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

Percentage Accurate: 97.7% → 99.1%

Time: 12.8s

Alternatives: 14

Speedup: 1.0×

• 33.0% 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: 99.1% 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 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. associate--l+ 98.0%

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

   2. fma-define 98.8%

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

   3. associate-/l* 99.2%

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

   4. fmm-def 99.6%

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

   5. distribute-neg-frac2 99.6%

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

   6. metadata-eval 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 98.3% 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 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. associate-+l- 98.0%

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

   2. +-commutative 98.0%

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

   3. *-commutative 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+l- 98.0%

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

   6. fma-define 98.4%

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

   7. *-commutative 98.4%

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

   8. associate-/l* 98.8%

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

   9. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-82}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625)))) (t_2 (+ c (* a (* b -0.25)))))
   (if (<= (* a b) -2e+57)
     t_2
     (if (<= (* a b) -2e-80)
       t_1
       (if (<= (* a b) 2e-82)
         (+ c (* x y))
         (if (<= (* a b) 2e+121) 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 + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double tmp;
	if ((a * b) <= -2e+57) {
		tmp = t_2;
	} else if ((a * b) <= -2e-80) {
		tmp = t_1;
	} else if ((a * b) <= 2e-82) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e+121) {
		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 + (z * (t * 0.0625d0))
    t_2 = c + (a * (b * (-0.25d0)))
    if ((a * b) <= (-2d+57)) then
        tmp = t_2
    else if ((a * b) <= (-2d-80)) then
        tmp = t_1
    else if ((a * b) <= 2d-82) then
        tmp = c + (x * y)
    else if ((a * b) <= 2d+121) 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 + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double tmp;
	if ((a * b) <= -2e+57) {
		tmp = t_2;
	} else if ((a * b) <= -2e-80) {
		tmp = t_1;
	} else if ((a * b) <= 2e-82) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = c + (a * (b * -0.25))
	tmp = 0
	if (a * b) <= -2e+57:
		tmp = t_2
	elif (a * b) <= -2e-80:
		tmp = t_1
	elif (a * b) <= 2e-82:
		tmp = c + (x * y)
	elif (a * b) <= 2e+121:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(a * b) <= -2e+57)
		tmp = t_2;
	elseif (Float64(a * b) <= -2e-80)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e-82)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 2e+121)
		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 + (z * (t * 0.0625));
	t_2 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((a * b) <= -2e+57)
		tmp = t_2;
	elseif ((a * b) <= -2e-80)
		tmp = t_1;
	elseif ((a * b) <= 2e-82)
		tmp = c + (x * y);
	elseif ((a * b) <= 2e+121)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+57], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2e-80], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e-82], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+121], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e57 or 2.00000000000000007e121 < (*.f64 a b)

   1. Initial program 94.2%

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

      1. associate--l+ 94.2%

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

      2. fma-define 96.5%

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

      3. associate-/l* 97.7%

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

      4. fmm-def 98.8%

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

      5. distribute-neg-frac2 98.8%

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

      6. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in a around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*r* 79.8%

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

   7. Simplified 79.8%

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

   if -2.0000000000000001e57 < (*.f64 a b) < -1.99999999999999992e-80 or 2e-82 < (*.f64 a b) < 2.00000000000000007e121

