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

Percentage Accurate: 97.7% → 97.7%

Time: 9.5s

Alternatives: 11

Speedup: 1.0×

• 33.3% 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: 97.7% 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: 97.7% 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 98.4%

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

Alternative 2: 44.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.235 \cdot 10^{+74}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.4 \cdot 10^{-150}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-286}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+123}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -3.235e+74)
   (* x y)
   (if (<= (* x y) -5.4e-150)
     (* 0.0625 (* z t))
     (if (<= (* x y) -8.2e-286)
       c
       (if (<= (* x y) 4.6e+123) (* (* a b) -0.25) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -3.235e+74) {
		tmp = x * y;
	} else if ((x * y) <= -5.4e-150) {
		tmp = 0.0625 * (z * t);
	} else if ((x * y) <= -8.2e-286) {
		tmp = c;
	} else if ((x * y) <= 4.6e+123) {
		tmp = (a * b) * -0.25;
	} 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) <= (-3.235d+74)) then
        tmp = x * y
    else if ((x * y) <= (-5.4d-150)) then
        tmp = 0.0625d0 * (z * t)
    else if ((x * y) <= (-8.2d-286)) then
        tmp = c
    else if ((x * y) <= 4.6d+123) then
        tmp = (a * b) * (-0.25d0)
    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) <= -3.235e+74) {
		tmp = x * y;
	} else if ((x * y) <= -5.4e-150) {
		tmp = 0.0625 * (z * t);
	} else if ((x * y) <= -8.2e-286) {
		tmp = c;
	} else if ((x * y) <= 4.6e+123) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -3.235e+74:
		tmp = x * y
	elif (x * y) <= -5.4e-150:
		tmp = 0.0625 * (z * t)
	elif (x * y) <= -8.2e-286:
		tmp = c
	elif (x * y) <= 4.6e+123:
		tmp = (a * b) * -0.25
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -3.235e+74)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.4e-150)
		tmp = Float64(0.0625 * Float64(z * t));
	elseif (Float64(x * y) <= -8.2e-286)
		tmp = c;
	elseif (Float64(x * y) <= 4.6e+123)
		tmp = Float64(Float64(a * b) * -0.25);
	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) <= -3.235e+74)
		tmp = x * y;
	elseif ((x * y) <= -5.4e-150)
		tmp = 0.0625 * (z * t);
	elseif ((x * y) <= -8.2e-286)
		tmp = c;
	elseif ((x * y) <= 4.6e+123)
		tmp = (a * b) * -0.25;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.235e+74], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.4e-150], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.2e-286], c, If[LessEqual[N[(x * y), $MachinePrecision], 4.6e+123], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.2350000000000001e74 or 4.59999999999999981e123 < (*.f64 x y)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 66.8%

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

   7. Simplified 66.8%

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

   if -3.2350000000000001e74 < (*.f64 x y) < -5.4000000000000003e-150

   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 47.7%

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

   7. Simplified 47.7%

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

   if -5.4000000000000003e-150 < (*.f64 x y) < -8.2e-286

   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 58.4%

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

   if -8.2e-286 < (*.f64 x y) < 4.59999999999999981e123

   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 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 43.2%

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

   7. Simplified 43.2%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.235 \cdot 10^{+74}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.4 \cdot 10^{-150}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-286}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+123}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot y + t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.55 \cdot 10^{-300}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+107}:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) -4.0)))
   (if (<= (* x y) -6.5e+131)
     (+ (* x y) t_1)
     (if (<= (* x y) -1.55e-300)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 2.6e+107) (+ c t_1) (+ (* x y) (* z (* t 0.0625))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((x * y) <= -6.5e+131) {
		tmp = (x * y) + t_1;
	} else if ((x * y) <= -1.55e-300) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2.6e+107) {
		tmp = c + t_1;
	} else {
		tmp = (x * y) + (z * (t * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / (-4.0d0)
    if ((x * y) <= (-6.5d+131)) then
        tmp = (x * y) + t_1
    else if ((x * y) <= (-1.55d-300)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 2.6d+107) then
        tmp = c + t_1
    else
        tmp = (x * y) + (z * (t * 0.0625d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / -4.0;
	double tmp;
	if ((x * y) <= -6.5e+131) {
		tmp = (x * y) + t_1;
	} else if ((x * y) <= -1.55e-300) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2.6e+107) {
		tmp = c + t_1;
	} else {
		tmp = (x * y) + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / -4.0
	tmp = 0
	if (x * y) <= -6.5e+131:
		tmp = (x * y) + t_1
	elif (x * y) <= -1.55e-300:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 2.6e+107:
		tmp = c + t_1
	else:
		tmp = (x * y) + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / -4.0)
	tmp = 0.0
	if (Float64(x * y) <= -6.5e+131)
		tmp = Float64(Float64(x * y) + t_1);
	elseif (Float64(x * y) <= -1.55e-300)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 2.6e+107)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / -4.0;
	tmp = 0.0;
	if ((x * y) <= -6.5e+131)
		tmp = (x * y) + t_1;
	elseif ((x * y) <= -1.55e-300)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 2.6e+107)
		tmp = c + t_1;
	else
		tmp = (x * y) + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.5e+131], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.55e-300], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.6e+107], N[(c + t$95$1), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -6.5e131

