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

Percentage Accurate: 97.6% → 98.9%

Time: 13.0s

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: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% 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 98.4%

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

   1. associate--l+ 98.4%

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

   2. fma-define 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* 98.8%

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

   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: 98.2% 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 98.4%

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

   1. associate-+l- 98.4%

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

   2. *-commutative 98.4%

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

   3. associate-+l- 98.4%

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

   4. fma-define 98.4%

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

   5. *-commutative 98.4%

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

   6. associate-/l* 98.4%

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

   7. associate-/l* 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 66.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_3 := y \cdot \left(x + \left(b \cdot -0.25\right) \cdot \frac{a}{y}\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+189}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+90}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25))))
        (t_2 (+ c (* z (* t 0.0625))))
        (t_3 (* y (+ x (* (* b -0.25) (/ a y))))))
   (if (<= (* x y) -2e+189)
     t_3
     (if (<= (* x y) -2e+122)
       t_2
       (if (<= (* x y) -5e+90)
         t_3
         (if (<= (* x y) -5e-135)
           t_1
           (if (<= (* x y) 0.0)
             t_2
             (if (<= (* x y) 1e-180)
               t_1
               (if (<= (* x y) 5e-69)
                 t_2
                 (if (<= (* x y) 1e-14)
                   t_1
                   (if (<= (* x y) 5e+102) t_2 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (z * (t * 0.0625));
	double t_3 = y * (x + ((b * -0.25) * (a / y)));
	double tmp;
	if ((x * y) <= -2e+189) {
		tmp = t_3;
	} else if ((x * y) <= -2e+122) {
		tmp = t_2;
	} else if ((x * y) <= -5e+90) {
		tmp = t_3;
	} else if ((x * y) <= -5e-135) {
		tmp = t_1;
	} else if ((x * y) <= 0.0) {
		tmp = t_2;
	} else if ((x * y) <= 1e-180) {
		tmp = t_1;
	} else if ((x * y) <= 5e-69) {
		tmp = t_2;
	} else if ((x * y) <= 1e-14) {
		tmp = t_1;
	} else if ((x * y) <= 5e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    t_2 = c + (z * (t * 0.0625d0))
    t_3 = y * (x + ((b * (-0.25d0)) * (a / y)))
    if ((x * y) <= (-2d+189)) then
        tmp = t_3
    else if ((x * y) <= (-2d+122)) then
        tmp = t_2
    else if ((x * y) <= (-5d+90)) then
        tmp = t_3
    else if ((x * y) <= (-5d-135)) then
        tmp = t_1
    else if ((x * y) <= 0.0d0) then
        tmp = t_2
    else if ((x * y) <= 1d-180) then
        tmp = t_1
    else if ((x * y) <= 5d-69) then
        tmp = t_2
    else if ((x * y) <= 1d-14) then
        tmp = t_1
    else if ((x * y) <= 5d+102) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (z * (t * 0.0625));
	double t_3 = y * (x + ((b * -0.25) * (a / y)));
	double tmp;
	if ((x * y) <= -2e+189) {
		tmp = t_3;
	} else if ((x * y) <= -2e+122) {
		tmp = t_2;
	} else if ((x * y) <= -5e+90) {
		tmp = t_3;
	} else if ((x * y) <= -5e-135) {
		tmp = t_1;
	} else if ((x * y) <= 0.0) {
		tmp = t_2;
	} else if ((x * y) <= 1e-180) {
		tmp = t_1;
	} else if ((x * y) <= 5e-69) {
		tmp = t_2;
	} else if ((x * y) <= 1e-14) {
		tmp = t_1;
	} else if ((x * y) <= 5e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (z * (t * 0.0625))
	t_3 = y * (x + ((b * -0.25) * (a / y)))
	tmp = 0
	if (x * y) <= -2e+189:
		tmp = t_3
	elif (x * y) <= -2e+122:
		tmp = t_2
	elif (x * y) <= -5e+90:
		tmp = t_3
	elif (x * y) <= -5e-135:
		tmp = t_1
	elif (x * y) <= 0.0:
		tmp = t_2
	elif (x * y) <= 1e-180:
		tmp = t_1
	elif (x * y) <= 5e-69:
		tmp = t_2
	elif (x * y) <= 1e-14:
		tmp = t_1
	elif (x * y) <= 5e+102:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_2 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_3 = Float64(y * Float64(x + Float64(Float64(b * -0.25) * Float64(a / y))))
	tmp = 0.0
	if (Float64(x * y) <= -2e+189)
		tmp = t_3;
	elseif (Float64(x * y) <= -2e+122)
		tmp = t_2;
	elseif (Float64(x * y) <= -5e+90)
		tmp = t_3;
	elseif (Float64(x * y) <= -5e-135)
		tmp = t_1;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e-180)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-69)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e-14)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+102)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	t_2 = c + (z * (t * 0.0625));
	t_3 = y * (x + ((b * -0.25) * (a / y)));
	tmp = 0.0;
	if ((x * y) <= -2e+189)
		tmp = t_3;
	elseif ((x * y) <= -2e+122)
		tmp = t_2;
	elseif ((x * y) <= -5e+90)
		tmp = t_3;
	elseif ((x * y) <= -5e-135)
		tmp = t_1;
	elseif ((x * y) <= 0.0)
		tmp = t_2;
	elseif ((x * y) <= 1e-180)
		tmp = t_1;
	elseif ((x * y) <= 5e-69)
		tmp = t_2;
	elseif ((x * y) <= 1e-14)
		tmp = t_1;
	elseif ((x * y) <= 5e+102)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x + N[(N[(b * -0.25), $MachinePrecision] * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+189], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2e+122], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5e+90], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -5e-135], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e-180], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-69], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e-14], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+102], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e189 or -2.00000000000000003e122 < (*.f64 x y) < -5.0000000000000004e90 or 5e102 < (*.f64 x y)

