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

Percentage Accurate: 97.7% → 98.6%

Time: 11.0s

Alternatives: 13

Speedup: 0.5×

• 33.7% 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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.5× speedup

Math

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

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) (+ c t_1) (+ c (* x y)))))

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 = c + t_1;
	} else {
		tmp = c + (x * y);
	}
	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 = c + t_1;
	} else {
		tmp = c + (x * y);
	}
	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 = c + t_1
	else:
		tmp = c + (x * y)
	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(c + t_1);
	else
		tmp = Float64(c + Float64(x * y));
	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 = c + t_1;
	else
		tmp = c + (x * y);
	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[(c + t$95$1), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +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) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 44.9%

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

4. Final simplification 98.1%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate--l+ 96.5%

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

   2. fma-define 97.3%

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

   3. associate-/l* 97.3%

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

   4. fma-neg 98.0%

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

   5. distribute-neg-frac2 98.0%

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

   6. metadata-eval 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. *-commutative 96.5%

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

   3. associate-+l- 96.5%

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

   4. fma-define 96.9%

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

   5. *-commutative 96.9%

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

   6. associate-/l* 96.9%

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

   7. associate-/l* 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 4: 66.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + t\_2\\ t_4 := x \cdot y + t\_2\\ \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+135}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \cdot y \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-66}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* 0.0625 (* z t)))
        (t_3 (+ c t_2))
        (t_4 (+ (* x y) t_2)))
   (if (<= (* x y) -3.2e+135)
     t_4
     (if (<= (* x y) -2.1e-33)
       t_1
       (if (<= (* x y) -3.6e-56)
         t_3
         (if (<= (* x y) 8.2e-178)
           t_1
           (if (<= (* x y) 1.4e-66)
             t_3
             (if (<= (* x y) 6.8e+92) t_1 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = c + t_2;
	double t_4 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -3.2e+135) {
		tmp = t_4;
	} else if ((x * y) <= -2.1e-33) {
		tmp = t_1;
	} else if ((x * y) <= -3.6e-56) {
		tmp = t_3;
	} else if ((x * y) <= 8.2e-178) {
		tmp = t_1;
	} else if ((x * y) <= 1.4e-66) {
		tmp = t_3;
	} else if ((x * y) <= 6.8e+92) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = 0.0625d0 * (z * t)
    t_3 = c + t_2
    t_4 = (x * y) + t_2
    if ((x * y) <= (-3.2d+135)) then
        tmp = t_4
    else if ((x * y) <= (-2.1d-33)) then
        tmp = t_1
    else if ((x * y) <= (-3.6d-56)) then
        tmp = t_3
    else if ((x * y) <= 8.2d-178) then
        tmp = t_1
    else if ((x * y) <= 1.4d-66) then
        tmp = t_3
    else if ((x * y) <= 6.8d+92) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = c + t_2;
	double t_4 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -3.2e+135) {
		tmp = t_4;
	} else if ((x * y) <= -2.1e-33) {
		tmp = t_1;
	} else if ((x * y) <= -3.6e-56) {
		tmp = t_3;
	} else if ((x * y) <= 8.2e-178) {
		tmp = t_1;
	} else if ((x * y) <= 1.4e-66) {
		tmp = t_3;
	} else if ((x * y) <= 6.8e+92) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = 0.0625 * (z * t)
	t_3 = c + t_2
	t_4 = (x * y) + t_2
	tmp = 0
	if (x * y) <= -3.2e+135:
		tmp = t_4
	elif (x * y) <= -2.1e-33:
		tmp = t_1
	elif (x * y) <= -3.6e-56:
		tmp = t_3
	elif (x * y) <= 8.2e-178:
		tmp = t_1
	elif (x * y) <= 1.4e-66:
		tmp = t_3
	elif (x * y) <= 6.8e+92:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(c + t_2)
	t_4 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(x * y) <= -3.2e+135)
		tmp = t_4;
	elseif (Float64(x * y) <= -2.1e-33)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.6e-56)
		tmp = t_3;
	elseif (Float64(x * y) <= 8.2e-178)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.4e-66)
		tmp = t_3;
	elseif (Float64(x * y) <= 6.8e+92)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = 0.0625 * (z * t);
	t_3 = c + t_2;
	t_4 = (x * y) + t_2;
	tmp = 0.0;
	if ((x * y) <= -3.2e+135)
		tmp = t_4;
	elseif ((x * y) <= -2.1e-33)
		tmp = t_1;
	elseif ((x * y) <= -3.6e-56)
		tmp = t_3;
	elseif ((x * y) <= 8.2e-178)
		tmp = t_1;
	elseif ((x * y) <= 1.4e-66)
		tmp = t_3;
	elseif ((x * y) <= 6.8e+92)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+135], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e-33], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.6e-56], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 8.2e-178], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.4e-66], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 6.8e+92], t$95$1, t$95$4]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.19999999999999975e135 or 6.7999999999999996e92 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in a around 0 80.9%

