
	if ((a * b) <= -5e+150) {
		tmp = t_1;
	} else if ((a * b) <= 1e+202) {
		tmp = (z / (16.0 / t)) + ((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 = b * (((0.0625d0 * (z * t)) / b) + (a * (-0.25d0)))
    if ((a * b) <= (-5d+150)) then
        tmp = t_1
    else if ((a * b) <= 1d+202) then
        tmp = (z / (16.0d0 / t)) + ((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 = b * (((0.0625 * (z * t)) / b) + (a * -0.25));
	double tmp;
	if ((a * b) <= -5e+150) {
		tmp = t_1;
	} else if ((a * b) <= 1e+202) {
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (((0.0625 * (z * t)) / b) + (a * -0.25))
	tmp = 0
	if (a * b) <= -5e+150:
		tmp = t_1
	elif (a * b) <= 1e+202:
		tmp = (z / (16.0 / t)) + ((x * y) + c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(Float64(Float64(0.0625 * Float64(z * t)) / b) + Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(a * b) <= -5e+150)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e+202)
		tmp = Float64(Float64(z / Float64(16.0 / t)) + 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 = b * (((0.0625 * (z * t)) / b) + (a * -0.25));
	tmp = 0.0;
	if ((a * b) <= -5e+150)
		tmp = t_1;
	elseif ((a * b) <= 1e+202)
		tmp = (z / (16.0 / t)) + ((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[(b * N[(N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+150], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e+202], N[(N[(z / N[(16.0 / t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.00000000000000009e150 or 9.999999999999999e201 < (*.f64 a b)

   1. Initial program 94.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 94.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 94.7%

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

      1. +-commutative N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right), \color{blue}{\left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)}\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a \cdot b}}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{t}{16}\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a} \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{1}{\frac{16}{t}}\right), \left(x \cdot y + c\right)\right), \left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      9. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{z}{\frac{16}{t}}\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a} \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{16}{t}\right)\right), \left(x \cdot y + c\right)\right), \left(\frac{\color{blue}{a} \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(x \cdot y + c\right)\right), \left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\left(x \cdot y\right), c\right)\right), \left(\frac{a \cdot \color{blue}{b}}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \left(\frac{a \cdot b}{\mathsf{neg}\left(-4\right)}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \mathsf{/.f64}\left(\left(a \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(-4\right)\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(\color{blue}{-4}\right)\right)\right)\right) \]

      16. metadata-eval 94.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right) \]

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} - \frac{-1}{4} \cdot a\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(-1 \cdot \frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} + \left(\mathsf{neg}\left(\frac{-1}{4} \cdot a\right)\right)\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(\frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b}\right)\right) + \left(\mathsf{neg}\left(\frac{-1}{4} \cdot a\right)\right)\right)\right)\right)\right) \]

      6. distribute-neg-out N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} + \frac{-1}{4} \cdot a\right)\right)\right)\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b} + \color{blue}{\frac{-1}{4} \cdot a}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}{b}\right), \color{blue}{\left(\frac{-1}{4} \cdot a\right)}\right)\right) \]

   9. Simplified 97.1%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \frac{t \cdot z}{b}\right)}, \mathsf{*.f64}\left(a, \frac{-1}{4}\right)\right)\right) \]
   11. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{\frac{1}{16} \cdot \left(t \cdot z\right)}{b}\right), \mathsf{*.f64}\left(\color{blue}{a}, \frac{-1}{4}\right)\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), b\right), \mathsf{*.f64}\left(\color{blue}{a}, \frac{-1}{4}\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), b\right), \mathsf{*.f64}\left(a, \frac{-1}{4}\right)\right)\right) \]

       4. *-lowering-*.f64 91.8%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), b\right), \mathsf{*.f64}\left(a, \frac{-1}{4}\right)\right)\right) \]

   12. Simplified 91.8%

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

   if -5.00000000000000009e150 < (*.f64 a b) < 9.999999999999999e201

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 91.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 91.5%

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

      1. associate-*r* N/A

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

      2. fma-define N/A

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

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, c + x \cdot y\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\frac{16}{t}}, z, c + x \cdot y\right) \]