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 89.4%

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

   4. Taylor expanded in y around inf 91.7%

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

      1. associate--l+ 91.7%

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

      2. associate-*r/ 91.7%

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

      3. div-sub 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-*r* 91.7%

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

      6. sub-neg 91.7%

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

      7. distribute-rgt-neg-in 91.7%

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

      8. distribute-rgt-neg-in 91.7%

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

      9. metadata-eval 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in c around 0 88.1%

      \[\leadsto y \cdot \left(x + \color{blue}{-0.25 \cdot \frac{a \cdot b}{y}}\right) \]
   8. Step-by-step derivation

      1. associate-*r/ 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*r* 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-/l* 87.0%

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

      6. *-commutative 87.0%

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

   9. Simplified 87.0%

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

   if -2e189 < (*.f64 x y) < -2.00000000000000003e122 or -5.0000000000000002e-135 < (*.f64 x y) < 0.0 or 1e-180 < (*.f64 x y) < 5.00000000000000033e-69 or 9.99999999999999999e-15 < (*.f64 x y) < 5e102

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -5.0000000000000004e90 < (*.f64 x y) < -5.0000000000000002e-135 or 0.0 < (*.f64 x y) < 1e-180 or 5.00000000000000033e-69 < (*.f64 x y) < 9.99999999999999999e-15