   1. Initial program 97.4%

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

      1. +-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 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in 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 85.7%

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

   7. Simplified 85.7%

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

   if -6.5e131 < (*.f64 x y) < -1.5500000000000001e-300

   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 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in c around inf

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

   10. Simplified 67.8%

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

   if -1.5500000000000001e-300 < (*.f64 x y) < 2.6000000000000001e107

   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 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 70.8%

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

   if 2.6000000000000001e107 < (*.f64 x y)

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 89.1%

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

   10. Simplified 89.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;x \cdot y \leq -1.55 \cdot 10^{-300}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+107}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -6.6 \cdot 10^{-302}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+104}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (* t 0.0625)))))
   (if (<= (* x y) -2.6e+131)
     t_1
     (if (<= (* x y) -6.6e-302)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 7.5e+104) (+ c (/ (* a b) -4.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (z * (t * 0.0625));
	double tmp;
	if ((x * y) <= -2.6e+131) {
		tmp = t_1;
	} else if ((x * y) <= -6.6e-302) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 7.5e+104) {
		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) + (z * (t * 0.0625d0))
    if ((x * y) <= (-2.6d+131)) then
        tmp = t_1
    else if ((x * y) <= (-6.6d-302)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 7.5d+104) 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) + (z * (t * 0.0625));
	double tmp;
	if ((x * y) <= -2.6e+131) {
		tmp = t_1;
	} else if ((x * y) <= -6.6e-302) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 7.5e+104) {
		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) + (z * (t * 0.0625))
	tmp = 0
	if (x * y) <= -2.6e+131:
		tmp = t_1
	elif (x * y) <= -6.6e-302:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 7.5e+104:
		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(z * Float64(t * 0.0625)))
	tmp = 0.0
	if (Float64(x * y) <= -2.6e+131)
		tmp = t_1;
	elseif (Float64(x * y) <= -6.6e-302)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 7.5e+104)
		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) + (z * (t * 0.0625));
	tmp = 0.0;
	if ((x * y) <= -2.6e+131)
		tmp = t_1;
	elseif ((x * y) <= -6.6e-302)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 7.5e+104)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e+131], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -6.6e-302], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+104], N[(c + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.6e131 or 7.5000000000000002e104 < (*.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 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 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 85.1%

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

   10. Simplified 85.1%

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

   if -2.6e131 < (*.f64 x y) < -6.6000000000000005e-302

   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 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in c around inf

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

   10. Simplified 67.8%

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

   if -6.6000000000000005e-302 < (*.f64 x y) < 7.5000000000000002e104

   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 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 70.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -6.6 \cdot 10^{-302}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+104}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c\\ \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -7.2 \cdot 10^{-300}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+108}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) c)))
   (if (<= (* x y) -2.2e+123)
     t_1
     (if (<= (* x y) -7.2e-300)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 3.6e+108) (+ 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) + c;
	double tmp;
	if ((x * y) <= -2.2e+123) {
		tmp = t_1;
	} else if ((x * y) <= -7.2e-300) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 3.6e+108) {
		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) + c
    if ((x * y) <= (-2.2d+123)) then
        tmp = t_1
    else if ((x * y) <= (-7.2d-300)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 3.6d+108) 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) + c;
	double tmp;
	if ((x * y) <= -2.2e+123) {
		tmp = t_1;
	} else if ((x * y) <= -7.2e-300) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 3.6e+108) {
		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) + c
	tmp = 0
	if (x * y) <= -2.2e+123:
		tmp = t_1
	elif (x * y) <= -7.2e-300:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 3.6e+108:
		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) + c)
	tmp = 0.0
	if (Float64(x * y) <= -2.2e+123)
		tmp = t_1;
	elseif (Float64(x * y) <= -7.2e-300)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 3.6e+108)
		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) + c;
	tmp = 0.0;
	if ((x * y) <= -2.2e+123)
		tmp = t_1;
	elseif ((x * y) <= -7.2e-300)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 3.6e+108)
		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] + c), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.2e+123], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -7.2e-300], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.6e+108], N[(c + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.19999999999999992e123 or 3.6e108 < (*.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 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 87.3%