      5. fma-define N/A

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

      6. associate-/r/ N/A

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

      7. clear-num N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{\frac{16}{t}}\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{16}{t}\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(c + x \cdot y\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(x \cdot y + \color{blue}{c}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right) \]

      13. *-lowering-*.f64 91.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right) \]

   9. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;b \cdot \left(\frac{0.0625 \cdot \left(z \cdot t\right)}{b} + a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+202}:\\ \;\;\;\;\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{0.0625 \cdot \left(z \cdot t\right)}{b} + a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) -4.0)))
   (if (<= (* a b) -5e+150)
     (+ (* 0.0625 (* z t)) t_1)
     (if (<= (* a b) 5e+136)
       (+ (/ z (/ 16.0 t)) (+ (* x y) c))
       (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -5e+150) {
		tmp = (0.0625 * (z * t)) + t_1;
	} else if ((a * b) <= 5e+136) {
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / (-4.0d0)
    if ((a * b) <= (-5d+150)) then
        tmp = (0.0625d0 * (z * t)) + t_1
    else if ((a * b) <= 5d+136) then
        tmp = (z / (16.0d0 / t)) + ((x * y) + c)
    else
        tmp = (x * y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -5e+150) {
		tmp = (0.0625 * (z * t)) + t_1;
	} else if ((a * b) <= 5e+136) {
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / -4.0
	tmp = 0
	if (a * b) <= -5e+150:
		tmp = (0.0625 * (z * t)) + t_1
	elif (a * b) <= 5e+136:
		tmp = (z / (16.0 / t)) + ((x * y) + c)
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / -4.0)
	tmp = 0.0
	if (Float64(a * b) <= -5e+150)
		tmp = Float64(Float64(0.0625 * Float64(z * t)) + t_1);
	elseif (Float64(a * b) <= 5e+136)
		tmp = Float64(Float64(z / Float64(16.0 / t)) + Float64(Float64(x * y) + c));
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / -4.0;
	tmp = 0.0;
	if ((a * b) <= -5e+150)
		tmp = (0.0625 * (z * t)) + t_1;
	elseif ((a * b) <= 5e+136)
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	else
		tmp = (x * y) + 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]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+150], N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+136], N[(N[(z / N[(16.0 / t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000009e150

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(\frac{1}{16}, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 89.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 89.7%

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

   if -5.00000000000000009e150 < (*.f64 a b) < 5.0000000000000002e136

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 93.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 93.2%

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

      1. associate-*r* N/A

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

      2. fma-define N/A

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

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, c + x \cdot y\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\frac{16}{t}}, z, c + x \cdot y\right) \]

      5. fma-define N/A

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

      6. associate-/r/ N/A

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

      7. clear-num N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{\frac{16}{t}}\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{16}{t}\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(c + x \cdot y\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(x \cdot y + \color{blue}{c}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right) \]

      13. *-lowering-*.f64 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right) \]

   9. Applied egg-rr 93.6%

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

   if 5.0000000000000002e136 < (*.f64 a b)

   1. Initial program 93.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 83.0%

      \[\leadsto \frac{a \cdot b}{-4} + \color{blue}{x \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+146}:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) -4.0)))
   (if (<= (* a b) -5e+146)
     (+ c t_1)
     (if (<= (* a b) 5e+136)
       (+ (/ z (/ 16.0 t)) (+ (* x y) c))
       (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -5e+146) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+136) {
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / (-4.0d0)
    if ((a * b) <= (-5d+146)) then
        tmp = c + t_1
    else if ((a * b) <= 5d+136) then
        tmp = (z / (16.0d0 / t)) + ((x * y) + c)
    else
        tmp = (x * y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -5e+146) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+136) {
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / -4.0
	tmp = 0
	if (a * b) <= -5e+146:
		tmp = c + t_1
	elif (a * b) <= 5e+136:
		tmp = (z / (16.0 / t)) + ((x * y) + c)
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / -4.0)
	tmp = 0.0
	if (Float64(a * b) <= -5e+146)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= 5e+136)
		tmp = Float64(Float64(z / Float64(16.0 / t)) + Float64(Float64(x * y) + c));
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / -4.0;
	tmp = 0.0;
	if ((a * b) <= -5e+146)
		tmp = c + t_1;
	elseif ((a * b) <= 5e+136)
		tmp = (z / (16.0 / t)) + ((x * y) + c);
	else
		tmp = (x * y) + 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]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+146], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+136], N[(N[(z / N[(16.0 / t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e146