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*r* 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+189}:\\ \;\;\;\;y \cdot \left(x + \left(b \cdot -0.25\right) \cdot \frac{a}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+122}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x + \left(b \cdot -0.25\right) \cdot \frac{a}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-135}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-180}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-69}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-14}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+102}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \left(b \cdot -0.25\right) \cdot \frac{a}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-190}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+105}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* x y) -3.1e+197)
     (* x y)
     (if (<= (* x y) -9e-209)
       t_1
       (if (<= (* x y) 1.55e-190)
         c
         (if (<= (* x y) 1.25e-53)
           t_1
           (if (<= (* x y) 7.5e+105) c (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((x * y) <= -3.1e+197) {
		tmp = x * y;
	} else if ((x * y) <= -9e-209) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e-190) {
		tmp = c;
	} else if ((x * y) <= 1.25e-53) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+105) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    if ((x * y) <= (-3.1d+197)) then
        tmp = x * y
    else if ((x * y) <= (-9d-209)) then
        tmp = t_1
    else if ((x * y) <= 1.55d-190) then
        tmp = c
    else if ((x * y) <= 1.25d-53) then
        tmp = t_1
    else if ((x * y) <= 7.5d+105) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((x * y) <= -3.1e+197) {
		tmp = x * y;
	} else if ((x * y) <= -9e-209) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e-190) {
		tmp = c;
	} else if ((x * y) <= 1.25e-53) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+105) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (x * y) <= -3.1e+197:
		tmp = x * y
	elif (x * y) <= -9e-209:
		tmp = t_1
	elif (x * y) <= 1.55e-190:
		tmp = c
	elif (x * y) <= 1.25e-53:
		tmp = t_1
	elif (x * y) <= 7.5e+105:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -3.1e+197)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -9e-209)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.55e-190)
		tmp = c;
	elseif (Float64(x * y) <= 1.25e-53)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.5e+105)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if ((x * y) <= -3.1e+197)
		tmp = x * y;
	elseif ((x * y) <= -9e-209)
		tmp = t_1;
	elseif ((x * y) <= 1.55e-190)
		tmp = c;
	elseif ((x * y) <= 1.25e-53)
		tmp = t_1;
	elseif ((x * y) <= 7.5e+105)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.1e+197], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -9e-209], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.55e-190], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.25e-53], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+105], c, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.1e197 or 7.5000000000000002e105 < (*.f64 x y)

   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 inf 75.2%

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

   4. Taylor expanded in c around inf 65.5%

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

   5. Taylor expanded in c around 0 71.9%

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

   if -3.1e197 < (*.f64 x y) < -8.9999999999999996e-209 or 1.54999999999999997e-190 < (*.f64 x y) < 1.25e-53

   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 z around 0 59.4%

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

   4. Taylor expanded in y around inf 49.8%

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

      1. associate--l+ 49.8%

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

      2. associate-*r/ 49.8%

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

      3. div-sub 51.9%

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

      4. *-commutative 51.9%

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

      5. associate-*r* 51.9%

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

      6. sub-neg 51.9%

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

      7. distribute-rgt-neg-in 51.9%

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

      8. distribute-rgt-neg-in 51.9%

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

      9. metadata-eval 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in a around inf 35.1%

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

      1. *-commutative 35.1%

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

      2. associate-*r* 35.1%

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

      3. *-commutative 35.1%

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

   9. Simplified 35.1%

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

   if -8.9999999999999996e-209 < (*.f64 x y) < 1.54999999999999997e-190 or 1.25e-53 < (*.f64 x y) < 7.5000000000000002e105

