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

Percentage Accurate: 97.7% → 97.7%

Time: 9.8s

Alternatives: 12

Speedup: 1.0×

• 32.6% 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 98.8%

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

Alternative 2: 68.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-182}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* a b) -4.0))))
   (if (<= (* a b) -4e+97)
     t_1
     (if (<= (* a b) -1e-182)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* a b) 5e+145) (+ (* x y) (* z (* t 0.0625))) 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) <= -4e+97) {
		tmp = t_1;
	} else if ((a * b) <= -1e-182) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 5e+145) {
		tmp = (x * y) + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((a * b) / (-4.0d0))
    if ((a * b) <= (-4d+97)) then
        tmp = t_1
    else if ((a * b) <= (-1d-182)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((a * b) <= 5d+145) then
        tmp = (x * y) + (z * (t * 0.0625d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4e+97) {
		tmp = t_1;
	} else if ((a * b) <= -1e-182) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 5e+145) {
		tmp = (x * y) + (z * (t * 0.0625));
	} 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) <= -4e+97:
		tmp = t_1
	elif (a * b) <= -1e-182:
		tmp = c + (0.0625 * (z * t))
	elif (a * b) <= 5e+145:
		tmp = (x * y) + (z * (t * 0.0625))
	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) <= -4e+97)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e-182)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 5e+145)
		tmp = Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625)));
	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) <= -4e+97)
		tmp = t_1;
	elseif ((a * b) <= -1e-182)
		tmp = c + (0.0625 * (z * t));
	elseif ((a * b) <= 5e+145)
		tmp = (x * y) + (z * (t * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+97], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e-182], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+145], N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.0000000000000003e97 or 4.99999999999999967e145 < (*.f64 a b)

   1. Initial program 97.4%

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

      1. +-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 89.9%

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

   7. Simplified 89.9%

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

   if -4.0000000000000003e97 < (*.f64 a b) < -1e-182

   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 91.5%

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

   7. Simplified 91.5%

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

   8. 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 74.4%

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

   if -1e-182 < (*.f64 a b) < 4.99999999999999967e145

   1. Initial program 99.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in c around 0

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

      1. +-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 70.6%

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

   10. Simplified 70.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-182}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-182}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (+ (* a -0.25) (/ c b)))))
   (if (<= (* a b) -2e+72)
     t_1
     (if (<= (* a b) -1e-182)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* a b) 5e+145) (+ (* x y) (* z (* t 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * ((a * -0.25) + (c / b));
	double tmp;
	if ((a * b) <= -2e+72) {
		tmp = t_1;
	} else if ((a * b) <= -1e-182) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 5e+145) {
		tmp = (x * y) + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * (-0.25d0)) + (c / b))
    if ((a * b) <= (-2d+72)) then
        tmp = t_1
    else if ((a * b) <= (-1d-182)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((a * b) <= 5d+145) then
        tmp = (x * y) + (z * (t * 0.0625d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * ((a * -0.25) + (c / b));
	double tmp;
	if ((a * b) <= -2e+72) {
		tmp = t_1;
	} else if ((a * b) <= -1e-182) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 5e+145) {
		tmp = (x * y) + (z * (t * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * ((a * -0.25) + (c / b))
	tmp = 0
	if (a * b) <= -2e+72:
		tmp = t_1
	elif (a * b) <= -1e-182:
		tmp = c + (0.0625 * (z * t))
	elif (a * b) <= 5e+145:
		tmp = (x * y) + (z * (t * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(Float64(a * -0.25) + Float64(c / b)))
	tmp = 0.0
	if (Float64(a * b) <= -2e+72)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e-182)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 5e+145)
		tmp = Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * ((a * -0.25) + (c / b));
	tmp = 0.0;
	if ((a * b) <= -2e+72)
		tmp = t_1;
	elseif ((a * b) <= -1e-182)
		tmp = c + (0.0625 * (z * t));
	elseif ((a * b) <= 5e+145)
		tmp = (x * y) + (z * (t * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(N[(a * -0.25), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+72], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e-182], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+145], N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.99999999999999989e72 or 4.99999999999999967e145 < (*.f64 a b)

