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

Percentage Accurate: 97.5% → 98.3%

Time: 9.8s

Alternatives: 11

Speedup: 0.5×

• 32.7% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1 + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ t_1 c) (* (* a b) -0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + c;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + c;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + c
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + c);
	else
		tmp = Float64(Float64(a * b) * -0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + c;
	else
		tmp = (a * b) * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + c), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 42.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-18}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{-179}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -3.5e+220)
     t_1
     (if (<= (* a b) -1e-18)
       (* 0.0625 (* z t))
       (if (<= (* a b) -8.2e-307)
         c
         (if (<= (* a b) 1.75e-179)
           (* x y)
           (if (<= (* a b) 2.4e+36) 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) <= -3.5e+220) {
		tmp = t_1;
	} else if ((a * b) <= -1e-18) {
		tmp = 0.0625 * (z * t);
	} else if ((a * b) <= -8.2e-307) {
		tmp = c;
	} else if ((a * b) <= 1.75e-179) {
		tmp = x * y;
	} else if ((a * b) <= 2.4e+36) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-3.5d+220)) then
        tmp = t_1
    else if ((a * b) <= (-1d-18)) then
        tmp = 0.0625d0 * (z * t)
    else if ((a * b) <= (-8.2d-307)) then
        tmp = c
    else if ((a * b) <= 1.75d-179) then
        tmp = x * y
    else if ((a * b) <= 2.4d+36) then
        tmp = c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -3.5e+220) {
		tmp = t_1;
	} else if ((a * b) <= -1e-18) {
		tmp = 0.0625 * (z * t);
	} else if ((a * b) <= -8.2e-307) {
		tmp = c;
	} else if ((a * b) <= 1.75e-179) {
		tmp = x * y;
	} else if ((a * b) <= 2.4e+36) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -3.5e+220:
		tmp = t_1
	elif (a * b) <= -1e-18:
		tmp = 0.0625 * (z * t)
	elif (a * b) <= -8.2e-307:
		tmp = c
	elif (a * b) <= 1.75e-179:
		tmp = x * y
	elif (a * b) <= 2.4e+36:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -3.5e+220)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e-18)
		tmp = Float64(0.0625 * Float64(z * t));
	elseif (Float64(a * b) <= -8.2e-307)
		tmp = c;
	elseif (Float64(a * b) <= 1.75e-179)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.4e+36)
		tmp = c;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -3.5e+220)
		tmp = t_1;
	elseif ((a * b) <= -1e-18)
		tmp = 0.0625 * (z * t);
	elseif ((a * b) <= -8.2e-307)
		tmp = c;
	elseif ((a * b) <= 1.75e-179)
		tmp = x * y;
	elseif ((a * b) <= 2.4e+36)
		tmp = c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.5e+220], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e-18], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -8.2e-307], c, If[LessEqual[N[(a * b), $MachinePrecision], 1.75e-179], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.4e+36], c, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -3.49999999999999986e220 or 2.39999999999999992e36 < (*.f64 a b)

   1. Initial program 93.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around 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 76.2%

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

   7. Simplified 76.2%

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

   if -3.49999999999999986e220 < (*.f64 a b) < -1.0000000000000001e-18

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-lowering-*.f64 49.9%

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

   7. Simplified 49.9%

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

   if -1.0000000000000001e-18 < (*.f64 a b) < -8.20000000000000064e-307 or 1.75000000000000012e-179 < (*.f64 a b) < 2.39999999999999992e36

