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

Percentage Accurate: 97.6% → 97.6%

Time: 9.0s

Alternatives: 12

Speedup: 1.0×

• 33.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

Alternative 2: 43.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -7.1 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1.35 \cdot 10^{-128}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) -7.1e+96)
     t_2
     (if (<= (* a b) -3.8e-22)
       t_1
       (if (<= (* a b) -1.35e-128)
         c
         (if (<= (* a b) 6.2e-46)
           (* x y)
           (if (<= (* a b) 8.6e+78) 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) <= -7.1e+96) {
		tmp = t_2;
	} else if ((a * b) <= -3.8e-22) {
		tmp = t_1;
	} else if ((a * b) <= -1.35e-128) {
		tmp = c;
	} else if ((a * b) <= 6.2e-46) {
		tmp = x * y;
	} else if ((a * b) <= 8.6e+78) {
		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) <= (-7.1d+96)) then
        tmp = t_2
    else if ((a * b) <= (-3.8d-22)) then
        tmp = t_1
    else if ((a * b) <= (-1.35d-128)) then
        tmp = c
    else if ((a * b) <= 6.2d-46) then
        tmp = x * y
    else if ((a * b) <= 8.6d+78) 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) <= -7.1e+96) {
		tmp = t_2;
	} else if ((a * b) <= -3.8e-22) {
		tmp = t_1;
	} else if ((a * b) <= -1.35e-128) {
		tmp = c;
	} else if ((a * b) <= 6.2e-46) {
		tmp = x * y;
	} else if ((a * b) <= 8.6e+78) {
		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) <= -7.1e+96:
		tmp = t_2
	elif (a * b) <= -3.8e-22:
		tmp = t_1
	elif (a * b) <= -1.35e-128:
		tmp = c
	elif (a * b) <= 6.2e-46:
		tmp = x * y
	elif (a * b) <= 8.6e+78:
		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) <= -7.1e+96)
		tmp = t_2;
	elseif (Float64(a * b) <= -3.8e-22)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.35e-128)
		tmp = c;
	elseif (Float64(a * b) <= 6.2e-46)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 8.6e+78)
		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) <= -7.1e+96)
		tmp = t_2;
	elseif ((a * b) <= -3.8e-22)
		tmp = t_1;
	elseif ((a * b) <= -1.35e-128)
		tmp = c;
	elseif ((a * b) <= 6.2e-46)
		tmp = x * y;
	elseif ((a * b) <= 8.6e+78)
		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], -7.1e+96], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -3.8e-22], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.35e-128], c, If[LessEqual[N[(a * b), $MachinePrecision], 6.2e-46], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.6e+78], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -7.09999999999999954e96 or 8.59999999999999962e78 < (*.f64 a b)

   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 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 71.1%

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

   7. Simplified 71.1%

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

   if -7.09999999999999954e96 < (*.f64 a b) < -3.80000000000000023e-22 or 6.2000000000000002e-46 < (*.f64 a b) < 8.59999999999999962e78

   1. Initial program 98.1%

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

      1. +-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 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in 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 48.5%

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

   7. Simplified 48.5%

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

   if -3.80000000000000023e-22 < (*.f64 a b) < -1.35000000000000003e-128

   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 c around inf

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

   7. Simplified 54.2%

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

   if -1.35000000000000003e-128 < (*.f64 a b) < 6.2000000000000002e-46

   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 50.3%

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

   7. Simplified 50.3%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.1 \cdot 10^{+96}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -1.35 \cdot 10^{-128}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{+78}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+172}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{-305}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* x y) -4e+172)
     (* x y)
     (if (<= (* x y) -1.9e-132)
       t_1
       (if (<= (* x y) 9.5e-305) c (if (<= (* x y) 1.45e+28) t_1 (* x y)))))))