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

   4. Taylor expanded in c around 0 77.6%

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

   if -3.19999999999999975e135 < (*.f64 x y) < -2.1e-33 or -3.59999999999999978e-56 < (*.f64 x y) < 8.1999999999999998e-178 or 1.4e-66 < (*.f64 x y) < 6.7999999999999996e92

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*r* 74.4%

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

   5. Simplified 74.4%

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

   if -2.1e-33 < (*.f64 x y) < -3.59999999999999978e-56 or 8.1999999999999998e-178 < (*.f64 x y) < 1.4e-66

   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

   3. Taylor expanded in z around inf 81.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-178}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-66}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+92}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.42 \cdot 10^{+182}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -1.36 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4.9 \cdot 10^{-54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (+ c (* 0.0625 (* z t))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -2.42e+182)
     t_3
     (if (<= (* x y) -1.36e-33)
       t_1
       (if (<= (* x y) -4.9e-54)
         t_2
         (if (<= (* x y) 8e-183)
           t_1
           (if (<= (* x y) 2.6e-65)
             t_2
             (if (<= (* x y) 5.2e+116) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.42e+182) {
		tmp = t_3;
	} else if ((x * y) <= -1.36e-33) {
		tmp = t_1;
	} else if ((x * y) <= -4.9e-54) {
		tmp = t_2;
	} else if ((x * y) <= 8e-183) {
		tmp = t_1;
	} else if ((x * y) <= 2.6e-65) {
		tmp = t_2;
	} else if ((x * y) <= 5.2e+116) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = c + (0.0625d0 * (z * t))
    t_3 = c + (x * y)
    if ((x * y) <= (-2.42d+182)) then
        tmp = t_3
    else if ((x * y) <= (-1.36d-33)) then
        tmp = t_1
    else if ((x * y) <= (-4.9d-54)) then
        tmp = t_2
    else if ((x * y) <= 8d-183) then
        tmp = t_1
    else if ((x * y) <= 2.6d-65) then
        tmp = t_2
    else if ((x * y) <= 5.2d+116) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.42e+182) {
		tmp = t_3;
	} else if ((x * y) <= -1.36e-33) {
		tmp = t_1;
	} else if ((x * y) <= -4.9e-54) {
		tmp = t_2;
	} else if ((x * y) <= 8e-183) {
		tmp = t_1;
	} else if ((x * y) <= 2.6e-65) {
		tmp = t_2;
	} else if ((x * y) <= 5.2e+116) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (0.0625 * (z * t))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -2.42e+182:
		tmp = t_3
	elif (x * y) <= -1.36e-33:
		tmp = t_1
	elif (x * y) <= -4.9e-54:
		tmp = t_2
	elif (x * y) <= 8e-183:
		tmp = t_1
	elif (x * y) <= 2.6e-65:
		tmp = t_2
	elif (x * y) <= 5.2e+116:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.42e+182)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.36e-33)
		tmp = t_1;
	elseif (Float64(x * y) <= -4.9e-54)
		tmp = t_2;
	elseif (Float64(x * y) <= 8e-183)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.6e-65)
		tmp = t_2;
	elseif (Float64(x * y) <= 5.2e+116)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = c + (0.0625 * (z * t));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.42e+182)
		tmp = t_3;
	elseif ((x * y) <= -1.36e-33)
		tmp = t_1;
	elseif ((x * y) <= -4.9e-54)
		tmp = t_2;
	elseif ((x * y) <= 8e-183)
		tmp = t_1;
	elseif ((x * y) <= 2.6e-65)
		tmp = t_2;
	elseif ((x * y) <= 5.2e+116)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.42e+182], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.36e-33], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4.9e-54], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 8e-183], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.6e-65], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5.2e+116], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.42000000000000005e182 or 5.19999999999999973e116 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 75.7%

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

   if -2.42000000000000005e182 < (*.f64 x y) < -1.36e-33 or -4.90000000000000021e-54 < (*.f64 x y) < 8.00000000000000004e-183 or 2.6000000000000001e-65 < (*.f64 x y) < 5.19999999999999973e116