   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 46.9%

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

   if -8.20000000000000064e-307 < (*.f64 a b) < 1.75000000000000012e-179

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 49.3%

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

   7. Simplified 49.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+220}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-18}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{-179}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 43.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -1.5 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -3.6 \cdot 10^{-304}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+37}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -1.5e+118)
     t_1
     (if (<= (* a b) -3.2e+57)
       (* x y)
       (if (<= (* a b) -3.6e-304)
         c
         (if (<= (* a b) 1.35e-179) (* x y) (if (<= (* a b) 4e+37) c t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.5e+118) {
		tmp = t_1;
	} else if ((a * b) <= -3.2e+57) {
		tmp = x * y;
	} else if ((a * b) <= -3.6e-304) {
		tmp = c;
	} else if ((a * b) <= 1.35e-179) {
		tmp = x * y;
	} else if ((a * b) <= 4e+37) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-1.5d+118)) then
        tmp = t_1
    else if ((a * b) <= (-3.2d+57)) then
        tmp = x * y
    else if ((a * b) <= (-3.6d-304)) then
        tmp = c
    else if ((a * b) <= 1.35d-179) then
        tmp = x * y
    else if ((a * b) <= 4d+37) then
        tmp = c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.5e+118) {
		tmp = t_1;
	} else if ((a * b) <= -3.2e+57) {
		tmp = x * y;
	} else if ((a * b) <= -3.6e-304) {
		tmp = c;
	} else if ((a * b) <= 1.35e-179) {
		tmp = x * y;
	} else if ((a * b) <= 4e+37) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -1.5e+118:
		tmp = t_1
	elif (a * b) <= -3.2e+57:
		tmp = x * y
	elif (a * b) <= -3.6e-304:
		tmp = c
	elif (a * b) <= 1.35e-179:
		tmp = x * y
	elif (a * b) <= 4e+37:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -1.5e+118)
		tmp = t_1;
	elseif (Float64(a * b) <= -3.2e+57)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -3.6e-304)
		tmp = c;
	elseif (Float64(a * b) <= 1.35e-179)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 4e+37)
		tmp = c;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -1.5e+118)
		tmp = t_1;
	elseif ((a * b) <= -3.2e+57)
		tmp = x * y;
	elseif ((a * b) <= -3.6e-304)
		tmp = c;
	elseif ((a * b) <= 1.35e-179)
		tmp = x * y;
	elseif ((a * b) <= 4e+37)
		tmp = c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.5e+118], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -3.2e+57], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3.6e-304], c, If[LessEqual[N[(a * b), $MachinePrecision], 1.35e-179], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4e+37], c, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.5e118 or 3.99999999999999982e37 < (*.f64 a b)

   1. Initial program 94.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 70.0%

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

   7. Simplified 70.0%

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

   if -1.5e118 < (*.f64 a b) < -3.20000000000000029e57 or -3.6000000000000001e-304 < (*.f64 a b) < 1.34999999999999994e-179

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 51.2%

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

   7. Simplified 51.2%

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

   if -3.20000000000000029e57 < (*.f64 a b) < -3.6000000000000001e-304 or 1.34999999999999994e-179 < (*.f64 a b) < 3.99999999999999982e37

   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 43.3%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.5 \cdot 10^{+118}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -3.6 \cdot 10^{-304}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+37}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -8.4 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* a b) -4.0))))
   (if (<= (* a b) -8.4e+120)
     t_1
     (if (<= (* a b) -3.6e-22)
       (+ (* x y) (* 0.0625 (* z t)))
       (if (<= (* a b) 1.16e+35) (+ (* 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) <= -8.4e+120) {
		tmp = t_1;
	} else if ((a * b) <= -3.6e-22) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 1.16e+35) {
		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 = (x * y) + ((a * b) / (-4.0d0))
    if ((a * b) <= (-8.4d+120)) then
        tmp = t_1
    else if ((a * b) <= (-3.6d-22)) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else if ((a * b) <= 1.16d+35) 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 = (x * y) + ((a * b) / -4.0);
	double tmp;
	if ((a * b) <= -8.4e+120) {
		tmp = t_1;
	} else if ((a * b) <= -3.6e-22) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 1.16e+35) {
		tmp = (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) <= -8.4e+120:
		tmp = t_1
	elif (a * b) <= -3.6e-22:
		tmp = (x * y) + (0.0625 * (z * t))
	elif (a * b) <= 1.16e+35:
		tmp = (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) <= -8.4e+120)
		tmp = t_1;
	elseif (Float64(a * b) <= -3.6e-22)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 1.16e+35)
		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 = (x * y) + ((a * b) / -4.0);
	tmp = 0.0;
	if ((a * b) <= -8.4e+120)
		tmp = t_1;
	elseif ((a * b) <= -3.6e-22)
		tmp = (x * y) + (0.0625 * (z * t));
	elseif ((a * b) <= 1.16e+35)
		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[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -8.4e+120], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -3.6e-22], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.16e+35], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.4000000000000002e120 or 1.1600000000000001e35 < (*.f64 a b)