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 ((x * y) <= -4e+172) {
		tmp = x * y;
	} else if ((x * y) <= -1.9e-132) {
		tmp = t_1;
	} else if ((x * y) <= 9.5e-305) {
		tmp = c;
	} else if ((x * y) <= 1.45e+28) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((x * y) <= (-4d+172)) then
        tmp = x * y
    else if ((x * y) <= (-1.9d-132)) then
        tmp = t_1
    else if ((x * y) <= 9.5d-305) then
        tmp = c
    else if ((x * y) <= 1.45d+28) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((x * y) <= -4e+172) {
		tmp = x * y;
	} else if ((x * y) <= -1.9e-132) {
		tmp = t_1;
	} else if ((x * y) <= 9.5e-305) {
		tmp = c;
	} else if ((x * y) <= 1.45e+28) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (x * y) <= -4e+172:
		tmp = x * y
	elif (x * y) <= -1.9e-132:
		tmp = t_1
	elif (x * y) <= 9.5e-305:
		tmp = c
	elif (x * y) <= 1.45e+28:
		tmp = t_1
	else:
		tmp = x * y
	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(x * y) <= -4e+172)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.9e-132)
		tmp = t_1;
	elseif (Float64(x * y) <= 9.5e-305)
		tmp = c;
	elseif (Float64(x * y) <= 1.45e+28)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((x * y) <= -4e+172)
		tmp = x * y;
	elseif ((x * y) <= -1.9e-132)
		tmp = t_1;
	elseif ((x * y) <= 9.5e-305)
		tmp = c;
	elseif ((x * y) <= 1.45e+28)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+172], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.9e-132], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 9.5e-305], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.45e+28], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000003e172 or 1.4500000000000001e28 < (*.f64 x y)

   1. Initial program 96.6%

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

      1. +-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 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 71.8%

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

   7. Simplified 71.8%

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

   if -4.0000000000000003e172 < (*.f64 x y) < -1.8999999999999998e-132 or 9.49999999999999902e-305 < (*.f64 x y) < 1.4500000000000001e28

   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 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 46.7%

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

   7. Simplified 46.7%

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

   if -1.8999999999999998e-132 < (*.f64 x y) < 9.49999999999999902e-305

   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 c around inf

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

   7. Simplified 48.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+172}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{-305}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+28}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* a b) -4.0))))
   (if (<= (* a b) -2e-24)
     t_1
     (if (<= (* a b) 5e-44)
       (+ (* x y) c)
       (if (<= (* a b) 2e+77) (+ (* x y) (* 0.0625 (* z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -2e-24) {
		tmp = t_1;
	} else if ((a * b) <= 5e-44) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 2e+77) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((a * b) / (-4.0d0))
    if ((a * b) <= (-2d-24)) then
        tmp = t_1
    else if ((a * b) <= 5d-44) then
        tmp = (x * y) + c
    else if ((a * b) <= 2d+77) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -2e-24) {
		tmp = t_1;
	} else if ((a * b) <= 5e-44) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 2e+77) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -2e-24:
		tmp = t_1
	elif (a * b) <= 5e-44:
		tmp = (x * y) + c
	elif (a * b) <= 2e+77:
		tmp = (x * y) + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -2e-24)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e-44)
		tmp = Float64(Float64(x * y) + c);
	elseif (Float64(a * b) <= 2e+77)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -2e-24)
		tmp = t_1;
	elseif ((a * b) <= 5e-44)
		tmp = (x * y) + c;
	elseif ((a * b) <= 2e+77)
		tmp = (x * y) + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e-24], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e-44], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+77], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.99999999999999985e-24 or 1.99999999999999997e77 < (*.f64 a b)

   1. Initial program 97.6%

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

      1. +-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 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in 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 75.8%

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

   7. Simplified 75.8%

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

   if -1.99999999999999985e-24 < (*.f64 a b) < 5.00000000000000039e-44

   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 97.8%

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

   7. Simplified 97.8%

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

   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 75.1%

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

   10. Simplified 75.1%

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

   if 5.00000000000000039e-44 < (*.f64 a b) < 1.99999999999999997e77

   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 c around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 70.8%