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

   7. Simplified 87.3%

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

   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 74.3%

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

   10. Simplified 74.3%

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

   if -2.19999999999999992e123 < (*.f64 x y) < -7.20000000000000031e-300

   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 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in c around inf

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

   10. Simplified 68.2%

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

   if -7.20000000000000031e-300 < (*.f64 x y) < 3.6e108

   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 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 70.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{elif}\;x \cdot y \leq -7.2 \cdot 10^{-300}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+108}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c\\ t_2 := \frac{a \cdot b}{-4} + t\_1\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t\_1 + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) c)) (t_2 (+ (/ (* a b) -4.0) t_1)))
   (if (<= (* a b) -5e+166)
     t_2
     (if (<= (* a b) 5e+43) (+ t_1 (* 0.0625 (* z t))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + c;
	double t_2 = ((a * b) / -4.0) + t_1;
	double tmp;
	if ((a * b) <= -5e+166) {
		tmp = t_2;
	} else if ((a * b) <= 5e+43) {
		tmp = t_1 + (0.0625 * (z * t));
	} 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 = (x * y) + c
    t_2 = ((a * b) / (-4.0d0)) + t_1
    if ((a * b) <= (-5d+166)) then
        tmp = t_2
    else if ((a * b) <= 5d+43) then
        tmp = t_1 + (0.0625d0 * (z * t))
    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 = (x * y) + c;
	double t_2 = ((a * b) / -4.0) + t_1;
	double tmp;
	if ((a * b) <= -5e+166) {
		tmp = t_2;
	} else if ((a * b) <= 5e+43) {
		tmp = t_1 + (0.0625 * (z * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + c
	t_2 = ((a * b) / -4.0) + t_1
	tmp = 0
	if (a * b) <= -5e+166:
		tmp = t_2
	elif (a * b) <= 5e+43:
		tmp = t_1 + (0.0625 * (z * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + c)
	t_2 = Float64(Float64(Float64(a * b) / -4.0) + t_1)
	tmp = 0.0
	if (Float64(a * b) <= -5e+166)
		tmp = t_2;
	elseif (Float64(a * b) <= 5e+43)
		tmp = Float64(t_1 + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + c;
	t_2 = ((a * b) / -4.0) + t_1;
	tmp = 0.0;
	if ((a * b) <= -5e+166)
		tmp = t_2;
	elseif ((a * b) <= 5e+43)
		tmp = t_1 + (0.0625 * (z * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+166], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 5e+43], N[(t$95$1 + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000002e166 or 5.0000000000000004e43 < (*.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 z around 0

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

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

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

      2. *-lowering-*.f64 86.1%

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

   7. Simplified 86.1%

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

   if -5.0000000000000002e166 < (*.f64 a b) < 5.0000000000000004e43

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 94.2%

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

   7. Simplified 94.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+166}:\\ \;\;\;\;\frac{a \cdot b}{-4} + \left(x \cdot y + c\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\left(x \cdot y + c\right) + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot b}{-4} + \left(x \cdot y + c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\left(x \cdot y + c\right) + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* a b) -4.0))))
   (if (<= (* a b) -5e+166)
     t_1
     (if (<= (* a b) 5e+43) (+ (+ (* x y) c) (* 0.0625 (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -5e+166) {
		tmp = t_1;
	} else if ((a * b) <= 5e+43) {
		tmp = ((x * y) + c) + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((a * b) / (-4.0d0))
    if ((a * b) <= (-5d+166)) then
        tmp = t_1
    else if ((a * b) <= 5d+43) then
        tmp = ((x * y) + c) + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -5e+166) {
		tmp = t_1;
	} else if ((a * b) <= 5e+43) {
		tmp = ((x * y) + c) + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -5e+166:
		tmp = t_1
	elif (a * b) <= 5e+43:
		tmp = ((x * y) + c) + (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) <= -5e+166)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e+43)
		tmp = Float64(Float64(Float64(x * y) + c) + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -5e+166)
		tmp = t_1;
	elseif ((a * b) <= 5e+43)
		tmp = ((x * y) + c) + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+166], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e+43], N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000002e166 or 5.0000000000000004e43 < (*.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 x around inf