   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 43.8%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-190}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+105}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;a \leq -8 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-235}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-33}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625)))
        (t_2 (+ c (* b (* a -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= a -8e+142)
     t_2
     (if (<= a -9.2e+111)
       t_1
       (if (<= a -2.6e+84)
         t_2
         (if (<= a -1.35e-235)
           t_3
           (if (<= a -2.3e-292) t_1 (if (<= a 6e-33) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if (a <= -8e+142) {
		tmp = t_2;
	} else if (a <= -9.2e+111) {
		tmp = t_1;
	} else if (a <= -2.6e+84) {
		tmp = t_2;
	} else if (a <= -1.35e-235) {
		tmp = t_3;
	} else if (a <= -2.3e-292) {
		tmp = t_1;
	} else if (a <= 6e-33) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = z * (t * 0.0625d0)
    t_2 = c + (b * (a * (-0.25d0)))
    t_3 = c + (x * y)
    if (a <= (-8d+142)) then
        tmp = t_2
    else if (a <= (-9.2d+111)) then
        tmp = t_1
    else if (a <= (-2.6d+84)) then
        tmp = t_2
    else if (a <= (-1.35d-235)) then
        tmp = t_3
    else if (a <= (-2.3d-292)) then
        tmp = t_1
    else if (a <= 6d-33) then
        tmp = t_3
    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 = z * (t * 0.0625);
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if (a <= -8e+142) {
		tmp = t_2;
	} else if (a <= -9.2e+111) {
		tmp = t_1;
	} else if (a <= -2.6e+84) {
		tmp = t_2;
	} else if (a <= -1.35e-235) {
		tmp = t_3;
	} else if (a <= -2.3e-292) {
		tmp = t_1;
	} else if (a <= 6e-33) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	t_2 = c + (b * (a * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if a <= -8e+142:
		tmp = t_2
	elif a <= -9.2e+111:
		tmp = t_1
	elif a <= -2.6e+84:
		tmp = t_2
	elif a <= -1.35e-235:
		tmp = t_3
	elif a <= -2.3e-292:
		tmp = t_1
	elif a <= 6e-33:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (a <= -8e+142)
		tmp = t_2;
	elseif (a <= -9.2e+111)
		tmp = t_1;
	elseif (a <= -2.6e+84)
		tmp = t_2;
	elseif (a <= -1.35e-235)
		tmp = t_3;
	elseif (a <= -2.3e-292)
		tmp = t_1;
	elseif (a <= 6e-33)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * (t * 0.0625);
	t_2 = c + (b * (a * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if (a <= -8e+142)
		tmp = t_2;
	elseif (a <= -9.2e+111)
		tmp = t_1;
	elseif (a <= -2.6e+84)
		tmp = t_2;
	elseif (a <= -1.35e-235)
		tmp = t_3;
	elseif (a <= -2.3e-292)
		tmp = t_1;
	elseif (a <= 6e-33)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+142], t$95$2, If[LessEqual[a, -9.2e+111], t$95$1, If[LessEqual[a, -2.6e+84], t$95$2, If[LessEqual[a, -1.35e-235], t$95$3, If[LessEqual[a, -2.3e-292], t$95$1, If[LessEqual[a, 6e-33], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.00000000000000041e142 or -9.20000000000000008e111 < a < -2.6000000000000001e84 or 6.0000000000000003e-33 < a

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-*r* 71.4%

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

   5. Simplified 71.4%

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

   if -8.00000000000000041e142 < a < -9.20000000000000008e111 or -1.3500000000000001e-235 < a < -2.2999999999999999e-292

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 70.5%

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

      1. associate-*r* 70.5%

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

      2. *-commutative 70.5%

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

      3. *-commutative 70.5%

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

      4. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf 70.5%

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

   7. Taylor expanded in t around inf 64.8%

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

   if -2.6000000000000001e84 < a < -1.3500000000000001e-235 or -2.2999999999999999e-292 < a < 6.0000000000000003e-33