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

   10. Simplified 70.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq 500000000:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -4e+88)
   (* b (+ (* a -0.25) (/ c b)))
   (if (<= (* a b) 500000000.0)
     (+ (* x y) c)
     (if (<= (* a b) 2e+77) (* 0.0625 (* z t)) (+ c (/ (* a b) -4.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -4e+88) {
		tmp = b * ((a * -0.25) + (c / b));
	} else if ((a * b) <= 500000000.0) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 2e+77) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = c + ((a * b) / -4.0);
	}
	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) <= (-4d+88)) then
        tmp = b * ((a * (-0.25d0)) + (c / b))
    else if ((a * b) <= 500000000.0d0) then
        tmp = (x * y) + c
    else if ((a * b) <= 2d+77) then
        tmp = 0.0625d0 * (z * t)
    else
        tmp = c + ((a * b) / (-4.0d0))
    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) <= -4e+88) {
		tmp = b * ((a * -0.25) + (c / b));
	} else if ((a * b) <= 500000000.0) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 2e+77) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = c + ((a * b) / -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -4e+88:
		tmp = b * ((a * -0.25) + (c / b))
	elif (a * b) <= 500000000.0:
		tmp = (x * y) + c
	elif (a * b) <= 2e+77:
		tmp = 0.0625 * (z * t)
	else:
		tmp = c + ((a * b) / -4.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -4e+88)
		tmp = Float64(b * Float64(Float64(a * -0.25) + Float64(c / b)));
	elseif (Float64(a * b) <= 500000000.0)
		tmp = Float64(Float64(x * y) + c);
	elseif (Float64(a * b) <= 2e+77)
		tmp = Float64(0.0625 * Float64(z * t));
	else
		tmp = Float64(c + Float64(Float64(a * b) / -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -4e+88)
		tmp = b * ((a * -0.25) + (c / b));
	elseif ((a * b) <= 500000000.0)
		tmp = (x * y) + c;
	elseif ((a * b) <= 2e+77)
		tmp = 0.0625 * (z * t);
	else
		tmp = c + ((a * b) / -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+88], N[(b * N[(N[(a * -0.25), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 500000000.0], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+77], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -3.99999999999999984e88

   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 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 75.5%

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

   8. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. /-lowering-/.f64 75.5%

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

   10. Simplified 75.5%

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

   if -3.99999999999999984e88 < (*.f64 a b) < 5e8

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 93.4%

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

   7. Simplified 93.4%

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

   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 68.5%

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

   10. Simplified 68.5%

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

   if 5e8 < (*.f64 a b) < 1.99999999999999997e77

   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 63.9%

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

   7. Simplified 63.9%

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

   if 1.99999999999999997e77 < (*.f64 a b)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. 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 95.9%

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

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 74.3%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq 500000000:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1780000000:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 1.7 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (/ (* a b) -4.0))))
   (if (<= (* a b) -1.35e+94)
     t_1
     (if (<= (* a b) 1780000000.0)
       (+ (* x y) c)
       (if (<= (* a b) 1.7e+77) (* 0.0625 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -1.35e+94) {
		tmp = t_1;
	} else if ((a * b) <= 1780000000.0) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 1.7e+77) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + ((a * b) / (-4.0d0))
    if ((a * b) <= (-1.35d+94)) then
        tmp = t_1
    else if ((a * b) <= 1780000000.0d0) then
        tmp = (x * y) + c
    else if ((a * b) <= 1.7d+77) then
        tmp = 0.0625d0 * (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -1.35e+94) {
		tmp = t_1;
	} else if ((a * b) <= 1780000000.0) {
		tmp = (x * y) + c;
	} else if ((a * b) <= 1.7e+77) {
		tmp = 0.0625 * (z * t);
	} 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) <= -1.35e+94:
		tmp = t_1
	elif (a * b) <= 1780000000.0:
		tmp = (x * y) + c
	elif (a * b) <= 1.7e+77:
		tmp = 0.0625 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -1.35e+94)
		tmp = t_1;
	elseif (Float64(a * b) <= 1780000000.0)
		tmp = Float64(Float64(x * y) + c);
	elseif (Float64(a * b) <= 1.7e+77)
		tmp = Float64(0.0625 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -1.35e+94)
		tmp = t_1;
	elseif ((a * b) <= 1780000000.0)
		tmp = (x * y) + c;
	elseif ((a * b) <= 1.7e+77)
		tmp = 0.0625 * (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.35e+94], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1780000000.0], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.7e+77], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.3500000000000001e94 or 1.69999999999999998e77 < (*.f64 a b)