   1. Initial program 94.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{a \cdot b}{-4} + \left(\frac{z \cdot t}{16} + \left(x \cdot y + c\right)\right)} \]
   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 80.6%

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

   7. Simplified 80.6%

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

   if -8.4000000000000002e120 < (*.f64 a b) < -3.5999999999999998e-22

   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 y around inf

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

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

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

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

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

      3. /-lowering-/.f64 96.3%

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

   7. Simplified 96.3%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-lowering-*.f64 83.9%

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

   10. Simplified 83.9%

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

   11. Taylor expanded in x around inf

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

   13. Simplified 80.0%

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

   if -3.5999999999999998e-22 < (*.f64 a b) < 1.1600000000000001e35

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 71.7%

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

   10. Simplified 71.7%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.4 \cdot 10^{+120}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \mathbf{elif}\;a \cdot b \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -3.6 \cdot 10^{+272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -3.6e+272)
     t_1
     (if (<= (* a b) -1.4e-18)
       (+ (* x y) (* 0.0625 (* z t)))
       (if (<= (* a b) 1.65e+48) (+ (* 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) <= -3.6e+272) {
		tmp = t_1;
	} else if ((a * b) <= -1.4e-18) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 1.65e+48) {
		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) <= (-3.6d+272)) then
        tmp = t_1
    else if ((a * b) <= (-1.4d-18)) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else if ((a * b) <= 1.65d+48) 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) <= -3.6e+272) {
		tmp = t_1;
	} else if ((a * b) <= -1.4e-18) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((a * b) <= 1.65e+48) {
		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) <= -3.6e+272:
		tmp = t_1
	elif (a * b) <= -1.4e-18:
		tmp = (x * y) + (0.0625 * (z * t))
	elif (a * b) <= 1.65e+48:
		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) <= -3.6e+272)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.4e-18)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 1.65e+48)
		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) <= -3.6e+272)
		tmp = t_1;
	elseif ((a * b) <= -1.4e-18)
		tmp = (x * y) + (0.0625 * (z * t));
	elseif ((a * b) <= 1.65e+48)
		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], -3.6e+272], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.4e-18], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.65e+48], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.5999999999999998e272 or 1.65000000000000011e48 < (*.f64 a b)

   1. Initial program 92.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 79.2%

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

   7. Simplified 79.2%

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

   if -3.5999999999999998e272 < (*.f64 a b) < -1.40000000000000006e-18

   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 y around inf

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

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

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

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

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

      3. /-lowering-/.f64 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-lowering-*.f64 74.8%

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

   10. Simplified 74.8%

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

   11. Taylor expanded in x around inf

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

   13. Simplified 68.0%

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

   if -1.40000000000000006e-18 < (*.f64 a b) < 1.65000000000000011e48

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 71.7%

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

   10. Simplified 71.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.6 \cdot 10^{+272}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -3.1 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-312}:\\ \;\;\;\;c - \left(z \cdot t\right) \cdot -0.0625\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -3.1e+221)
     t_1
     (if (<= (* a b) -1e-312)
       (- c (* (* z t) -0.0625))
       (if (<= (* a b) 1.55e+48) (+ (* 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) <= -3.1e+221) {
		tmp = t_1;
	} else if ((a * b) <= -1e-312) {
		tmp = c - ((z * t) * -0.0625);
	} else if ((a * b) <= 1.55e+48) {
		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) <= (-3.1d+221)) then
        tmp = t_1
    else if ((a * b) <= (-1d-312)) then
        tmp = c - ((z * t) * (-0.0625d0))
    else if ((a * b) <= 1.55d+48) 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) <= -3.1e+221) {
		tmp = t_1;
	} else if ((a * b) <= -1e-312) {
		tmp = c - ((z * t) * -0.0625);
	} else if ((a * b) <= 1.55e+48) {
		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) <= -3.1e+221:
		tmp = t_1
	elif (a * b) <= -1e-312:
		tmp = c - ((z * t) * -0.0625)
	elif (a * b) <= 1.55e+48:
		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) <= -3.1e+221)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e-312)
		tmp = Float64(c - Float64(Float64(z * t) * -0.0625));
	elseif (Float64(a * b) <= 1.55e+48)
		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) <= -3.1e+221)
		tmp = t_1;
	elseif ((a * b) <= -1e-312)
		tmp = c - ((z * t) * -0.0625);
	elseif ((a * b) <= 1.55e+48)
		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], -3.1e+221], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e-312], N[(c - N[(N[(z * t), $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.55e+48], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.10000000000000006e221 or 1.55000000000000003e48 < (*.f64 a b)

