Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.3% → 97.7%

Time: 9.6s

Alternatives: 12

Speedup: 0.4×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.7%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
2. Step-by-step derivation

   1. +-commutative 93.7%

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

   2. fma-define 96.1%

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

   3. +-commutative 96.1%

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

   4. fma-define 97.7%

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

   5. fma-define 98.8%

      \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)\right) \]

3. Simplified 98.8%

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

Alternative 2: 98.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 37.5%

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

   4. Taylor expanded in z around inf 37.5%

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

      1. associate-+r+ 37.5%

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

      2. associate-/l* 56.3%

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

      3. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 98.4%

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

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+115} \lor \neg \left(c \cdot i \leq 8 \cdot 10^{+121}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.7e+115) (not (<= (* c i) 8e+121)))
   (+ (* c i) (* z t))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.7e+115) || !((c * i) <= 8e+121)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-3.7d+115)) .or. (.not. ((c * i) <= 8d+121))) then
        tmp = (c * i) + (z * t)
    else
        tmp = (a * b) + ((x * y) + (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 i) {
	double tmp;
	if (((c * i) <= -3.7e+115) || !((c * i) <= 8e+121)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.7e+115) or not ((c * i) <= 8e+121):
		tmp = (c * i) + (z * t)
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.7e+115) || !(Float64(c * i) <= 8e+121))
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.7e+115) || ~(((c * i) <= 8e+121)))
		tmp = (c * i) + (z * t);
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.7e+115], N[Not[LessEqual[N[(c * i), $MachinePrecision], 8e+121]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.70000000000000006e115 or 8.0000000000000003e121 < (*.f64 c i)

   1. Initial program 86.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.2%

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

      1. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around inf 79.1%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 79.1%

         \[\leadsto \color{blue}{z \cdot t} + c \cdot i \]

   8. Simplified 79.1%

      \[\leadsto \color{blue}{z \cdot t} + c \cdot i \]

   if -3.70000000000000006e115 < (*.f64 c i) < 8.0000000000000003e121

   1. Initial program 97.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 91.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+115} \lor \neg \left(c \cdot i \leq 8 \cdot 10^{+121}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -6.4 \cdot 10^{+72}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{+120}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -6.4e+72)
     (+ (* c i) t_1)
     (if (<= (* c i) 1.55e+120) (+ (* a b) t_1) (+ (* c i) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -6.4e+72) {
		tmp = (c * i) + t_1;
	} else if ((c * i) <= 1.55e+120) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-6.4d+72)) then
        tmp = (c * i) + t_1
    else if ((c * i) <= 1.55d+120) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + (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 i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -6.4e+72) {
		tmp = (c * i) + t_1;
	} else if ((c * i) <= 1.55e+120) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -6.4e+72:
		tmp = (c * i) + t_1
	elif (c * i) <= 1.55e+120:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -6.4e+72)
		tmp = Float64(Float64(c * i) + t_1);
	elseif (Float64(c * i) <= 1.55e+120)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -6.4e+72)
		tmp = (c * i) + t_1;
	elseif ((c * i) <= 1.55e+120)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -6.4e+72], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.55e+120], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.4000000000000003e72

   1. Initial program 93.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 86.9%

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

   if -6.4000000000000003e72 < (*.f64 c i) < 1.54999999999999987e120

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 91.9%

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

   if 1.54999999999999987e120 < (*.f64 c i)

   1. Initial program 78.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.4%

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

      1. associate-/l* 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in z around inf 76.7%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 76.7%

         \[\leadsto \color{blue}{z \cdot t} + c \cdot i \]

   8. Simplified 76.7%

      \[\leadsto \color{blue}{z \cdot t} + c \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.4 \cdot 10^{+72}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{+120}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.2 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-142}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.75 \cdot 10^{+200}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -6.2e+140)
   (* a b)
   (if (<= (* a b) 8.6e-142)
     (* z t)
     (if (<= (* a b) 2.75e+200) (* c i) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -6.2e+140) {
		tmp = a * b;
	} else if ((a * b) <= 8.6e-142) {
		tmp = z * t;
	} else if ((a * b) <= 2.75e+200) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-6.2d+140)) then
        tmp = a * b
    else if ((a * b) <= 8.6d-142) then
        tmp = z * t
    else if ((a * b) <= 2.75d+200) then
        tmp = c * i
    else
        tmp = a * b
    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 i) {
	double tmp;
	if ((a * b) <= -6.2e+140) {
		tmp = a * b;
	} else if ((a * b) <= 8.6e-142) {
		tmp = z * t;
	} else if ((a * b) <= 2.75e+200) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -6.2e+140:
		tmp = a * b
	elif (a * b) <= 8.6e-142:
		tmp = z * t
	elif (a * b) <= 2.75e+200:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -6.2e+140)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 8.6e-142)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.75e+200)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -6.2e+140)
		tmp = a * b;
	elseif ((a * b) <= 8.6e-142)
		tmp = z * t;
	elseif ((a * b) <= 2.75e+200)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -6.2e+140], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.6e-142], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.75e+200], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.2000000000000001e140 or 2.75e200 < (*.f64 a b)