   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 77.6%

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

   if -1.3500000000000001e94 < (*.f64 a b) < 1.78e9

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 92.7%

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

   7. Simplified 92.7%

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

   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 67.4%

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

   10. Simplified 67.4%

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

   if 1.78e9 < (*.f64 a b) < 1.69999999999999998e77

   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 63.9%

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

   7. Simplified 63.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 1780000000:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;a \cdot b \leq 1.7 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+96}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;t\_1 + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (/ (* a b) -4.0)))
   (if (<= (* a b) -5e+96)
     (+ t_2 t_1)
     (if (<= (* a b) 2e+77) (+ t_1 (+ (* x y) c)) (+ (* x y) 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) / -4.0;
	double tmp;
	if ((a * b) <= -5e+96) {
		tmp = t_2 + t_1;
	} else if ((a * b) <= 2e+77) {
		tmp = t_1 + ((x * y) + c);
	} else {
		tmp = (x * y) + 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) / (-4.0d0)
    if ((a * b) <= (-5d+96)) then
        tmp = t_2 + t_1
    else if ((a * b) <= 2d+77) then
        tmp = t_1 + ((x * y) + c)
    else
        tmp = (x * y) + 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) / -4.0;
	double tmp;
	if ((a * b) <= -5e+96) {
		tmp = t_2 + t_1;
	} else if ((a * b) <= 2e+77) {
		tmp = t_1 + ((x * y) + c);
	} else {
		tmp = (x * y) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) / -4.0
	tmp = 0
	if (a * b) <= -5e+96:
		tmp = t_2 + t_1
	elif (a * b) <= 2e+77:
		tmp = t_1 + ((x * y) + c)
	else:
		tmp = (x * y) + 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) / -4.0)
	tmp = 0.0
	if (Float64(a * b) <= -5e+96)
		tmp = Float64(t_2 + t_1);
	elseif (Float64(a * b) <= 2e+77)
		tmp = Float64(t_1 + Float64(Float64(x * y) + c));
	else
		tmp = Float64(Float64(x * y) + 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) / -4.0;
	tmp = 0.0;
	if ((a * b) <= -5e+96)
		tmp = t_2 + t_1;
	elseif ((a * b) <= 2e+77)
		tmp = t_1 + ((x * y) + c);
	else
		tmp = (x * y) + 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] / -4.0), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+96], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+77], N[(t$95$1 + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000004e96

   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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}\right) \]
   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 87.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), -4\right), \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 87.4%

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

   if -5.0000000000000004e96 < (*.f64 a b) < 1.99999999999999997e77

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. 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 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 92.1%

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

   7. Simplified 92.1%

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

   if 1.99999999999999997e77 < (*.f64 a b)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. 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 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in 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 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+96}:\\ \;\;\;\;\frac{a \cdot b}{-4} + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* a b) -4.0))))
   (if (<= (* a b) -2e+123)
     t_1
     (if (<= (* a b) 2e+77) (+ (* 0.0625 (* z 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 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -2e+123) {
		tmp = t_1;
	} else if ((a * b) <= 2e+77) {
		tmp = (0.0625 * (z * 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 = (x * y) + ((a * b) / (-4.0d0))
    if ((a * b) <= (-2d+123)) then
        tmp = t_1
    else if ((a * b) <= 2d+77) then
        tmp = (0.0625d0 * (z * 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 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -2e+123) {
		tmp = t_1;
	} else if ((a * b) <= 2e+77) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -2e+123:
		tmp = t_1
	elif (a * b) <= 2e+77:
		tmp = (0.0625 * (z * t)) + ((x * y) + c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -2e+123)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e+77)
		tmp = Float64(Float64(0.0625 * Float64(z * 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 = (x * y) + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -2e+123)
		tmp = t_1;
	elseif ((a * b) <= 2e+77)
		tmp = (0.0625 * (z * 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[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+123], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e+77], N[(N[(0.0625 * N[(z * 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) < -1.99999999999999996e123 or 1.99999999999999997e77 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in 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 85.6%

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

   7. Simplified 85.6%

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

   if -1.99999999999999996e123 < (*.f64 a b) < 1.99999999999999997e77

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. 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 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 90.9%