   1. Initial program 93.3%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around 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 76.9%

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

   7. Simplified 76.9%

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

   if -3.10000000000000006e221 < (*.f64 a b) < -9.9999999999847e-313

   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 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

         \[\leadsto c + z \cdot \left(\left(\mathsf{neg}\left(\frac{-1}{16}\right)\right) \cdot t\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto c + z \cdot \left(\mathsf{neg}\left(\frac{-1}{16} \cdot t\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto c + \left(\mathsf{neg}\left(z \cdot \left(\frac{-1}{16} \cdot t\right)\right)\right) \]

      6. unsub-neg N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. *-lowering-*.f64 67.8%

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

   10. Simplified 67.8%

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

   if -9.9999999999847e-313 < (*.f64 a b) < 1.55000000000000003e48

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 72.6%

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

   10. Simplified 72.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.1 \cdot 10^{+221}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-312}:\\ \;\;\;\;c - \left(z \cdot t\right) \cdot -0.0625\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \frac{a \cdot b}{-4}\\ \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+101}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1 + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (/ (* a b) -4.0)))
   (if (<= (* a b) -6e+101)
     (+ t_2 t_1)
     (if (<= (* a b) 2.1e+35) (+ t_1 (+ (* x y) c)) (+ (* x y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -6e+101) {
		tmp = t_2 + t_1;
	} else if ((a * b) <= 2.1e+35) {
		tmp = t_1 + ((x * y) + c);
	} else {
		tmp = (x * y) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (a * b) / (-4.0d0)
    if ((a * b) <= (-6d+101)) then
        tmp = t_2 + t_1
    else if ((a * b) <= 2.1d+35) then
        tmp = t_1 + ((x * y) + c)
    else
        tmp = (x * y) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) / -4.0;
	double tmp;
	if ((a * b) <= -6e+101) {
		tmp = t_2 + t_1;
	} else if ((a * b) <= 2.1e+35) {
		tmp = t_1 + ((x * y) + c);
	} else {
		tmp = (x * y) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) / -4.0
	tmp = 0
	if (a * b) <= -6e+101:
		tmp = t_2 + t_1
	elif (a * b) <= 2.1e+35:
		tmp = t_1 + ((x * y) + c)
	else:
		tmp = (x * y) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) / -4.0)
	tmp = 0.0
	if (Float64(a * b) <= -6e+101)
		tmp = Float64(t_2 + t_1);
	elseif (Float64(a * b) <= 2.1e+35)
		tmp = Float64(t_1 + Float64(Float64(x * y) + c));
	else
		tmp = Float64(Float64(x * y) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) / -4.0;
	tmp = 0.0;
	if ((a * b) <= -6e+101)
		tmp = t_2 + t_1;
	elseif ((a * b) <= 2.1e+35)
		tmp = t_1 + ((x * y) + c);
	else
		tmp = (x * y) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -6e+101], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.1e+35], N[(t$95$1 + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.99999999999999986e101

   1. Initial program 90.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-lowering-*.f64 81.8%

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

   7. Simplified 81.8%

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

   if -5.99999999999999986e101 < (*.f64 a b) < 2.0999999999999999e35

   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 96.8%

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

   7. Simplified 96.8%

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

   if 2.0999999999999999e35 < (*.f64 a b)