   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 a around 0 87.4%

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

   4. Taylor expanded in t around inf 75.9%

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

      1. associate-*r* 75.9%

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

      2. *-commutative 75.9%

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

   6. Simplified 75.9%

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

   if -1.99999999999999992e-80 < (*.f64 a b) < 2e-82

   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 a around 0 96.0%

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

   4. Taylor expanded in t around 0 70.5%

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

      1. +-commutative 70.5%

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

   6. Simplified 70.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+57}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-80}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-82}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+121}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2.25e+91)
   (* x y)
   (if (<= (* x y) 0.0)
     c
     (if (<= (* x y) 1.55e-30) (* b (* a -0.25)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -2.25e+91) {
		tmp = x * y;
	} else if ((x * y) <= 0.0) {
		tmp = c;
	} else if ((x * y) <= 1.55e-30) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-2.25d+91)) then
        tmp = x * y
    else if ((x * y) <= 0.0d0) then
        tmp = c
    else if ((x * y) <= 1.55d-30) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -2.25e+91) {
		tmp = x * y;
	} else if ((x * y) <= 0.0) {
		tmp = c;
	} else if ((x * y) <= 1.55e-30) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -2.25e+91:
		tmp = x * y
	elif (x * y) <= 0.0:
		tmp = c
	elif (x * y) <= 1.55e-30:
		tmp = b * (a * -0.25)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -2.25e+91)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 0.0)
		tmp = c;
	elseif (Float64(x * y) <= 1.55e-30)
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -2.25e+91)
		tmp = x * y;
	elseif ((x * y) <= 0.0)
		tmp = c;
	elseif ((x * y) <= 1.55e-30)
		tmp = b * (a * -0.25);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.25e+91], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.55e-30], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.25e91 or 1.54999999999999995e-30 < (*.f64 x y)

   1. Initial program 96.4%

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

   3. Taylor expanded in a around 0 82.5%

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

   4. Taylor expanded in y around inf 78.5%

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

      1. associate-*r/ 78.5%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in z around -inf 68.9%

      \[\leadsto c + \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 68.9%

         \[\leadsto c + \color{blue}{\left(-z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]

      2. *-commutative 68.9%

         \[\leadsto c + \left(-\color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in 68.9%

         \[\leadsto c + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot \left(-z\right)} \]

      4. +-commutative 68.9%

         \[\leadsto c + \color{blue}{\left(-0.0625 \cdot t + -1 \cdot \frac{x \cdot y}{z}\right)} \cdot \left(-z\right) \]

      5. mul-1-neg 68.9%

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

      6. unsub-neg 68.9%

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

      7. *-commutative 68.9%

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

      8. associate-/l* 62.1%

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

   9. Simplified 62.1%

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

   10. Taylor expanded in x around inf 51.8%

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

   if -2.25e91 < (*.f64 x y) < 0.0

   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

   3. Taylor expanded in c around inf 38.5%

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

   if 0.0 < (*.f64 x y) < 1.54999999999999995e-30

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0 95.8%

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

   4. Taylor expanded in t around 0 76.2%

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

   5. Taylor expanded in b around inf 68.6%

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

   6. Taylor expanded in c around 0 49.2%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-246}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* z (* t 0.0625))))
   (if (<= z -2.3e+82)
     t_2
     (if (<= z -3.85e-44)
       t_1
       (if (<= z -1.3e-246) (* x y) (if (<= z 1.1e-79) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if (z <= -2.3e+82) {
		tmp = t_2;
	} else if (z <= -3.85e-44) {
		tmp = t_1;
	} else if (z <= -1.3e-246) {
		tmp = x * y;
	} else if (z <= 1.1e-79) {
		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 = b * (a * (-0.25d0))
    t_2 = z * (t * 0.0625d0)
    if (z <= (-2.3d+82)) then
        tmp = t_2
    else if (z <= (-3.85d-44)) then
        tmp = t_1
    else if (z <= (-1.3d-246)) then
        tmp = x * y
    else if (z <= 1.1d-79) 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 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if (z <= -2.3e+82) {
		tmp = t_2;
	} else if (z <= -3.85e-44) {
		tmp = t_1;
	} else if (z <= -1.3e-246) {
		tmp = x * y;
	} else if (z <= 1.1e-79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = z * (t * 0.0625)
	tmp = 0
	if z <= -2.3e+82:
		tmp = t_2
	elif z <= -3.85e-44:
		tmp = t_1
	elif z <= -1.3e-246:
		tmp = x * y
	elif z <= 1.1e-79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (z <= -2.3e+82)
		tmp = t_2;
	elseif (z <= -3.85e-44)
		tmp = t_1;
	elseif (z <= -1.3e-246)
		tmp = Float64(x * y);
	elseif (z <= 1.1e-79)
		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 = b * (a * -0.25);
	t_2 = z * (t * 0.0625);
	tmp = 0.0;
	if (z <= -2.3e+82)
		tmp = t_2;
	elseif (z <= -3.85e-44)
		tmp = t_1;
	elseif (z <= -1.3e-246)
		tmp = x * y;
	elseif (z <= 1.1e-79)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+82], t$95$2, If[LessEqual[z, -3.85e-44], t$95$1, If[LessEqual[z, -1.3e-246], N[(x * y), $MachinePrecision], If[LessEqual[z, 1.1e-79], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999988e82 or 1.0999999999999999e-79 < z