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

   7. Simplified 90.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+77}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{-24}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* 0.0625 (* z t)))))
   (if (<= (* x y) -4.8e+168)
     t_1
     (if (<= (* x y) 1.35e-24) (+ c (/ (* a b) -4.0)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -4.8e+168) {
		tmp = t_1;
	} else if ((x * y) <= 1.35e-24) {
		tmp = c + ((a * b) / -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (0.0625d0 * (z * t))
    if ((x * y) <= (-4.8d+168)) then
        tmp = t_1
    else if ((x * y) <= 1.35d-24) then
        tmp = c + ((a * b) / (-4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -4.8e+168) {
		tmp = t_1;
	} else if ((x * y) <= 1.35e-24) {
		tmp = c + ((a * b) / -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + (0.0625 * (z * t))
	tmp = 0
	if (x * y) <= -4.8e+168:
		tmp = t_1
	elif (x * y) <= 1.35e-24:
		tmp = c + ((a * b) / -4.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -4.8e+168)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.35e-24)
		tmp = Float64(c + Float64(Float64(a * b) / -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + (0.0625 * (z * t));
	tmp = 0.0;
	if ((x * y) <= -4.8e+168)
		tmp = t_1;
	elseif ((x * y) <= 1.35e-24)
		tmp = c + ((a * b) / -4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.8e+168], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.35e-24], N[(c + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.80000000000000019e168 or 1.35000000000000003e-24 < (*.f64 x y)

   1. Initial program 97.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 97.0%

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

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 81.6%

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

   7. Simplified 81.6%

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

   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. +-lowering-+.f64 N/A

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

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

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

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

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

      4. *-lowering-*.f64 78.7%

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

   10. Simplified 78.7%

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

   if -4.80000000000000019e168 < (*.f64 x y) < 1.35000000000000003e-24

   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 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 67.8%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+168}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{-24}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{+218}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -1.65e+94) t_1 (if (<= (* a b) 7e+218) (+ (* 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 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.65e+94) {
		tmp = t_1;
	} else if ((a * b) <= 7e+218) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-1.65d+94)) then
        tmp = t_1
    else if ((a * b) <= 7d+218) then
        tmp = (x * y) + c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.65e+94) {
		tmp = t_1;
	} else if ((a * b) <= 7e+218) {
		tmp = (x * y) + 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) <= -1.65e+94:
		tmp = t_1
	elif (a * b) <= 7e+218:
		tmp = (x * y) + 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) <= -1.65e+94)
		tmp = t_1;
	elseif (Float64(a * b) <= 7e+218)
		tmp = Float64(Float64(x * y) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -1.65e+94)
		tmp = t_1;
	elseif ((a * b) <= 7e+218)
		tmp = (x * y) + c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.65e+94], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 7e+218], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.65e94 or 7.00000000000000038e218 < (*.f64 a b)

   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 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 78.4%

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

   7. Simplified 78.4%

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

   if -1.65e94 < (*.f64 a b) < 7.00000000000000038e218

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in a around 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 88.1%

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

   7. Simplified 88.1%

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

   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 62.2%

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

   10. Simplified 62.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{+218}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -7e+95) (* x y) (if (<= (* x y) 1.9e-119) 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) <= -7e+95) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e-119) {
		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) <= (-7d+95)) then
        tmp = x * y
    else if ((x * y) <= 1.9d-119) 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) <= -7e+95) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e-119) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -7e+95:
		tmp = x * y
	elif (x * y) <= 1.9e-119:
		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) <= -7e+95)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.9e-119)
		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) <= -7e+95)
		tmp = x * y;
	elseif ((x * y) <= 1.9e-119)
		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], -7e+95], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e-119], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.99999999999999999e95 or 1.89999999999999987e-119 < (*.f64 x y)

   1. Initial program 97.6%

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

      1. +-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 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 55.0%

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

   7. Simplified 55.0%

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

   if -6.99999999999999999e95 < (*.f64 x y) < 1.89999999999999987e-119

   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 c around inf

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

   7. Simplified 35.1%

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

Alternative 12: 23.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 98.8%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
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 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in c around inf

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

7. Simplified 20.6%

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

Reproduce

herbie shell --seed 2024158 
(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))