   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 56.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+142}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+84}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-235}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-33}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ t_2 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-271}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+42}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))) (t_2 (* a (* b -0.25))))
   (if (<= b -6.8e-60)
     t_2
     (if (<= b -2.5e-141)
       t_1
       (if (<= b -2.05e-271)
         c
         (if (<= b 1.5e-49)
           t_1
           (if (<= b 3.7e+42) c (if (<= b 4.5e+95) (* x y) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (b <= -6.8e-60) {
		tmp = t_2;
	} else if (b <= -2.5e-141) {
		tmp = t_1;
	} else if (b <= -2.05e-271) {
		tmp = c;
	} else if (b <= 1.5e-49) {
		tmp = t_1;
	} else if (b <= 3.7e+42) {
		tmp = c;
	} else if (b <= 4.5e+95) {
		tmp = x * y;
	} 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 = z * (t * 0.0625d0)
    t_2 = a * (b * (-0.25d0))
    if (b <= (-6.8d-60)) then
        tmp = t_2
    else if (b <= (-2.5d-141)) then
        tmp = t_1
    else if (b <= (-2.05d-271)) then
        tmp = c
    else if (b <= 1.5d-49) then
        tmp = t_1
    else if (b <= 3.7d+42) then
        tmp = c
    else if (b <= 4.5d+95) then
        tmp = x * y
    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 = z * (t * 0.0625);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (b <= -6.8e-60) {
		tmp = t_2;
	} else if (b <= -2.5e-141) {
		tmp = t_1;
	} else if (b <= -2.05e-271) {
		tmp = c;
	} else if (b <= 1.5e-49) {
		tmp = t_1;
	} else if (b <= 3.7e+42) {
		tmp = c;
	} else if (b <= 4.5e+95) {
		tmp = x * y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	t_2 = a * (b * -0.25)
	tmp = 0
	if b <= -6.8e-60:
		tmp = t_2
	elif b <= -2.5e-141:
		tmp = t_1
	elif b <= -2.05e-271:
		tmp = c
	elif b <= 1.5e-49:
		tmp = t_1
	elif b <= 3.7e+42:
		tmp = c
	elif b <= 4.5e+95:
		tmp = x * y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	t_2 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (b <= -6.8e-60)
		tmp = t_2;
	elseif (b <= -2.5e-141)
		tmp = t_1;
	elseif (b <= -2.05e-271)
		tmp = c;
	elseif (b <= 1.5e-49)
		tmp = t_1;
	elseif (b <= 3.7e+42)
		tmp = c;
	elseif (b <= 4.5e+95)
		tmp = Float64(x * y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * (t * 0.0625);
	t_2 = a * (b * -0.25);
	tmp = 0.0;
	if (b <= -6.8e-60)
		tmp = t_2;
	elseif (b <= -2.5e-141)
		tmp = t_1;
	elseif (b <= -2.05e-271)
		tmp = c;
	elseif (b <= 1.5e-49)
		tmp = t_1;
	elseif (b <= 3.7e+42)
		tmp = c;
	elseif (b <= 4.5e+95)
		tmp = x * y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-60], t$95$2, If[LessEqual[b, -2.5e-141], t$95$1, If[LessEqual[b, -2.05e-271], c, If[LessEqual[b, 1.5e-49], t$95$1, If[LessEqual[b, 3.7e+42], c, If[LessEqual[b, 4.5e+95], N[(x * y), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.80000000000000013e-60 or 4.50000000000000017e95 < b

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 73.6%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. associate--l+ 65.4%

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

      2. associate-*r/ 65.4%

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

      3. div-sub 68.5%

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

      4. *-commutative 68.5%

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

      5. associate-*r* 68.5%

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

      6. sub-neg 68.5%

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

      7. distribute-rgt-neg-in 68.5%

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

      8. distribute-rgt-neg-in 68.5%

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

      9. metadata-eval 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in a around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

   9. Simplified 45.5%

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

   if -6.80000000000000013e-60 < b < -2.5e-141 or -2.0500000000000001e-271 < b < 1.5e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.2%

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

      1. associate-*r* 65.2%

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

      2. *-commutative 65.2%

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

      3. *-commutative 65.2%

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

      4. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in z around inf 58.5%

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

   7. Taylor expanded in t around inf 38.9%

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

   if -2.5e-141 < b < -2.0500000000000001e-271 or 1.5e-49 < b < 3.69999999999999996e42