   1. Initial program 89.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 69.9%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -6.2000000000000001e140 < (*.f64 a b) < 8.5999999999999995e-142

   1. Initial program 95.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 45.5%

      \[\leadsto \color{blue}{t \cdot z} \]

   if 8.5999999999999995e-142 < (*.f64 a b) < 2.75e200

   1. Initial program 94.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 37.8%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.2 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-142}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.75 \cdot 10^{+200}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -26000000000000.0)
   (* z t)
   (if (<= z -9.2e-153)
     (* a b)
     (if (<= z 8e-132) (* x y) (if (<= z 2.1e-28) (* c i) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -26000000000000.0) {
		tmp = z * t;
	} else if (z <= -9.2e-153) {
		tmp = a * b;
	} else if (z <= 8e-132) {
		tmp = x * y;
	} else if (z <= 2.1e-28) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (z <= (-26000000000000.0d0)) then
        tmp = z * t
    else if (z <= (-9.2d-153)) then
        tmp = a * b
    else if (z <= 8d-132) then
        tmp = x * y
    else if (z <= 2.1d-28) then
        tmp = c * i
    else
        tmp = 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 i) {
	double tmp;
	if (z <= -26000000000000.0) {
		tmp = z * t;
	} else if (z <= -9.2e-153) {
		tmp = a * b;
	} else if (z <= 8e-132) {
		tmp = x * y;
	} else if (z <= 2.1e-28) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -26000000000000.0:
		tmp = z * t
	elif z <= -9.2e-153:
		tmp = a * b
	elif z <= 8e-132:
		tmp = x * y
	elif z <= 2.1e-28:
		tmp = c * i
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -26000000000000.0)
		tmp = Float64(z * t);
	elseif (z <= -9.2e-153)
		tmp = Float64(a * b);
	elseif (z <= 8e-132)
		tmp = Float64(x * y);
	elseif (z <= 2.1e-28)
		tmp = Float64(c * i);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -26000000000000.0)
		tmp = z * t;
	elseif (z <= -9.2e-153)
		tmp = a * b;
	elseif (z <= 8e-132)
		tmp = x * y;
	elseif (z <= 2.1e-28)
		tmp = c * i;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -26000000000000.0], N[(z * t), $MachinePrecision], If[LessEqual[z, -9.2e-153], N[(a * b), $MachinePrecision], If[LessEqual[z, 8e-132], N[(x * y), $MachinePrecision], If[LessEqual[z, 2.1e-28], N[(c * i), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e13 or 2.10000000000000006e-28 < z

   1. Initial program 90.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 52.5%

      \[\leadsto \color{blue}{t \cdot z} \]

   if -2.6e13 < z < -9.19999999999999988e-153

   1. Initial program 94.1%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 34.3%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -9.19999999999999988e-153 < z < 7.9999999999999999e-132

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 34.0%

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

   if 7.9999999999999999e-132 < z < 2.10000000000000006e-28

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 58.3%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;z \leq -0.003:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-132}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-114}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= z -0.003)
     t_1
     (if (<= z -3e-132)
       (+ (* x y) (* a b))
       (if (<= z 8.6e-114) (+ (* x y) (* c i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if (z <= -0.003) {
		tmp = t_1;
	} else if (z <= -3e-132) {
		tmp = (x * y) + (a * b);
	} else if (z <= 8.6e-114) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if (z <= (-0.003d0)) then
        tmp = t_1
    else if (z <= (-3d-132)) then
        tmp = (x * y) + (a * b)
    else if (z <= 8.6d-114) then
        tmp = (x * y) + (c * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if (z <= -0.003) {
		tmp = t_1;
	} else if (z <= -3e-132) {
		tmp = (x * y) + (a * b);
	} else if (z <= 8.6e-114) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if z <= -0.003:
		tmp = t_1
	elif z <= -3e-132:
		tmp = (x * y) + (a * b)
	elif z <= 8.6e-114:
		tmp = (x * y) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (z <= -0.003)
		tmp = t_1;
	elseif (z <= -3e-132)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (z <= 8.6e-114)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if (z <= -0.003)
		tmp = t_1;
	elseif (z <= -3e-132)
		tmp = (x * y) + (a * b);
	elseif (z <= 8.6e-114)
		tmp = (x * y) + (c * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.003], t$95$1, If[LessEqual[z, -3e-132], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-114], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0030000000000000001 or 8.6000000000000001e-114 < z

   1. Initial program 92.1%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 77.0%

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

   4. Taylor expanded in x around 0 62.3%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -0.0030000000000000001 < z < -3e-132

