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

Percentage Accurate: 98.0% → 99.0%

Time: 9.2s

Alternatives: 10

Speedup: 1.0×

• 31.9% 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: 98.0% 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: 99.0% 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 99.2%

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

   1. associate--l+ 99.2%

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

   2. fma-define 99.6%

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

   3. associate-/l* 99.6%

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

   4. fma-neg 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 99.2%

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

   1. associate-+l- 99.2%

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

   2. *-commutative 99.2%

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

   3. associate-+l- 99.2%

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

   4. fma-define 99.6%

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

   5. *-commutative 99.6%

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

   6. associate-/l* 99.6%

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

   7. associate-/l* 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 3: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.58 \cdot 10^{-145}:\\ \;\;\;\;c + a \cdot \frac{b}{-4}\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -3.7e+39)
     t_2
     (if (<= (* x y) 4.4e-209)
       t_1
       (if (<= (* x y) 1.58e-145)
         (+ c (* a (/ b -4.0)))
         (if (<= (* x y) 8.8e+71) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.7e+39) {
		tmp = t_2;
	} else if ((x * y) <= 4.4e-209) {
		tmp = t_1;
	} else if ((x * y) <= 1.58e-145) {
		tmp = c + (a * (b / -4.0));
	} else if ((x * y) <= 8.8e+71) {
		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 + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-3.7d+39)) then
        tmp = t_2
    else if ((x * y) <= 4.4d-209) then
        tmp = t_1
    else if ((x * y) <= 1.58d-145) then
        tmp = c + (a * (b / (-4.0d0)))
    else if ((x * y) <= 8.8d+71) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.7e+39) {
		tmp = t_2;
	} else if ((x * y) <= 4.4e-209) {
		tmp = t_1;
	} else if ((x * y) <= 1.58e-145) {
		tmp = c + (a * (b / -4.0));
	} else if ((x * y) <= 8.8e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -3.7e+39:
		tmp = t_2
	elif (x * y) <= 4.4e-209:
		tmp = t_1
	elif (x * y) <= 1.58e-145:
		tmp = c + (a * (b / -4.0))
	elif (x * y) <= 8.8e+71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3.7e+39)
		tmp = t_2;
	elseif (Float64(x * y) <= 4.4e-209)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.58e-145)
		tmp = Float64(c + Float64(a * Float64(b / -4.0)));
	elseif (Float64(x * y) <= 8.8e+71)
		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 + (t * (z * 0.0625));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -3.7e+39)
		tmp = t_2;
	elseif ((x * y) <= 4.4e-209)
		tmp = t_1;
	elseif ((x * y) <= 1.58e-145)
		tmp = c + (a * (b / -4.0));
	elseif ((x * y) <= 8.8e+71)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.7e+39], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4.4e-209], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.58e-145], N[(c + N[(a * N[(b / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.8e+71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.70000000000000012e39 or 8.79999999999999978e71 < (*.f64 x y)

   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 x around inf 87.3%

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

   4. Taylor expanded in a around 0 78.3%

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

      1. +-commutative 78.3%

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

   6. Simplified 78.3%

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

   if -3.70000000000000012e39 < (*.f64 x y) < 4.40000000000000019e-209 or 1.58000000000000003e-145 < (*.f64 x y) < 8.79999999999999978e71

   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 97.3%

      \[\leadsto \left(\color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \frac{a \cdot b}{4}\right) + c \]
   4. Step-by-step derivation

      1. *-commutative 97.3%

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

      2. *-commutative 97.3%

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

      3. associate-*r* 97.3%

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

      4. *-commutative 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in a around 0 73.0%

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

      1. associate-*r* 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 73.0%

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

   8. Simplified 73.0%

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

   if 4.40000000000000019e-209 < (*.f64 x y) < 1.58000000000000003e-145

   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 inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. metadata-eval 81.8%