   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 33.6%

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

   if 3.69999999999999996e42 < b < 4.50000000000000017e95

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 66.5%

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

   4. Taylor expanded in c around inf 50.9%

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

   5. Taylor expanded in c around 0 58.5%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-271}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+42}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;b \leq -5.9 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-270}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+95}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625))))
        (t_2 (+ c (* b (* a -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= b -5.9e-46)
     t_2
     (if (<= b -5.3e-169)
       t_1
       (if (<= b -2.8e-270)
         t_3
         (if (<= b 1.8e-50) t_1 (if (<= b 2.3e+95) t_3 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 + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if (b <= -5.9e-46) {
		tmp = t_2;
	} else if (b <= -5.3e-169) {
		tmp = t_1;
	} else if (b <= -2.8e-270) {
		tmp = t_3;
	} else if (b <= 1.8e-50) {
		tmp = t_1;
	} else if (b <= 2.3e+95) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c + (z * (t * 0.0625d0))
    t_2 = c + (b * (a * (-0.25d0)))
    t_3 = c + (x * y)
    if (b <= (-5.9d-46)) then
        tmp = t_2
    else if (b <= (-5.3d-169)) then
        tmp = t_1
    else if (b <= (-2.8d-270)) then
        tmp = t_3
    else if (b <= 1.8d-50) then
        tmp = t_1
    else if (b <= 2.3d+95) then
        tmp = t_3
    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 + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if (b <= -5.9e-46) {
		tmp = t_2;
	} else if (b <= -5.3e-169) {
		tmp = t_1;
	} else if (b <= -2.8e-270) {
		tmp = t_3;
	} else if (b <= 1.8e-50) {
		tmp = t_1;
	} else if (b <= 2.3e+95) {
		tmp = t_3;
	} 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 + (b * (a * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if b <= -5.9e-46:
		tmp = t_2
	elif b <= -5.3e-169:
		tmp = t_1
	elif b <= -2.8e-270:
		tmp = t_3
	elif b <= 1.8e-50:
		tmp = t_1
	elif b <= 2.3e+95:
		tmp = t_3
	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(b * Float64(a * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (b <= -5.9e-46)
		tmp = t_2;
	elseif (b <= -5.3e-169)
		tmp = t_1;
	elseif (b <= -2.8e-270)
		tmp = t_3;
	elseif (b <= 1.8e-50)
		tmp = t_1;
	elseif (b <= 2.3e+95)
		tmp = t_3;
	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 + (b * (a * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if (b <= -5.9e-46)
		tmp = t_2;
	elseif (b <= -5.3e-169)
		tmp = t_1;
	elseif (b <= -2.8e-270)
		tmp = t_3;
	elseif (b <= 1.8e-50)
		tmp = t_1;
	elseif (b <= 2.3e+95)
		tmp = t_3;
	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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.9e-46], t$95$2, If[LessEqual[b, -5.3e-169], t$95$1, If[LessEqual[b, -2.8e-270], t$95$3, If[LessEqual[b, 1.8e-50], t$95$1, If[LessEqual[b, 2.3e+95], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8999999999999999e-46 or 2.29999999999999997e95 < b

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. *-commutative 59.4%

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

      3. associate-*r* 59.4%

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

   5. Simplified 59.4%

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

   if -5.8999999999999999e-46 < b < -5.3e-169 or -2.7999999999999999e-270 < b < 1.7999999999999999e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -5.3e-169 < b < -2.7999999999999999e-270 or 1.7999999999999999e-50 < b < 2.29999999999999997e95

   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 inf 66.9%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{-46}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-169}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-270}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-50}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+95}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+40}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+40)
     (- (+ c (* x y)) t_1)
     (if (<= (* a b) 2e+110) (+ c (+ (* x y) t_2)) (- (+ c t_2) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+40) {
		tmp = (c + (x * y)) - t_1;
	} else if ((a * b) <= 2e+110) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+40)) then
        tmp = (c + (x * y)) - t_1
    else if ((a * b) <= 2d+110) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + t_2) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+40) {
		tmp = (c + (x * y)) - t_1;
	} else if ((a * b) <= 2e+110) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+40:
		tmp = (c + (x * y)) - t_1
	elif (a * b) <= 2e+110:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+40)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(a * b) <= 2e+110)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+40)
		tmp = (c + (x * y)) - t_1;
	elseif ((a * b) <= 2e+110)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + t_2) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+40], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+110], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000003e40