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{c}\right) \]
   6. Step-by-step derivation

   7. Simplified 87.8%

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

   if -4.9999999999999999e146 < (*.f64 a b) < 5.0000000000000002e136

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 93.3%

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

      1. associate-*r* N/A

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

      2. fma-define N/A

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

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, c + x \cdot y\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\frac{16}{t}}, z, c + x \cdot y\right) \]

      5. fma-define N/A

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

      6. associate-/r/ N/A

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

      7. clear-num N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{\frac{16}{t}}\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{16}{t}\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(c + x \cdot y\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \left(x \cdot y + \color{blue}{c}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right) \]

      13. *-lowering-*.f64 93.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(16, t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right) \]

   9. Applied egg-rr 93.7%

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

   if 5.0000000000000002e136 < (*.f64 a b)

   1. Initial program 93.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 83.0%

      \[\leadsto \frac{a \cdot b}{-4} + \color{blue}{x \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+146}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{16}{t}} + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+146}:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) -4.0)))
   (if (<= (* a b) -5e+146)
     (+ c t_1)
     (if (<= (* a b) 5e+136)
       (+ (* 0.0625 (* z t)) (+ (* x y) c))
       (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -5e+146) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+136) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / (-4.0d0)
    if ((a * b) <= (-5d+146)) then
        tmp = c + t_1
    else if ((a * b) <= 5d+136) then
        tmp = (0.0625d0 * (z * t)) + ((x * y) + c)
    else
        tmp = (x * y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -5e+146) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+136) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / -4.0
	tmp = 0
	if (a * b) <= -5e+146:
		tmp = c + t_1
	elif (a * b) <= 5e+136:
		tmp = (0.0625 * (z * t)) + ((x * y) + c)
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / -4.0)
	tmp = 0.0
	if (Float64(a * b) <= -5e+146)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= 5e+136)
		tmp = Float64(Float64(0.0625 * Float64(z * t)) + Float64(Float64(x * y) + c));
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / -4.0;
	tmp = 0.0;
	if ((a * b) <= -5e+146)
		tmp = c + t_1;
	elseif ((a * b) <= 5e+136)
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	else
		tmp = (x * y) + 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]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+146], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+136], N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e146

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{c}\right) \]
   6. Step-by-step derivation

   7. Simplified 87.8%

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

   if -4.9999999999999999e146 < (*.f64 a b) < 5.0000000000000002e136

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 93.3%

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

   if 5.0000000000000002e136 < (*.f64 a b)

   1. Initial program 93.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 83.0%

      \[\leadsto \frac{a \cdot b}{-4} + \color{blue}{x \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+146}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+150)
   (* a (/ b -4.0))
   (if (<= (* a b) 5e+136) (+ (* x y) c) (* (* 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+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= 5e+136) {
		tmp = (x * y) + c;
	} else {
		tmp = (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+150)) then
        tmp = a * (b / (-4.0d0))
    else if ((a * b) <= 5d+136) then
        tmp = (x * y) + c
    else
        tmp = (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+150) {
		tmp = a * (b / -4.0);
	} else if ((a * b) <= 5e+136) {
		tmp = (x * y) + c;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+150:
		tmp = a * (b / -4.0)
	elif (a * b) <= 5e+136:
		tmp = (x * y) + c
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+150)
		tmp = Float64(a * Float64(b / -4.0));
	elseif (Float64(a * b) <= 5e+136)
		tmp = Float64(Float64(x * y) + c);
	else
		tmp = 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+150)
		tmp = a * (b / -4.0);
	elseif ((a * b) <= 5e+136)
		tmp = (x * y) + c;
	else
		tmp = (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+150], N[(a * N[(b / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+136], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000009e150