   1. Initial program 97.5%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in c around inf

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

   7. Simplified 83.5%

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

   8. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. /-lowering-/.f64 84.7%

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

   10. Simplified 84.7%

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

   if -1.99999999999999989e72 < (*.f64 a b) < -1e-182

   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 93.0%

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

   7. Simplified 93.0%

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

   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 74.5%

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

   if -1e-182 < (*.f64 a b) < 4.99999999999999967e145

   1. Initial program 99.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in c around 0

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

      1. +-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 70.6%

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

   10. Simplified 70.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-182}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 44.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -1.22 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -3.9 \cdot 10^{-200}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -1.22e+88)
     t_1
     (if (<= (* a b) -3.9e-200) c (if (<= (* a b) 5.6e+100) (* 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) <= -1.22e+88) {
		tmp = t_1;
	} else if ((a * b) <= -3.9e-200) {
		tmp = c;
	} else if ((a * b) <= 5.6e+100) {
		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) <= (-1.22d+88)) then
        tmp = t_1
    else if ((a * b) <= (-3.9d-200)) then
        tmp = c
    else if ((a * b) <= 5.6d+100) 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) <= -1.22e+88) {
		tmp = t_1;
	} else if ((a * b) <= -3.9e-200) {
		tmp = c;
	} else if ((a * b) <= 5.6e+100) {
		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) <= -1.22e+88:
		tmp = t_1
	elif (a * b) <= -3.9e-200:
		tmp = c
	elif (a * b) <= 5.6e+100:
		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) <= -1.22e+88)
		tmp = t_1;
	elseif (Float64(a * b) <= -3.9e-200)
		tmp = c;
	elseif (Float64(a * b) <= 5.6e+100)
		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) <= -1.22e+88)
		tmp = t_1;
	elseif ((a * b) <= -3.9e-200)
		tmp = c;
	elseif ((a * b) <= 5.6e+100)
		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], -1.22e+88], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -3.9e-200], c, If[LessEqual[N[(a * b), $MachinePrecision], 5.6e+100], N[(x * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.22e88 or 5.5999999999999996e100 < (*.f64 a b)

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 69.5%

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

   7. Simplified 69.5%

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

   if -1.22e88 < (*.f64 a b) < -3.89999999999999999e-200

   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 38.2%

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

   if -3.89999999999999999e-200 < (*.f64 a b) < 5.5999999999999996e100

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 35.4%

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

   7. Simplified 35.4%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.22 \cdot 10^{+88}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -3.9 \cdot 10^{-200}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* a b) -4.0))))
   (if (<= (* a b) -4e+97)
     t_1
     (if (<= (* a b) 5e+145) (+ (* 0.0625 (* z t)) (+ (* x y) c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4e+97) {
		tmp = t_1;
	} else if ((a * b) <= 5e+145) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((a * b) / (-4.0d0))
    if ((a * b) <= (-4d+97)) then
        tmp = t_1
    else if ((a * b) <= 5d+145) then
        tmp = (0.0625d0 * (z * t)) + ((x * y) + c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4e+97) {
		tmp = t_1;
	} else if ((a * b) <= 5e+145) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -4e+97:
		tmp = t_1
	elif (a * b) <= 5e+145:
		tmp = (0.0625 * (z * t)) + ((x * y) + c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -4e+97)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e+145)
		tmp = Float64(Float64(0.0625 * Float64(z * t)) + Float64(Float64(x * y) + c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -4e+97)
		tmp = t_1;
	elseif ((a * b) <= 5e+145)
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+97], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e+145], N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.0000000000000003e97 or 4.99999999999999967e145 < (*.f64 a b)