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 88.4%

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

   if -5.00000000000000003e40 < (*.f64 a b) < 2e110

   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 97.2%

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

   if 2e110 < (*.f64 a b)

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+40}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+110}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* a (* b -0.25))))
   (if (<= a -1.4e+198)
     t_2
     (if (<= a -1e+138)
       t_1
       (if (<= a -6.5e+112) (* z (* t 0.0625)) (if (<= a 6e-33) 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 + (x * y);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (a <= -1.4e+198) {
		tmp = t_2;
	} else if (a <= -1e+138) {
		tmp = t_1;
	} else if (a <= -6.5e+112) {
		tmp = z * (t * 0.0625);
	} else if (a <= 6e-33) {
		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 + (x * y)
    t_2 = a * (b * (-0.25d0))
    if (a <= (-1.4d+198)) then
        tmp = t_2
    else if (a <= (-1d+138)) then
        tmp = t_1
    else if (a <= (-6.5d+112)) then
        tmp = z * (t * 0.0625d0)
    else if (a <= 6d-33) 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 + (x * y);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (a <= -1.4e+198) {
		tmp = t_2;
	} else if (a <= -1e+138) {
		tmp = t_1;
	} else if (a <= -6.5e+112) {
		tmp = z * (t * 0.0625);
	} else if (a <= 6e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = a * (b * -0.25)
	tmp = 0
	if a <= -1.4e+198:
		tmp = t_2
	elif a <= -1e+138:
		tmp = t_1
	elif a <= -6.5e+112:
		tmp = z * (t * 0.0625)
	elif a <= 6e-33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (a <= -1.4e+198)
		tmp = t_2;
	elseif (a <= -1e+138)
		tmp = t_1;
	elseif (a <= -6.5e+112)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (a <= 6e-33)
		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 + (x * y);
	t_2 = a * (b * -0.25);
	tmp = 0.0;
	if (a <= -1.4e+198)
		tmp = t_2;
	elseif (a <= -1e+138)
		tmp = t_1;
	elseif (a <= -6.5e+112)
		tmp = z * (t * 0.0625);
	elseif (a <= 6e-33)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+198], t$95$2, If[LessEqual[a, -1e+138], t$95$1, If[LessEqual[a, -6.5e+112], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4e198 or 6.0000000000000003e-33 < a

   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 z around 0 84.7%

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

   4. Taylor expanded in y around inf 74.0%

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

      1. associate--l+ 74.0%

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

      2. associate-*r/ 74.0%

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

      3. div-sub 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-*r* 76.3%

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

      6. sub-neg 76.3%

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

      7. distribute-rgt-neg-in 76.3%

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

      8. distribute-rgt-neg-in 76.3%

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

      9. metadata-eval 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in a around inf 55.5%

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

      1. *-commutative 55.5%

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

      2. associate-*r* 55.5%

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

      3. *-commutative 55.5%

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

   9. Simplified 55.5%

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

   if -1.4e198 < a < -1e138 or -6.4999999999999998e112 < a < 6.0000000000000003e-33

   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 x around inf 54.7%

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

   if -1e138 < a < -6.4999999999999998e112

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 33.9%

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

      1. associate-*r* 33.9%

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

      2. *-commutative 33.9%

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

      3. *-commutative 33.9%

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

      4. *-commutative 33.9%

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

   5. Simplified 33.9%

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

   6. Taylor expanded in z around inf 33.9%

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

   7. Taylor expanded in t around inf 34.0%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+198}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+138}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-33}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+40} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+90}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+40) (not (<= (* a b) 5e+90)))
   (- (+ 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) <= -5e+40) || !((a * b) <= 5e+90)) {
		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) <= (-5d+40)) .or. (.not. ((a * b) <= 5d+90))) 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) <= -5e+40) || !((a * b) <= 5e+90)) {
		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) <= -5e+40) or not ((a * b) <= 5e+90):
		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) <= -5e+40) || !(Float64(a * b) <= 5e+90))
		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) <= -5e+40) || ~(((a * b) <= 5e+90)))
		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], -5e+40], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+90]], $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) < -5.00000000000000003e40 or 5.0000000000000004e90 < (*.f64 a b)