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*r* 71.3%

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

   5. Simplified 71.3%

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

   if -1.36e-33 < (*.f64 x y) < -4.90000000000000021e-54 or 8.00000000000000004e-183 < (*.f64 x y) < 2.6000000000000001e-65

   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

   3. Taylor expanded in z around inf 81.3%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.42 \cdot 10^{+182}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.36 \cdot 10^{-33}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -4.9 \cdot 10^{-54}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{-183}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+114} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{-20} \lor \neg \left(a \cdot b \leq 0.001\right) \land a \cdot b \leq 10^{+160}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+114)
         (not
          (or (<= (* a b) 5e-20)
              (and (not (<= (* a b) 0.001)) (<= (* a b) 1e+160)))))
   (+ c (- (* x y) (* (* a b) 0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+114) || !(((a * b) <= 5e-20) || (!((a * b) <= 0.001) && ((a * b) <= 1e+160)))) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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) <= (-2d+114)) .or. (.not. ((a * b) <= 5d-20) .or. (.not. ((a * b) <= 0.001d0)) .and. ((a * b) <= 1d+160))) then
        tmp = c + ((x * y) - ((a * b) * 0.25d0))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    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) <= -2e+114) || !(((a * b) <= 5e-20) || (!((a * b) <= 0.001) && ((a * b) <= 1e+160)))) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2e+114) or not (((a * b) <= 5e-20) or (not ((a * b) <= 0.001) and ((a * b) <= 1e+160))):
		tmp = c + ((x * y) - ((a * b) * 0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2e+114) || !((Float64(a * b) <= 5e-20) || (!(Float64(a * b) <= 0.001) && (Float64(a * b) <= 1e+160))))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2e+114) || ~((((a * b) <= 5e-20) || (~(((a * b) <= 0.001)) && ((a * b) <= 1e+160)))))
		tmp = c + ((x * y) - ((a * b) * 0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+114], N[Not[Or[LessEqual[N[(a * b), $MachinePrecision], 5e-20], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 0.001]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 1e+160]]]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2e114 or 4.9999999999999999e-20 < (*.f64 a b) < 1e-3 or 1.00000000000000001e160 < (*.f64 a b)

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 90.9%

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

   if -2e114 < (*.f64 a b) < 4.9999999999999999e-20 or 1e-3 < (*.f64 a b) < 1.00000000000000001e160

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 94.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+114} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{-20} \lor \neg \left(a \cdot b \leq 0.001\right) \land a \cdot b \leq 10^{+160}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -2.1e+74)
     t_2
     (if (<= (* x y) -1.9e-251)
       t_1
       (if (<= (* x y) -5.5e-284)
         (* a (* b -0.25))
         (if (<= (* x y) 3.6e+116) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+74) {
		tmp = t_2;
	} else if ((x * y) <= -1.9e-251) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-284) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 3.6e+116) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (0.0625d0 * (z * t))
    t_2 = c + (x * y)
    if ((x * y) <= (-2.1d+74)) then
        tmp = t_2
    else if ((x * y) <= (-1.9d-251)) then
        tmp = t_1
    else if ((x * y) <= (-5.5d-284)) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 3.6d+116) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+74) {
		tmp = t_2;
	} else if ((x * y) <= -1.9e-251) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-284) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 3.6e+116) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (z * t))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -2.1e+74:
		tmp = t_2
	elif (x * y) <= -1.9e-251:
		tmp = t_1
	elif (x * y) <= -5.5e-284:
		tmp = a * (b * -0.25)
	elif (x * y) <= 3.6e+116:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+74)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.9e-251)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.5e-284)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 3.6e+116)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (0.0625 * (z * t));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.1e+74)
		tmp = t_2;
	elseif ((x * y) <= -1.9e-251)
		tmp = t_1;
	elseif ((x * y) <= -5.5e-284)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 3.6e+116)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+74], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.9e-251], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-284], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.6e+116], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0999999999999999e74 or 3.59999999999999971e116 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf 70.3%

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

   if -2.0999999999999999e74 < (*.f64 x y) < -1.8999999999999999e-251 or -5.4999999999999995e-284 < (*.f64 x y) < 3.59999999999999971e116

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 65.2%

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

   if -1.8999999999999999e-251 < (*.f64 x y) < -5.4999999999999995e-284

   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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   4. Taylor expanded in c around 0 100.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in t around 0 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-*l* 97.5%