   1. Initial program 97.4%

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

      1. +-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 89.9%

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

   7. Simplified 89.9%

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

   if -4.0000000000000003e97 < (*.f64 a b) < 4.99999999999999967e145

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 92.4%

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

   7. Simplified 92.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (+ (* a -0.25) (/ c b)))))
   (if (<= (* a b) -2e+72)
     t_1
     (if (<= (* a b) 5e+145) (+ 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 = b * ((a * -0.25) + (c / b));
	double tmp;
	if ((a * b) <= -2e+72) {
		tmp = t_1;
	} else if ((a * b) <= 5e+145) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * (-0.25d0)) + (c / b))
    if ((a * b) <= (-2d+72)) then
        tmp = t_1
    else if ((a * b) <= 5d+145) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * ((a * -0.25) + (c / b));
	double tmp;
	if ((a * b) <= -2e+72) {
		tmp = t_1;
	} else if ((a * b) <= 5e+145) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * ((a * -0.25) + (c / b))
	tmp = 0
	if (a * b) <= -2e+72:
		tmp = t_1
	elif (a * b) <= 5e+145:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(Float64(a * -0.25) + Float64(c / b)))
	tmp = 0.0
	if (Float64(a * b) <= -2e+72)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e+145)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * ((a * -0.25) + (c / b));
	tmp = 0.0;
	if ((a * b) <= -2e+72)
		tmp = t_1;
	elseif ((a * b) <= 5e+145)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(N[(a * -0.25), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+72], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e+145], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.99999999999999989e72 or 4.99999999999999967e145 < (*.f64 a b)

   1. Initial program 97.5%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in c around inf

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

   7. Simplified 83.5%

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

   8. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. /-lowering-/.f64 84.7%

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

   10. Simplified 84.7%

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

   if -1.99999999999999989e72 < (*.f64 a b) < 4.99999999999999967e145

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in 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 64.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -4.3 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (/ (* a b) -4.0))))
   (if (<= (* a b) -4.3e+45)
     t_1
     (if (<= (* a b) 3.8e+145) (+ c (* 0.0625 (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4.3e+45) {
		tmp = t_1;
	} else if ((a * b) <= 3.8e+145) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + ((a * b) / (-4.0d0))
    if ((a * b) <= (-4.3d+45)) then
        tmp = t_1
    else if ((a * b) <= 3.8d+145) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -4.3e+45) {
		tmp = t_1;
	} else if ((a * b) <= 3.8e+145) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((a * b) / -4.0)
	tmp = 0
	if (a * b) <= -4.3e+45:
		tmp = t_1
	elif (a * b) <= 3.8e+145:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) / -4.0))
	tmp = 0.0
	if (Float64(a * b) <= -4.3e+45)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.8e+145)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -4.3e+45)
		tmp = t_1;
	elseif ((a * b) <= 3.8e+145)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4.3e+45], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+145], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.3000000000000003e45 or 3.80000000000000012e145 < (*.f64 a b)

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in c around inf

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

   7. Simplified 82.4%

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

   if -4.3000000000000003e45 < (*.f64 a b) < 3.80000000000000012e145

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 93.1%

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

   7. Simplified 93.1%

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

   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 64.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.3 \cdot 10^{+45}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+145}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -8.1 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -8.1e+96)
     t_1
     (if (<= (* a b) 1.1e+157) (+ 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 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -8.1e+96) {
		tmp = t_1;
	} else if ((a * b) <= 1.1e+157) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-8.1d+96)) then
        tmp = t_1
    else if ((a * b) <= 1.1d+157) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -8.1e+96) {
		tmp = t_1;
	} else if ((a * b) <= 1.1e+157) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -8.1e+96:
		tmp = t_1
	elif (a * b) <= 1.1e+157:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -8.1e+96)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.1e+157)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -8.1e+96)
		tmp = t_1;
	elseif ((a * b) <= 1.1e+157)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -8.1e+96], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.1e+157], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8.1000000000000002e96 or 1.1000000000000001e157 < (*.f64 a b)

   1. Initial program 97.4%

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

      1. +-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 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 76.4%