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 87.8%

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

   if -5.00000000000000003e40 < (*.f64 a b) < 5.0000000000000004e90

   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 97.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+40} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+90}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+197}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+29}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \left(b \cdot -0.25\right) \cdot \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1.9e+197)
   (+ c (* b (* a -0.25)))
   (if (<= a 1.15e+29)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* y (+ x (* (* b -0.25) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.9e+197) {
		tmp = c + (b * (a * -0.25));
	} else if (a <= 1.15e+29) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = y * (x + ((b * -0.25) * (a / 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 <= (-1.9d+197)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (a <= 1.15d+29) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = y * (x + ((b * (-0.25d0)) * (a / 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 <= -1.9e+197) {
		tmp = c + (b * (a * -0.25));
	} else if (a <= 1.15e+29) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = y * (x + ((b * -0.25) * (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.9e+197:
		tmp = c + (b * (a * -0.25))
	elif a <= 1.15e+29:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = y * (x + ((b * -0.25) * (a / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.9e+197)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (a <= 1.15e+29)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(y * Float64(x + Float64(Float64(b * -0.25) * Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.9e+197)
		tmp = c + (b * (a * -0.25));
	elseif (a <= 1.15e+29)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = y * (x + ((b * -0.25) * (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1.9e+197], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+29], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(N[(b * -0.25), $MachinePrecision] * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e197

   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 a around inf 95.0%

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

      1. *-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 95.0%

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

   5. Simplified 95.0%

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

   if -1.9000000000000001e197 < a < 1.1500000000000001e29

   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 87.3%

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

   if 1.1500000000000001e29 < a

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 82.8%

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

   4. Taylor expanded in y around inf 75.0%

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

      1. associate--l+ 75.0%

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

      2. associate-*r/ 75.0%

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

      3. div-sub 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*r* 78.3%

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

      6. sub-neg 78.3%

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

      7. distribute-rgt-neg-in 78.3%

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

      8. distribute-rgt-neg-in 78.3%

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

      9. metadata-eval 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in c around 0 68.9%

      \[\leadsto y \cdot \left(x + \color{blue}{-0.25 \cdot \frac{a \cdot b}{y}}\right) \]
   8. Step-by-step derivation

      1. associate-*r/ 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*r* 68.9%

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

      4. *-commutative 68.9%

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

      5. associate-/l* 67.3%

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

      6. *-commutative 67.3%

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

   9. Simplified 67.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+197}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+29}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \left(b \cdot -0.25\right) \cdot \frac{a}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+24} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.4e+24) (not (<= (* x y) 2.9e+104))) (* 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) <= -2.4e+24) || !((x * y) <= 2.9e+104)) {
		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) <= (-2.4d+24)) .or. (.not. ((x * y) <= 2.9d+104))) 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) <= -2.4e+24) || !((x * y) <= 2.9e+104)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.4e+24) or not ((x * y) <= 2.9e+104):
		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) <= -2.4e+24) || !(Float64(x * y) <= 2.9e+104))
		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) <= -2.4e+24) || ~(((x * y) <= 2.9e+104)))
		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], -2.4e+24], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+104]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.4000000000000001e24 or 2.8999999999999998e104 < (*.f64 x y)

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 65.3%

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

   4. Taylor expanded in c around inf 58.0%

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

   5. Taylor expanded in c around 0 60.0%

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

   if -2.4000000000000001e24 < (*.f64 x y) < 2.8999999999999998e104

   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 32.2%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+24} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.6% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 14: 22.6% 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 98.4%

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

3. Taylor expanded in c around inf 21.8%

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

Reproduce

herbie shell --seed 2024087 
(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))