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 82.1%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{-4}\right), \color{blue}{a}\right) \]

      7. /-lowering-/.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, -4\right), a\right) \]

   9. Applied egg-rr 84.2%

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

   if -5.00000000000000009e150 < (*.f64 a b) < 5.0000000000000002e136

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(c + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{c} + x \cdot y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(c + x \cdot y\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 93.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 93.2%

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

   8. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 65.8%

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

   if 5.0000000000000002e136 < (*.f64 a b)

   1. Initial program 93.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 93.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 73.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \frac{b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+136}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.05 \cdot 10^{+211}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1.4e+28) (* x y) (if (<= (* x y) 2.05e+211) 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) <= -1.4e+28) {
		tmp = x * y;
	} else if ((x * y) <= 2.05e+211) {
		tmp = 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) <= (-1.4d+28)) then
        tmp = x * y
    else if ((x * y) <= 2.05d+211) then
        tmp = 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) <= -1.4e+28) {
		tmp = x * y;
	} else if ((x * y) <= 2.05e+211) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1.4e+28:
		tmp = x * y
	elif (x * y) <= 2.05e+211:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1.4e+28)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.05e+211)
		tmp = 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) <= -1.4e+28)
		tmp = x * y;
	elseif ((x * y) <= 2.05e+211)
		tmp = 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], -1.4e+28], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.05e+211], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.4000000000000001e28 or 2.0499999999999999e211 < (*.f64 x y)

   1. Initial program 95.2%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 95.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 64.7%

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

   if -1.4000000000000001e28 < (*.f64 x y) < 2.0499999999999999e211

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

      17. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   6. Step-by-step derivation

   7. Simplified 37.0%

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

Alternative 16: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (a / (-4.0 / b)) + (((z * t) / 16.0) + ((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 = (a / ((-4.0d0) / b)) + (((z * t) / 16.0d0) + ((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 (a / (-4.0 / b)) + (((z * t) / 16.0) + ((x * y) + c));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. +-commutative N/A

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

   2. sub-neg N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

   6. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   10. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

   12. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

   13. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

   17. *-lowering-*.f64 97.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

3. Simplified 97.8%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \frac{b}{-4}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \frac{1}{\frac{-4}{b}}\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \color{blue}{16}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{a}{\frac{-4}{b}}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(a, \left(\frac{-4}{b}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

   5. /-lowering-/.f64 98.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(a, \mathsf{/.f64}\left(-4, b\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \color{blue}{16}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

6. Applied egg-rr 98.0%

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

Alternative 17: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

3. Final simplification 97.8%

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

Alternative 18: 22.5% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 97.8%

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

   1. +-commutative N/A

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

   2. sub-neg N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{a \cdot b}{4}\right)\right), \color{blue}{\left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)}\right) \]

   6. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{a \cdot b}{\mathsf{neg}\left(4\right)}\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(a \cdot b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(\color{blue}{c} + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\mathsf{neg}\left(4\right)\right)\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(c + \left(x \cdot y + \frac{z \cdot t}{16}\right)\right)\right) \]

   10. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\left(c + x \cdot y\right) + \color{blue}{\frac{z \cdot t}{16}}\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \left(\frac{z \cdot t}{16} + \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

   12. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\left(\frac{z \cdot t}{16}\right), \color{blue}{\left(c + x \cdot y\right)}\right)\right) \]

   13. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\color{blue}{c} + x \cdot y\right)\right)\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(c + x \cdot y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(x \cdot y + \color{blue}{c}\right)\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{c}\right)\right)\right) \]

   17. *-lowering-*.f64 97.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right)\right)\right) \]

3. Simplified 97.8%

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

5. Taylor expanded in c around inf

   \[\leadsto \color{blue}{c} \]
6. Step-by-step derivation

7. Simplified 28.0%

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

Reproduce

herbie shell --seed 2024160 
(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))