   1. Initial program 96.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 72.4%

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

   4. Taylor expanded in t around 0 61.2%

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

   if -3e-132 < z < 8.6000000000000001e-114

   1. Initial program 97.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.6%

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

      1. associate-/l* 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in x around inf 60.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.003:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-132}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-114}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+40} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -5e+40) (not (<= (* z t) 5e+52)))
   (+ (* c i) (* z t))
   (+ (* x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -5e+40) || !((z * t) <= 5e+52)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (((z * t) <= (-5d+40)) .or. (.not. ((z * t) <= 5d+52))) then
        tmp = (c * i) + (z * t)
    else
        tmp = (x * y) + (a * b)
    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 i) {
	double tmp;
	if (((z * t) <= -5e+40) || !((z * t) <= 5e+52)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -5e+40) or not ((z * t) <= 5e+52):
		tmp = (c * i) + (z * t)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+40) || !(Float64(z * t) <= 5e+52))
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((z * t) <= -5e+40) || ~(((z * t) <= 5e+52)))
		tmp = (c * i) + (z * t);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+40], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+52]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.00000000000000003e40 or 5e52 < (*.f64 z t)

   1. Initial program 92.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.4%

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

      1. associate-/l* 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in z around inf 77.0%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 77.0%

         \[\leadsto \color{blue}{z \cdot t} + c \cdot i \]

   8. Simplified 77.0%

      \[\leadsto \color{blue}{z \cdot t} + c \cdot i \]

   if -5.00000000000000003e40 < (*.f64 z t) < 5e52

   1. Initial program 95.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 71.5%

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

   4. Taylor expanded in t around 0 68.1%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+40} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 5.3 \cdot 10^{+228}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.6e+248) (not (<= (* c i) 5.3e+228)))
   (* c i)
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.6e+248) || !((c * i) <= 5.3e+228)) {
		tmp = c * i;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-1.6d+248)) .or. (.not. ((c * i) <= 5.3d+228))) then
        tmp = c * i
    else
        tmp = (a * b) + (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 i) {
	double tmp;
	if (((c * i) <= -1.6e+248) || !((c * i) <= 5.3e+228)) {
		tmp = c * i;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.6e+248) or not ((c * i) <= 5.3e+228):
		tmp = c * i
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.6e+248) || !(Float64(c * i) <= 5.3e+228))
		tmp = Float64(c * i);
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.6e+248) || ~(((c * i) <= 5.3e+228)))
		tmp = c * i;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.6e+248], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.3e+228]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.59999999999999992e248 or 5.2999999999999999e228 < (*.f64 c i)

   1. Initial program 79.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 81.3%

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

   if -1.59999999999999992e248 < (*.f64 c i) < 5.2999999999999999e228

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 86.6%

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

   4. Taylor expanded in x around 0 64.1%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 5.3 \cdot 10^{+228}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-8} \lor \neg \left(z \leq 1.4 \cdot 10^{-120}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -9.2e-8) (not (<= z 1.4e-120)))
   (+ (* a b) (* z t))
   (+ (* x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -9.2e-8) || !(z <= 1.4e-120)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-9.2d-8)) .or. (.not. (z <= 1.4d-120))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (x * y) + (a * b)
    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 i) {
	double tmp;
	if ((z <= -9.2e-8) || !(z <= 1.4e-120)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -9.2e-8) or not (z <= 1.4e-120):
		tmp = (a * b) + (z * t)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -9.2e-8) || !(z <= 1.4e-120))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -9.2e-8) || ~((z <= 1.4e-120)))
		tmp = (a * b) + (z * t);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -9.2e-8], N[Not[LessEqual[z, 1.4e-120]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000003e-8 or 1.39999999999999997e-120 < z

   1. Initial program 92.1%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 77.0%

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

   4. Taylor expanded in x around 0 62.3%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -9.2000000000000003e-8 < z < 1.39999999999999997e-120

   1. Initial program 96.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 69.9%

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

   4. Taylor expanded in t around 0 62.2%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-8} \lor \neg \left(z \leq 1.4 \cdot 10^{-120}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.16 \cdot 10^{+115} \lor \neg \left(c \cdot i \leq 6.8 \cdot 10^{+61}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.16e+115) (not (<= (* c i) 6.8e+61))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.16e+115) || !((c * i) <= 6.8e+61)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-1.16d+115)) .or. (.not. ((c * i) <= 6.8d+61))) then
        tmp = c * i
    else
        tmp = a * b
    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 i) {
	double tmp;
	if (((c * i) <= -1.16e+115) || !((c * i) <= 6.8e+61)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.16e+115) or not ((c * i) <= 6.8e+61):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.16e+115) || !(Float64(c * i) <= 6.8e+61))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.16e+115) || ~(((c * i) <= 6.8e+61)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.16e+115], N[Not[LessEqual[N[(c * i), $MachinePrecision], 6.8e+61]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.16e115 or 6.80000000000000051e61 < (*.f64 c i)

   1. Initial program 87.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 61.2%

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

   if -1.16e115 < (*.f64 c i) < 6.80000000000000051e61

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 31.6%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.16 \cdot 10^{+115} \lor \neg \left(c \cdot i \leq 6.8 \cdot 10^{+61}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 26.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 93.7%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
2. Add Preprocessing

3. Taylor expanded in a around inf 25.1%

   \[\leadsto \color{blue}{a \cdot b} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024123 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))