   1. Initial program 98.1%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+101}:\\ \;\;\;\;\frac{a \cdot b}{-4} + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.95 \cdot 10^{+271}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{+34}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -1.95e+271)
   (* (* a b) -0.25)
   (if (<= (* a b) 1.75e+34)
     (+ (* 0.0625 (* z t)) (+ (* x y) c))
     (+ (* x y) (/ (* a b) -4.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1.95e+271) {
		tmp = (a * b) * -0.25;
	} else if ((a * b) <= 1.75e+34) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + ((a * b) / -4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-1.95d+271)) then
        tmp = (a * b) * (-0.25d0)
    else if ((a * b) <= 1.75d+34) then
        tmp = (0.0625d0 * (z * t)) + ((x * y) + c)
    else
        tmp = (x * y) + ((a * b) / (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1.95e+271) {
		tmp = (a * b) * -0.25;
	} else if ((a * b) <= 1.75e+34) {
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	} else {
		tmp = (x * y) + ((a * b) / -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -1.95e+271:
		tmp = (a * b) * -0.25
	elif (a * b) <= 1.75e+34:
		tmp = (0.0625 * (z * t)) + ((x * y) + c)
	else:
		tmp = (x * y) + ((a * b) / -4.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -1.95e+271)
		tmp = Float64(Float64(a * b) * -0.25);
	elseif (Float64(a * b) <= 1.75e+34)
		tmp = Float64(Float64(0.0625 * Float64(z * t)) + Float64(Float64(x * y) + c));
	else
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) / -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -1.95e+271)
		tmp = (a * b) * -0.25;
	elseif ((a * b) <= 1.75e+34)
		tmp = (0.0625 * (z * t)) + ((x * y) + c);
	else
		tmp = (x * y) + ((a * b) / -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.95e+271], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.75e+34], N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.95e271

   1. Initial program 78.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 91.0%

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

   7. Simplified 91.0%

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

   if -1.95e271 < (*.f64 a b) < 1.74999999999999999e34

   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 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%

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

   if 1.74999999999999999e34 < (*.f64 a b)

   1. Initial program 98.1%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. distribute-neg-frac2 N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

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

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

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

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

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

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

      15. +-commutative N/A

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

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

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

      17. *-lowering-*.f64 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.95 \cdot 10^{+271}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{+34}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(x \cdot y + c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \frac{a \cdot b}{-4}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -4.4e+205)
     t_1
     (if (<= (* a b) 1.65e+48) (+ (* 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) <= -4.4e+205) {
		tmp = t_1;
	} else if ((a * b) <= 1.65e+48) {
		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) <= (-4.4d+205)) then
        tmp = t_1
    else if ((a * b) <= 1.65d+48) 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) <= -4.4e+205) {
		tmp = t_1;
	} else if ((a * b) <= 1.65e+48) {
		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) <= -4.4e+205:
		tmp = t_1
	elif (a * b) <= 1.65e+48:
		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) <= -4.4e+205)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.65e+48)
		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) <= -4.4e+205)
		tmp = t_1;
	elseif ((a * b) <= 1.65e+48)
		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], -4.4e+205], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.65e+48], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.3999999999999997e205 or 1.65000000000000011e48 < (*.f64 a b)

   1. Initial program 93.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around 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 75.0%

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

   7. Simplified 75.0%

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

   if -4.3999999999999997e205 < (*.f64 a b) < 1.65000000000000011e48

   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 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 65.9%

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

   10. Simplified 65.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+205}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{+82}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -6e+21) (* x y) (if (<= (* x y) 1.42e+82) 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) <= -6e+21) {
		tmp = x * y;
	} else if ((x * y) <= 1.42e+82) {
		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) <= (-6d+21)) then
        tmp = x * y
    else if ((x * y) <= 1.42d+82) 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) <= -6e+21) {
		tmp = x * y;
	} else if ((x * y) <= 1.42e+82) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -6e+21:
		tmp = x * y
	elif (x * y) <= 1.42e+82:
		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) <= -6e+21)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.42e+82)
		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) <= -6e+21)
		tmp = x * y;
	elseif ((x * y) <= 1.42e+82)
		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], -6e+21], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.42e+82], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6e21 or 1.41999999999999993e82 < (*.f64 x y)

   1. Initial program 95.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 59.2%

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

   7. Simplified 59.2%

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

   if -6e21 < (*.f64 x y) < 1.41999999999999993e82

   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 32.6%

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

Alternative 11: 22.7% 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 98.0%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
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 98.0%

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

3. Simplified 98.0%

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

5. Taylor expanded in c around inf

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

7. Simplified 24.8%

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

Reproduce

herbie shell --seed 2024164 
(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))