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 83.9%

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

   4. Taylor expanded in y around inf 74.4%

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

      1. associate-*r/ 74.4%

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

      2. associate-*r* 74.4%

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

      3. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in z around -inf 84.8%

      \[\leadsto c + \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 84.8%

         \[\leadsto c + \color{blue}{\left(-z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]

      2. *-commutative 84.8%

         \[\leadsto c + \left(-\color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in 84.8%

         \[\leadsto c + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot \left(-z\right)} \]

      4. +-commutative 84.8%

         \[\leadsto c + \color{blue}{\left(-0.0625 \cdot t + -1 \cdot \frac{x \cdot y}{z}\right)} \cdot \left(-z\right) \]

      5. mul-1-neg 84.8%

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

      6. unsub-neg 84.8%

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

      7. *-commutative 84.8%

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

      8. associate-/l* 81.5%

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

   9. Simplified 81.5%

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

   10. Taylor expanded in t around inf 49.0%

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

       1. associate-*r* 49.0%

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

       2. *-commutative 49.0%

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

   12. Simplified 49.0%

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

   if -2.29999999999999988e82 < z < -3.85000000000000015e-44 or -1.2999999999999999e-246 < z < 1.0999999999999999e-79

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 79.3%

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

   4. Taylor expanded in t around 0 71.6%

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

   5. Taylor expanded in b around inf 67.2%

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

   6. Taylor expanded in c around 0 41.8%

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

   if -3.85000000000000015e-44 < z < -1.2999999999999999e-246

   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 a around 0 76.1%

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

   4. Taylor expanded in y around inf 73.0%

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

      1. associate-*r/ 73.0%

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

      2. associate-*r* 73.0%

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

      3. *-commutative 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in z around -inf 58.4%

      \[\leadsto c + \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.4%

         \[\leadsto c + \color{blue}{\left(-z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]

      2. *-commutative 58.4%

         \[\leadsto c + \left(-\color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in 58.4%

         \[\leadsto c + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot \left(-z\right)} \]

      4. +-commutative 58.4%

         \[\leadsto c + \color{blue}{\left(-0.0625 \cdot t + -1 \cdot \frac{x \cdot y}{z}\right)} \cdot \left(-z\right) \]

      5. mul-1-neg 58.4%

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

      6. unsub-neg 58.4%

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

      7. *-commutative 58.4%

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

      8. associate-/l* 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in x around inf 38.1%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-246}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+57} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+57) (not (<= (* a b) 2e+121)))
   (- (+ 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+57) || !((a * b) <= 2e+121)) {
		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+57)) .or. (.not. ((a * b) <= 2d+121))) 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+57) || !((a * b) <= 2e+121)) {
		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+57) or not ((a * b) <= 2e+121):
		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+57) || !(Float64(a * b) <= 2e+121))
		tmp = Float64(Float64(c + 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+57) || ~(((a * b) <= 2e+121)))
		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+57], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+121]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $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) < -2.0000000000000001e57 or 2.00000000000000007e121 < (*.f64 a b)

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 92.0%

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

   if -2.0000000000000001e57 < (*.f64 a b) < 2.00000000000000007e121

   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 a around 0 92.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+57} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+57} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;c + \left(x \cdot y - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+57) (not (<= (* a b) 2e+121)))
   (+ c (- (* x y) (/ a (/ 4.0 b))))
   (+ 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+57) || !((a * b) <= 2e+121)) {
		tmp = c + ((x * y) - (a / (4.0 / b)));
	} 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+57)) .or. (.not. ((a * b) <= 2d+121))) then
        tmp = c + ((x * y) - (a / (4.0d0 / b)))
    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+57) || !((a * b) <= 2e+121)) {
		tmp = c + ((x * y) - (a / (4.0 / b)));
	} 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+57) or not ((a * b) <= 2e+121):
		tmp = c + ((x * y) - (a / (4.0 / b)))
	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+57) || !(Float64(a * b) <= 2e+121))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(a / Float64(4.0 / b))));
	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+57) || ~(((a * b) <= 2e+121)))
		tmp = c + ((x * y) - (a / (4.0 / b)));
	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+57], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+121]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(a / N[(4.0 / b), $MachinePrecision]), $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) < -2.0000000000000001e57 or 2.00000000000000007e121 < (*.f64 a b)