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

      3. distribute-lft-neg-in 81.8%

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

      4. *-commutative 81.8%

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

      5. distribute-lft-neg-in 81.8%

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

      6. metadata-eval 81.8%

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

      7. associate-/l* 81.8%

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

      8. *-rgt-identity 81.8%

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

      9. associate-*l/ 81.8%

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

      10. distribute-lft-neg-in 81.8%

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

      11. distribute-rgt-neg-out 81.8%

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

      12. metadata-eval 81.8%

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

      13. distribute-neg-frac2 81.8%

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

      14. distribute-frac-neg 81.8%

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

      15. distribute-rgt-neg-out 81.8%

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

      16. remove-double-neg 81.8%

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

      17. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{-209}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.58 \cdot 10^{-145}:\\ \;\;\;\;c + a \cdot \frac{b}{-4}\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{+71}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;c + \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+39}:\\ \;\;\;\;c + \left(z \cdot \left(t \cdot 0.0625\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (<= (* x y) -3.8e+39)
     (+ c (- (* x y) t_1))
     (if (<= (* x y) 3e+39)
       (+ c (- (* z (* t 0.0625)) t_1))
       (+ 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 t_1 = (a * b) / 4.0;
	double tmp;
	if ((x * y) <= -3.8e+39) {
		tmp = c + ((x * y) - t_1);
	} else if ((x * y) <= 3e+39) {
		tmp = c + ((z * (t * 0.0625)) - t_1);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    if ((x * y) <= (-3.8d+39)) then
        tmp = c + ((x * y) - t_1)
    else if ((x * y) <= 3d+39) then
        tmp = c + ((z * (t * 0.0625d0)) - t_1)
    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 t_1 = (a * b) / 4.0;
	double tmp;
	if ((x * y) <= -3.8e+39) {
		tmp = c + ((x * y) - t_1);
	} else if ((x * y) <= 3e+39) {
		tmp = c + ((z * (t * 0.0625)) - t_1);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if (x * y) <= -3.8e+39:
		tmp = c + ((x * y) - t_1)
	elif (x * y) <= 3e+39:
		tmp = c + ((z * (t * 0.0625)) - t_1)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (Float64(x * y) <= -3.8e+39)
		tmp = Float64(c + Float64(Float64(x * y) - t_1));
	elseif (Float64(x * y) <= 3e+39)
		tmp = Float64(c + Float64(Float64(z * Float64(t * 0.0625)) - t_1));
	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)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if ((x * y) <= -3.8e+39)
		tmp = c + ((x * y) - t_1);
	elseif ((x * y) <= 3e+39)
		tmp = c + ((z * (t * 0.0625)) - t_1);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.8e+39], N[(c + N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e+39], N[(c + N[(N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.7999999999999998e39

   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 x around inf 87.5%

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

   if -3.7999999999999998e39 < (*.f64 x y) < 3e39

   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 98.2%

      \[\leadsto \left(\color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \frac{a \cdot b}{4}\right) + c \]
   4. Step-by-step derivation

      1. *-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 98.2%

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

      4. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   if 3e39 < (*.f64 x y)

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 79.4%

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

   4. Taylor expanded in a around 0 80.9%

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

   5. Taylor expanded in t around 0 94.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;c + \left(x \cdot y - \frac{a \cdot b}{4}\right)\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+39}:\\ \;\;\;\;c + \left(z \cdot \left(t \cdot 0.0625\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+126} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+62}\right):\\ \;\;\;\;c + \left(x \cdot y - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+126) (not (<= (* a b) 4e+62)))
   (+ c (- (* x y) (/ (* a b) 4.0)))
   (+ 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+126) || !((a * b) <= 4e+62)) {
		tmp = c + ((x * y) - ((a * b) / 4.0));
	} 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+126)) .or. (.not. ((a * b) <= 4d+62))) then
        tmp = c + ((x * y) - ((a * b) / 4.0d0))
    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+126) || !((a * b) <= 4e+62)) {
		tmp = c + ((x * y) - ((a * b) / 4.0));
	} 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+126) or not ((a * b) <= 4e+62):
		tmp = c + ((x * y) - ((a * b) / 4.0))
	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+126) || !(Float64(a * b) <= 4e+62))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) / 4.0)));
	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+126) || ~(((a * b) <= 4e+62)))
		tmp = c + ((x * y) - ((a * b) / 4.0));
	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+126], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4e+62]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $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) < -9.99999999999999925e125 or 4.00000000000000014e62 < (*.f64 a b)

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 86.2%

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

   if -9.99999999999999925e125 < (*.f64 a b) < 4.00000000000000014e62

   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 t around inf 91.4%

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

   4. Taylor expanded in a around 0 89.2%

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

   5. Taylor expanded in t around 0 97.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+126} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+62}\right):\\ \;\;\;\;c + \left(x \cdot y - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-72} \lor \neg \left(b \leq 4.2 \cdot 10^{+245}\right):\\ \;\;\;\;c + a \cdot \frac{b}{-4}\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -9.5e-72) (not (<= b 4.2e+245)))
   (+ c (* a (/ b -4.0)))
   (+ 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 ((b <= -9.5e-72) || !(b <= 4.2e+245)) {
		tmp = c + (a * (b / -4.0));
	} 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 ((b <= (-9.5d-72)) .or. (.not. (b <= 4.2d+245))) then
        tmp = c + (a * (b / (-4.0d0)))
    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 ((b <= -9.5e-72) || !(b <= 4.2e+245)) {
		tmp = c + (a * (b / -4.0));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -9.5e-72) or not (b <= 4.2e+245):
		tmp = c + (a * (b / -4.0))
	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 ((b <= -9.5e-72) || !(b <= 4.2e+245))
		tmp = Float64(c + Float64(a * Float64(b / -4.0)));
	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 ((b <= -9.5e-72) || ~((b <= 4.2e+245)))
		tmp = c + (a * (b / -4.0));
	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[b, -9.5e-72], N[Not[LessEqual[b, 4.2e+245]], $MachinePrecision]], N[(c + N[(a * N[(b / -4.0), $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 b < -9.4999999999999998e-72 or 4.19999999999999992e245 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. associate-*r* 59.1%