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

      1. *-lowering-*.f64 82.4%

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

   7. Simplified 82.4%

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

   if -5.0000000000000002e166 < (*.f64 a b) < 5.0000000000000004e43

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 94.2%

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

   7. Simplified 94.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+166}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\left(x \cdot y + c\right) + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -2.15 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+242}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -2.15e+163)
     t_1
     (if (<= (* a b) 4.8e+242) (+ (* 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) <= -2.15e+163) {
		tmp = t_1;
	} else if ((a * b) <= 4.8e+242) {
		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) <= (-2.15d+163)) then
        tmp = t_1
    else if ((a * b) <= 4.8d+242) 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) <= -2.15e+163) {
		tmp = t_1;
	} else if ((a * b) <= 4.8e+242) {
		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) <= -2.15e+163:
		tmp = t_1
	elif (a * b) <= 4.8e+242:
		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) <= -2.15e+163)
		tmp = t_1;
	elseif (Float64(a * b) <= 4.8e+242)
		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) <= -2.15e+163)
		tmp = t_1;
	elseif ((a * b) <= 4.8e+242)
		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], -2.15e+163], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4.8e+242], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.1500000000000001e163 or 4.80000000000000024e242 < (*.f64 a b)

   1. Initial program 97.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 80.6%

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

   7. Simplified 80.6%

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

   if -2.1500000000000001e163 < (*.f64 a b) < 4.80000000000000024e242

   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 90.6%

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

   7. Simplified 90.6%

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

   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 62.6%

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

   10. Simplified 62.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.15 \cdot 10^{+163}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+242}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -1.75 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+242}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -1.75e+142) t_1 (if (<= (* a b) 4.8e+242) (* x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.75e+142) {
		tmp = t_1;
	} else if ((a * b) <= 4.8e+242) {
		tmp = x * y;
	} 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) <= (-1.75d+142)) then
        tmp = t_1
    else if ((a * b) <= 4.8d+242) then
        tmp = x * y
    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) <= -1.75e+142) {
		tmp = t_1;
	} else if ((a * b) <= 4.8e+242) {
		tmp = x * y;
	} 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) <= -1.75e+142:
		tmp = t_1
	elif (a * b) <= 4.8e+242:
		tmp = x * y
	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) <= -1.75e+142)
		tmp = t_1;
	elseif (Float64(a * b) <= 4.8e+242)
		tmp = Float64(x * y);
	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) <= -1.75e+142)
		tmp = t_1;
	elseif ((a * b) <= 4.8e+242)
		tmp = x * y;
	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], -1.75e+142], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4.8e+242], N[(x * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.74999999999999999e142 or 4.80000000000000024e242 < (*.f64 a b)

   1. Initial program 97.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. 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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 77.3%

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

   7. Simplified 77.3%

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

   if -1.74999999999999999e142 < (*.f64 a b) < 4.80000000000000024e242

   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 x around inf

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

      1. *-lowering-*.f64 38.4%

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

   7. Simplified 38.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.75 \cdot 10^{+142}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+242}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+104}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2.6e+132) (* x y) (if (<= (* x y) 4.5e+104) 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) <= -2.6e+132) {
		tmp = x * y;
	} else if ((x * y) <= 4.5e+104) {
		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) <= (-2.6d+132)) then
        tmp = x * y
    else if ((x * y) <= 4.5d+104) 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) <= -2.6e+132) {
		tmp = x * y;
	} else if ((x * y) <= 4.5e+104) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -2.6e+132:
		tmp = x * y
	elif (x * y) <= 4.5e+104:
		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) <= -2.6e+132)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 4.5e+104)
		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) <= -2.6e+132)
		tmp = x * y;
	elseif ((x * y) <= 4.5e+104)
		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], -2.6e+132], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.5e+104], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.6e132 or 4.4999999999999998e104 < (*.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 71.7%

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

   7. Simplified 71.7%

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

   if -2.6e132 < (*.f64 x y) < 4.4999999999999998e104

   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 c around inf

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

   7. Simplified 29.4%

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

Alternative 11: 22.2% 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 98.4%

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

   1. +-commutative N/A

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

   2. sub-neg N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

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

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

   6. distribute-neg-frac2 N/A

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

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

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

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

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

   9. metadata-eval N/A

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

   10. associate-+r+ N/A

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

   11. +-commutative N/A

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

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

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

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

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

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

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

   15. +-commutative N/A

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

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

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

   17. *-lowering-*.f64 98.4%

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

3. Simplified 98.4%

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

5. Taylor expanded in c around inf

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

7. Simplified 20.8%

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

Reproduce

herbie shell --seed 2024138 
(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))