   1. Initial program 94.2%

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

      1. associate-+l- 94.2%

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

      2. +-commutative 94.2%

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

      3. *-commutative 94.2%

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

      4. +-commutative 94.2%

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

      5. associate-+l- 94.2%

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

      6. fma-define 95.4%

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

      7. *-commutative 95.4%

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

      8. associate-/l* 96.5%

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

      9. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.5%

         \[\leadsto \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \color{blue}{\frac{1}{\frac{4}{b}}}\right) + c \]

      2. un-div-inv 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in x around inf 91.9%

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

   if -2.0000000000000001e57 < (*.f64 a b) < 2.00000000000000007e121

   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 a around 0 92.4%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+57} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;c + \left(x \cdot y - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+167} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+124}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+167) (not (<= (* a b) 5e+124)))
   (+ c (* 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) <= -1e+167) || !((a * b) <= 5e+124)) {
		tmp = c + (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) <= (-1d+167)) .or. (.not. ((a * b) <= 5d+124))) then
        tmp = c + (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) <= -1e+167) || !((a * b) <= 5e+124)) {
		tmp = c + (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) <= -1e+167) or not ((a * b) <= 5e+124):
		tmp = c + (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) <= -1e+167) || !(Float64(a * b) <= 5e+124))
		tmp = Float64(c + Float64(a * Float64(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) <= -1e+167) || ~(((a * b) <= 5e+124)))
		tmp = c + (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], -1e+167], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+124]], $MachinePrecision]], N[(c + N[(a * N[(b * -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) < -1e167 or 4.9999999999999996e124 < (*.f64 a b)

   1. Initial program 92.4%

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

      1. associate--l+ 92.4%

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

      2. fma-define 95.4%

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

      3. associate-/l* 96.9%

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

      4. fmm-def 98.5%

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

      5. distribute-neg-frac2 98.5%

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

      6. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in a around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*r* 86.7%

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

   7. Simplified 86.7%

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

   if -1e167 < (*.f64 a b) < 4.9999999999999996e124

   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 a around 0 90.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+167} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+124}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-37}:\\ \;\;\;\;\left(c + t\_1\right) - t\_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+121}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* a b) -5e-37)
     (- (+ c t_1) t_2)
     (if (<= (* a b) 2e+121) (+ c (+ (* x y) t_1)) (- (+ 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) * 0.25;
	double tmp;
	if ((a * b) <= -5e-37) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 2e+121) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (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) * 0.25d0
    if ((a * b) <= (-5d-37)) then
        tmp = (c + t_1) - t_2
    else if ((a * b) <= 2d+121) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + (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) * 0.25;
	double tmp;
	if ((a * b) <= -5e-37) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 2e+121) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (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) * 0.25
	tmp = 0
	if (a * b) <= -5e-37:
		tmp = (c + t_1) - t_2
	elif (a * b) <= 2e+121:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + (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) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -5e-37)
		tmp = Float64(Float64(c + t_1) - t_2);
	elseif (Float64(a * b) <= 2e+121)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + 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) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -5e-37)
		tmp = (c + t_1) - t_2;
	elseif ((a * b) <= 2e+121)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + (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] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e-37], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+121], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999997e-37

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 87.5%

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

   if -4.9999999999999997e-37 < (*.f64 a b) < 2.00000000000000007e121

   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 a around 0 93.4%

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

   if 2.00000000000000007e121 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 97.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-37}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+121}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+150}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3e+102) (not (<= (* x y) 7.5e+150)))
   (+ c (* x y))
   (+ c (* z (* t 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -3e+102) || !((x * y) <= 7.5e+150)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-3d+102)) .or. (.not. ((x * y) <= 7.5d+150))) then
        tmp = c + (x * y)
    else
        tmp = c + (z * (t * 0.0625d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -3e+102) || !((x * y) <= 7.5e+150)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3e+102) or not ((x * y) <= 7.5e+150):
		tmp = c + (x * y)
	else:
		tmp = c + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -3e+102) || !(Float64(x * y) <= 7.5e+150))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -3e+102) || ~(((x * y) <= 7.5e+150)))
		tmp = c + (x * y);
	else
		tmp = c + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3e+102], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.5e+150]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.9999999999999998e102 or 7.4999999999999998e150 < (*.f64 x y)