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

      2. metadata-eval 59.1%

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

      3. distribute-lft-neg-in 59.1%

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

      4. *-commutative 59.1%

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

      5. distribute-lft-neg-in 59.1%

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

      6. metadata-eval 59.1%

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

      7. associate-/l* 59.1%

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

      8. *-rgt-identity 59.1%

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

      9. associate-*l/ 59.1%

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

      10. distribute-lft-neg-in 59.1%

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

      11. distribute-rgt-neg-out 59.1%

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

      12. metadata-eval 59.1%

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

      13. distribute-neg-frac2 59.1%

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

      14. distribute-frac-neg 59.1%

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

      15. distribute-rgt-neg-out 59.1%

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

      16. remove-double-neg 59.1%

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

      17. associate-/l* 59.1%

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

   5. Simplified 59.1%

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

   if -9.4999999999999998e-72 < b < 4.19999999999999992e245

   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 t around inf 89.0%

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

   4. Taylor expanded in a around 0 80.0%

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

   5. Taylor expanded in t around 0 86.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-72} \lor \neg \left(b \leq 4.2 \cdot 10^{+245}\right):\\ \;\;\;\;c + a \cdot \frac{b}{-4}\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+40} \lor \neg \left(x \cdot y \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.7e+40) (not (<= (* x y) 4.5e+71)))
   (+ c (* x y))
   (+ c (* t (* z 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.7e+40) || !((x * y) <= 4.5e+71)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 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) <= (-1.7d+40)) .or. (.not. ((x * y) <= 4.5d+71))) then
        tmp = c + (x * y)
    else
        tmp = c + (t * (z * 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) <= -1.7e+40) || !((x * y) <= 4.5e+71)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.7e+40) or not ((x * y) <= 4.5e+71):
		tmp = c + (x * y)
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.7e+40) || !(Float64(x * y) <= 4.5e+71))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.7e+40) || ~(((x * y) <= 4.5e+71)))
		tmp = c + (x * y);
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.7e+40], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.5e+71]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.69999999999999994e40 or 4.50000000000000043e71 < (*.f64 x y)

   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 x around inf 87.3%

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

   4. Taylor expanded in a around 0 78.3%

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

      1. +-commutative 78.3%

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

   6. Simplified 78.3%

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

   if -1.69999999999999994e40 < (*.f64 x y) < 4.50000000000000043e71

   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 97.5%

      \[\leadsto \left(\color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \frac{a \cdot b}{4}\right) + c \]
   4. Step-by-step derivation

      1. *-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*r* 97.5%

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

      4. *-commutative 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in a around 0 69.7%

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

      1. associate-*r* 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-*r* 69.7%

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

   8. Simplified 69.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+40} \lor \neg \left(x \cdot y \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.0% 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 99.2%

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

3. Final simplification 99.2%

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

Alternative 9: 49.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ c + x \cdot y \end{array} \]

FPCore

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

C

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

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)
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);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around inf 73.3%

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

4. Taylor expanded in a around 0 52.8%

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

   1. +-commutative 52.8%

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

6. Simplified 52.8%

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

7. Final simplification 52.8%

   \[\leadsto c + x \cdot y \]
8. Add Preprocessing

Alternative 10: 22.3% 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 99.2%

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

3. Taylor expanded in a around inf 46.7%

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

   1. associate-*r* 46.7%

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

   2. metadata-eval 46.7%

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

   3. distribute-lft-neg-in 46.7%

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

   4. *-commutative 46.7%

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

   5. distribute-lft-neg-in 46.7%

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

   6. metadata-eval 46.7%

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

   7. associate-/l* 46.7%

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

   8. *-rgt-identity 46.7%

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

   9. associate-*l/ 46.7%

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

   10. distribute-lft-neg-in 46.7%

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

   11. distribute-rgt-neg-out 46.7%

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

   12. metadata-eval 46.7%

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

   13. distribute-neg-frac2 46.7%

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

   14. distribute-frac-neg 46.7%

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

   15. distribute-rgt-neg-out 46.7%

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

   16. remove-double-neg 46.7%

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

   17. associate-/l* 46.7%

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

5. Simplified 46.7%

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

6. Taylor expanded in a around 0 25.4%

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

Reproduce

herbie shell --seed 2024086 
(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))