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

      3. *-commutative 97.5%

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

   7. Simplified 97.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-251}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+116}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+119}\right):\\ \;\;\;\;c + \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -6.5e+75) (not (<= (* x y) 5e+119)))
     (+ c (- (* x y) t_1))
     (+ c (- (* 0.0625 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -6.5e+75) || !((x * y) <= 5e+119)) {
		tmp = c + ((x * y) - t_1);
	} else {
		tmp = c + ((0.0625 * (z * t)) - 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 (((x * y) <= (-6.5d+75)) .or. (.not. ((x * y) <= 5d+119))) then
        tmp = c + ((x * y) - t_1)
    else
        tmp = c + ((0.0625d0 * (z * t)) - 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 (((x * y) <= -6.5e+75) || !((x * y) <= 5e+119)) {
		tmp = c + ((x * y) - t_1);
	} else {
		tmp = c + ((0.0625 * (z * t)) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -6.5e+75) or not ((x * y) <= 5e+119):
		tmp = c + ((x * y) - t_1)
	else:
		tmp = c + ((0.0625 * (z * t)) - 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(x * y) <= -6.5e+75) || !(Float64(x * y) <= 5e+119))
		tmp = Float64(c + Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(z * t)) - 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 (((x * y) <= -6.5e+75) || ~(((x * y) <= 5e+119)))
		tmp = c + ((x * y) - t_1);
	else
		tmp = c + ((0.0625 * (z * t)) - 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[Or[LessEqual[N[(x * y), $MachinePrecision], -6.5e+75], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+119]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.4999999999999998e75 or 4.9999999999999999e119 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 84.3%

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

   if -6.4999999999999998e75 < (*.f64 x y) < 4.9999999999999999e119

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 95.3%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+119}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+178} \lor \neg \left(a \leq -2.2 \cdot 10^{+137}\right) \land \left(a \leq -1.75 \cdot 10^{+102} \lor \neg \left(a \leq 2.45 \cdot 10^{+38}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.6e+178)
         (and (not (<= a -2.2e+137))
              (or (<= a -1.75e+102) (not (<= a 2.45e+38)))))
   (* a (* b -0.25))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.6e+178) || (!(a <= -2.2e+137) && ((a <= -1.75e+102) || !(a <= 2.45e+38)))) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (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 ((a <= (-1.6d+178)) .or. (.not. (a <= (-2.2d+137))) .and. (a <= (-1.75d+102)) .or. (.not. (a <= 2.45d+38))) then
        tmp = a * (b * (-0.25d0))
    else
        tmp = c + (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 ((a <= -1.6e+178) || (!(a <= -2.2e+137) && ((a <= -1.75e+102) || !(a <= 2.45e+38)))) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.6e+178) or (not (a <= -2.2e+137) and ((a <= -1.75e+102) or not (a <= 2.45e+38))):
		tmp = a * (b * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.6e+178) || (!(a <= -2.2e+137) && ((a <= -1.75e+102) || !(a <= 2.45e+38))))
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.6e+178) || (~((a <= -2.2e+137)) && ((a <= -1.75e+102) || ~((a <= 2.45e+38)))))
		tmp = a * (b * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.6e+178], And[N[Not[LessEqual[a, -2.2e+137]], $MachinePrecision], Or[LessEqual[a, -1.75e+102], N[Not[LessEqual[a, 2.45e+38]], $MachinePrecision]]]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e178 or -2.20000000000000015e137 < a < -1.75000000000000005e102 or 2.45000000000000001e38 < a

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   4. Taylor expanded in c around 0 66.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in t around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. associate-*l* 58.6%

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

      3. *-commutative 58.6%

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

   7. Simplified 58.6%

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

   if -1.6e178 < a < -2.20000000000000015e137 or -1.75000000000000005e102 < a < 2.45000000000000001e38