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 84.9%

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

   4. Taylor expanded in t around 0 74.1%

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

      1. +-commutative 74.1%

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

   6. Simplified 74.1%

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

   if -2.9999999999999998e102 < (*.f64 x y) < 7.4999999999999998e150

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 68.9%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+150}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+91} \lor \neg \left(x \cdot y \leq 3.1 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.8e+91) (not (<= (* x y) 3.1e-31))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.8e+91) || !((x * y) <= 3.1e-31)) {
		tmp = x * y;
	} 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 (((x * y) <= (-2.8d+91)) .or. (.not. ((x * y) <= 3.1d-31))) then
        tmp = x * y
    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 (((x * y) <= -2.8e+91) || !((x * y) <= 3.1e-31)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.8e+91) or not ((x * y) <= 3.1e-31):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.8e+91) || !(Float64(x * y) <= 3.1e-31))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2.8e+91) || ~(((x * y) <= 3.1e-31)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.8e+91], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.1e-31]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.7999999999999999e91 or 3.1e-31 < (*.f64 x y)

   1. Initial program 96.4%

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

   3. Taylor expanded in a around 0 82.5%

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

   4. Taylor expanded in y around inf 78.5%

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

      1. associate-*r/ 78.5%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in z around -inf 68.9%

      \[\leadsto c + \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 68.9%

         \[\leadsto c + \color{blue}{\left(-z \cdot \left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right)\right)} \]

      2. *-commutative 68.9%

         \[\leadsto c + \left(-\color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in 68.9%

         \[\leadsto c + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{z} + -0.0625 \cdot t\right) \cdot \left(-z\right)} \]

      4. +-commutative 68.9%

         \[\leadsto c + \color{blue}{\left(-0.0625 \cdot t + -1 \cdot \frac{x \cdot y}{z}\right)} \cdot \left(-z\right) \]

      5. mul-1-neg 68.9%

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

      6. unsub-neg 68.9%

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

      7. *-commutative 68.9%

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

      8. associate-/l* 62.1%

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

   9. Simplified 62.1%

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

   10. Taylor expanded in x around inf 51.8%

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

   if -2.7999999999999999e91 < (*.f64 x y) < 3.1e-31

   1. Initial program 99.3%

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

   3. Taylor expanded in c around inf 36.1%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+91} \lor \neg \left(x \cdot y \leq 3.1 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

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 + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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. Add Preprocessing

3. Final simplification 98.0%

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

Alternative 13: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.96 \cdot 10^{+96} \lor \neg \left(a \leq 3 \cdot 10^{-118}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.96e+96) (not (<= a 3e-118)))
   (* b (* a -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 <= -1.96e+96) || !(a <= 3e-118)) {
		tmp = b * (a * -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 <= (-1.96d+96)) .or. (.not. (a <= 3d-118))) then
        tmp = b * (a * (-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 <= -1.96e+96) || !(a <= 3e-118)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.96e+96) or not (a <= 3e-118):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.96e+96) || !(a <= 3e-118))
		tmp = Float64(b * Float64(a * -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 <= -1.96e+96) || ~((a <= 3e-118)))
		tmp = b * (a * -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, -1.96e+96], N[Not[LessEqual[a, 3e-118]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.96e96 or 3.00000000000000018e-118 < a

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 81.5%

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

   4. Taylor expanded in t around 0 62.7%

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

   5. Taylor expanded in b around inf 55.6%

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

   6. Taylor expanded in c around 0 46.8%

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

   if -1.96e96 < a < 3.00000000000000018e-118

   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 a around 0 91.0%

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

   4. Taylor expanded in t around 0 59.9%

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

      1. +-commutative 59.9%

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

   6. Simplified 59.9%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.96 \cdot 10^{+96} \lor \neg \left(a \leq 3 \cdot 10^{-118}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in c around inf 25.6%

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

Reproduce

herbie shell --seed 2024191 
(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))