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

   7. Simplified 76.4%

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

   if -8.1000000000000002e96 < (*.f64 a b) < 1.1000000000000001e157

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in c around inf

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

   10. Simplified 65.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.1 \cdot 10^{+96}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -5.8e+228)
     t_1
     (if (<= (* a b) 1.75e+139) (+ (* 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) <= -5.8e+228) {
		tmp = t_1;
	} else if ((a * b) <= 1.75e+139) {
		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) <= (-5.8d+228)) then
        tmp = t_1
    else if ((a * b) <= 1.75d+139) 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) <= -5.8e+228) {
		tmp = t_1;
	} else if ((a * b) <= 1.75e+139) {
		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) <= -5.8e+228:
		tmp = t_1
	elif (a * b) <= 1.75e+139:
		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) <= -5.8e+228)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.75e+139)
		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) <= -5.8e+228)
		tmp = t_1;
	elseif ((a * b) <= 1.75e+139)
		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], -5.8e+228], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.75e+139], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.80000000000000003e228 or 1.74999999999999989e139 < (*.f64 a b)

   1. Initial program 96.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 82.6%

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

   7. Simplified 82.6%

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

   if -5.80000000000000003e228 < (*.f64 a b) < 1.74999999999999989e139

   1. Initial program 99.5%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 88.7%

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

   7. Simplified 88.7%

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

   8. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 55.4%

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

   10. Simplified 55.4%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+228}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2.65 \cdot 10^{+150}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -1.15e+52)
     t_1
     (if (<= (* a b) 2.65e+150) (* 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 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.15e+52) {
		tmp = t_1;
	} else if ((a * b) <= 2.65e+150) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-1.15d+52)) then
        tmp = t_1
    else if ((a * b) <= 2.65d+150) then
        tmp = 0.0625d0 * (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.15e+52) {
		tmp = t_1;
	} else if ((a * b) <= 2.65e+150) {
		tmp = 0.0625 * (z * t);
	} 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) <= -1.15e+52:
		tmp = t_1
	elif (a * b) <= 2.65e+150:
		tmp = 0.0625 * (z * t)
	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) <= -1.15e+52)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.65e+150)
		tmp = Float64(0.0625 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -1.15e+52)
		tmp = t_1;
	elseif ((a * b) <= 2.65e+150)
		tmp = 0.0625 * (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.15e+52], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.65e+150], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.15e52 or 2.65000000000000007e150 < (*.f64 a b)

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in 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 70.2%

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

   7. Simplified 70.2%

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

   if -1.15e52 < (*.f64 a b) < 2.65000000000000007e150

   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 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 40.6%

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

   7. Simplified 40.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+52}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 2.65 \cdot 10^{+150}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+133}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1.1e+74) (* x y) (if (<= (* x y) 4.4e+133) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1.1e+74) {
		tmp = x * y;
	} else if ((x * y) <= 4.4e+133) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-1.1d+74)) then
        tmp = x * y
    else if ((x * y) <= 4.4d+133) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1.1e+74) {
		tmp = x * y;
	} else if ((x * y) <= 4.4e+133) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1.1e+74:
		tmp = x * y
	elif (x * y) <= 4.4e+133:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1.1e+74)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 4.4e+133)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -1.1e+74)
		tmp = x * y;
	elseif ((x * y) <= 4.4e+133)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.1e+74], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.4e+133], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.1000000000000001e74 or 4.4e133 < (*.f64 x y)

   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

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

      1. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

   if -1.1000000000000001e74 < (*.f64 x y) < 4.4e133

   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 28.8%

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

Alternative 12: 22.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. +-commutative N/A

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

   2. sub-neg N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

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

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

   6. distribute-neg-frac2 N/A

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

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

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

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

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

   9. metadata-eval N/A

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

   10. associate-+r+ N/A

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

   11. +-commutative N/A

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

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

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

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

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

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

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

   15. +-commutative N/A

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

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

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

   17. *-lowering-*.f64 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in c around inf

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

7. Simplified 22.1%

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

Reproduce

herbie shell --seed 2024152 
(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))