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 62.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+178} \lor \neg \left(a \leq -2.2 \cdot 10^{+137}\right) \land \left(a \leq -1.75 \cdot 10^{+102} \lor \neg \left(a \leq 2.45 \cdot 10^{+38}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.02 \cdot 10^{-280}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-97}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= a -3.5e+92)
     t_1
     (if (<= a -2.02e-280)
       c
       (if (<= a 6.2e-222) (* z (* t 0.0625)) (if (<= a 1.15e-97) 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 <= -3.5e+92) {
		tmp = t_1;
	} else if (a <= -2.02e-280) {
		tmp = c;
	} else if (a <= 6.2e-222) {
		tmp = z * (t * 0.0625);
	} else if (a <= 1.15e-97) {
		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 <= (-3.5d+92)) then
        tmp = t_1
    else if (a <= (-2.02d-280)) then
        tmp = c
    else if (a <= 6.2d-222) then
        tmp = z * (t * 0.0625d0)
    else if (a <= 1.15d-97) 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 <= -3.5e+92) {
		tmp = t_1;
	} else if (a <= -2.02e-280) {
		tmp = c;
	} else if (a <= 6.2e-222) {
		tmp = z * (t * 0.0625);
	} else if (a <= 1.15e-97) {
		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 <= -3.5e+92:
		tmp = t_1
	elif a <= -2.02e-280:
		tmp = c
	elif a <= 6.2e-222:
		tmp = z * (t * 0.0625)
	elif a <= 1.15e-97:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (a <= -3.5e+92)
		tmp = t_1;
	elseif (a <= -2.02e-280)
		tmp = c;
	elseif (a <= 6.2e-222)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (a <= 1.15e-97)
		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 <= -3.5e+92)
		tmp = t_1;
	elseif (a <= -2.02e-280)
		tmp = c;
	elseif (a <= 6.2e-222)
		tmp = z * (t * 0.0625);
	elseif (a <= 1.15e-97)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+92], t$95$1, If[LessEqual[a, -2.02e-280], c, If[LessEqual[a, 6.2e-222], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-97], c, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.49999999999999986e92 or 1.14999999999999997e-97 < a

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 73.6%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   4. Taylor expanded in c around 0 58.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in t around 0 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*l* 47.2%

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

      3. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if -3.49999999999999986e92 < a < -2.0199999999999999e-280 or 6.19999999999999959e-222 < a < 1.14999999999999997e-97

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 62.0%

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

   4. Taylor expanded in x around 0 38.7%

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

   if -2.0199999999999999e-280 < a < 6.19999999999999959e-222

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 64.4%

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

   4. Taylor expanded in t around inf 43.7%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

   6. Simplified 43.7%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -2.02 \cdot 10^{-280}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-97}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+150}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= b -8e+89)
     t_1
     (if (<= b 2.1e+150) (+ c (+ (* x y) (* 0.0625 (* z t)))) (+ 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 (b <= -8e+89) {
		tmp = t_1;
	} else if (b <= 2.1e+150) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + 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 (b <= (-8d+89)) then
        tmp = t_1
    else if (b <= 2.1d+150) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + 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 (b <= -8e+89) {
		tmp = t_1;
	} else if (b <= 2.1e+150) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if b <= -8e+89:
		tmp = t_1
	elif b <= 2.1e+150:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (b <= -8e+89)
		tmp = t_1;
	elseif (b <= 2.1e+150)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + 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 (b <= -8e+89)
		tmp = t_1;
	elseif (b <= 2.1e+150)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+89], t$95$1, If[LessEqual[b, 2.1e+150], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.99999999999999996e89

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   4. Taylor expanded in c around 0 75.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in t around 0 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-*l* 60.7%

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

      3. *-commutative 60.7%

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

   7. Simplified 60.7%

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

   if -7.99999999999999996e89 < b < 2.09999999999999998e150

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 84.4%

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

   if 2.09999999999999998e150 < b

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*r* 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+150}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+92} \lor \neg \left(a \leq 4 \cdot 10^{-97}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -3.5e+92) (not (<= a 4e-97))) (* a (* b -0.25)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.5e+92) || !(a <= 4e-97)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c;
	}
	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 <= (-3.5d+92)) .or. (.not. (a <= 4d-97))) then
        tmp = a * (b * (-0.25d0))
    else
        tmp = c
    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 <= -3.5e+92) || !(a <= 4e-97)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -3.5e+92) or not (a <= 4e-97):
		tmp = a * (b * -0.25)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -3.5e+92) || !(a <= 4e-97))
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -3.5e+92) || ~((a <= 4e-97)))
		tmp = a * (b * -0.25);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -3.5e+92], N[Not[LessEqual[a, 4e-97]], $MachinePrecision]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if a < -3.49999999999999986e92 or 4.00000000000000014e-97 < a

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 73.6%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]

   4. Taylor expanded in c around 0 58.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in t around 0 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*l* 47.2%

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

      3. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if -3.49999999999999986e92 < a < 4.00000000000000014e-97

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 61.5%

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

   4. Taylor expanded in x around 0 36.1%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+92} \lor \neg \left(a \leq 4 \cdot 10^{-97}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 21.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in x around inf 49.9%

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

4. Taylor expanded in x around 0 24.8%

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

5. Final simplification 24.8%

   \[\leadsto c \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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))