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

Percentage Accurate: 95.7% → 97.0%

Time: 14.0s

Alternatives: 12

Speedup: 0.4×

• 42.3% 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: 95.7% 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: 97.0% accurate, 0.4× speedup

Math

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

FPCore

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * z), $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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z + c \cdot i\\ t_2 := t \cdot z + x \cdot y\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+71}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* t z) (* c i)))
        (t_2 (+ (* t z) (* x y)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* a b) -1e+71)
     t_3
     (if (<= (* a b) -5e-215)
       t_1
       (if (<= (* a b) 0.0)
         t_2
         (if (<= (* a b) 1.2e-60) t_1 (if (<= (* a b) 1e+75) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * z) + (c * i);
	double t_2 = (t * z) + (x * y);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -1e+71) {
		tmp = t_3;
	} else if ((a * b) <= -5e-215) {
		tmp = t_1;
	} else if ((a * b) <= 0.0) {
		tmp = t_2;
	} else if ((a * b) <= 1.2e-60) {
		tmp = t_1;
	} else if ((a * b) <= 1e+75) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * z) + (c * i)
    t_2 = (t * z) + (x * y)
    t_3 = (a * b) + (c * i)
    if ((a * b) <= (-1d+71)) then
        tmp = t_3
    else if ((a * b) <= (-5d-215)) then
        tmp = t_1
    else if ((a * b) <= 0.0d0) then
        tmp = t_2
    else if ((a * b) <= 1.2d-60) then
        tmp = t_1
    else if ((a * b) <= 1d+75) 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 i) {
	double t_1 = (t * z) + (c * i);
	double t_2 = (t * z) + (x * y);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -1e+71) {
		tmp = t_3;
	} else if ((a * b) <= -5e-215) {
		tmp = t_1;
	} else if ((a * b) <= 0.0) {
		tmp = t_2;
	} else if ((a * b) <= 1.2e-60) {
		tmp = t_1;
	} else if ((a * b) <= 1e+75) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t * z) + (c * i)
	t_2 = (t * z) + (x * y)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -1e+71:
		tmp = t_3
	elif (a * b) <= -5e-215:
		tmp = t_1
	elif (a * b) <= 0.0:
		tmp = t_2
	elif (a * b) <= 1.2e-60:
		tmp = t_1
	elif (a * b) <= 1e+75:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t * z) + Float64(c * i))
	t_2 = Float64(Float64(t * z) + Float64(x * y))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -1e+71)
		tmp = t_3;
	elseif (Float64(a * b) <= -5e-215)
		tmp = t_1;
	elseif (Float64(a * b) <= 0.0)
		tmp = t_2;
	elseif (Float64(a * b) <= 1.2e-60)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e+75)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t * z) + (c * i);
	t_2 = (t * z) + (x * y);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -1e+71)
		tmp = t_3;
	elseif ((a * b) <= -5e-215)
		tmp = t_1;
	elseif ((a * b) <= 0.0)
		tmp = t_2;
	elseif ((a * b) <= 1.2e-60)
		tmp = t_1;
	elseif ((a * b) <= 1e+75)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+71], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -5e-215], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 0.0], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1.2e-60], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e+75], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1e71 or 9.99999999999999927e74 < (*.f64 a b)

   1. Initial program 94.9%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1e71 < (*.f64 a b) < -4.99999999999999956e-215 or 0.0 < (*.f64 a b) < 1.20000000000000005e-60

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.99999999999999956e-215 < (*.f64 a b) < 0.0 or 1.20000000000000005e-60 < (*.f64 a b) < 9.99999999999999927e74

   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 t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-215}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;t \cdot z + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{-45}:\\ \;\;\;\;t \cdot z + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1e+64)
   (+ (* a b) (* c i))
   (if (<= (* a b) -5e-215)
     (+ (* x y) (* c i))
     (if (<= (* a b) 0.0)
       (+ (* t z) (* x y))
       (if (<= (* a b) 1e-45)
         (+ (* t z) (* c i))
         (* a (+ b (/ (* x y) a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1e+64) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 0.0) {
		tmp = (t * z) + (x * y);
	} else if ((a * b) <= 1e-45) {
		tmp = (t * z) + (c * i);
	} else {
		tmp = a * (b + ((x * y) / a));
	}
	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) <= (-1d+64)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= (-5d-215)) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 0.0d0) then
        tmp = (t * z) + (x * y)
    else if ((a * b) <= 1d-45) then
        tmp = (t * z) + (c * i)
    else
        tmp = a * (b + ((x * y) / a))
    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) <= -1e+64) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 0.0) {
		tmp = (t * z) + (x * y);
	} else if ((a * b) <= 1e-45) {
		tmp = (t * z) + (c * i);
	} else {
		tmp = a * (b + ((x * y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1e+64:
		tmp = (a * b) + (c * i)
	elif (a * b) <= -5e-215:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 0.0:
		tmp = (t * z) + (x * y)
	elif (a * b) <= 1e-45:
		tmp = (t * z) + (c * i)
	else:
		tmp = a * (b + ((x * y) / a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1e+64)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= -5e-215)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(Float64(t * z) + Float64(x * y));
	elseif (Float64(a * b) <= 1e-45)
		tmp = Float64(Float64(t * z) + Float64(c * i));
	else
		tmp = Float64(a * Float64(b + Float64(Float64(x * y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1e+64)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= -5e-215)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 0.0)
		tmp = (t * z) + (x * y);
	elseif ((a * b) <= 1e-45)
		tmp = (t * z) + (c * i);
	else
		tmp = a * (b + ((x * y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+64], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-215], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-45], N[(N[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(b + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -1.00000000000000002e64

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.00000000000000002e64 < (*.f64 a b) < -4.99999999999999956e-215

   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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.99999999999999956e-215 < (*.f64 a b) < 0.0

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 0.0 < (*.f64 a b) < 9.99999999999999984e-46

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 9.99999999999999984e-46 < (*.f64 a b)

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-215}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;t \cdot z + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{-45}:\\ \;\;\;\;t \cdot z + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1e+64)
   (+ (* a b) (* c i))
   (if (<= (* a b) -5e-215)
     (+ (* x y) (* c i))
     (if (<= (* a b) 0.0)
       (+ (* t z) (* x y))
       (if (<= (* a b) 1e-45) (+ (* t z) (* c i)) (+ (* 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 ((a * b) <= -1e+64) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 0.0) {
		tmp = (t * z) + (x * y);
	} else if ((a * b) <= 1e-45) {
		tmp = (t * z) + (c * i);
	} 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 ((a * b) <= (-1d+64)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= (-5d-215)) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 0.0d0) then
        tmp = (t * z) + (x * y)
    else if ((a * b) <= 1d-45) then
        tmp = (t * z) + (c * i)
    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 ((a * b) <= -1e+64) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 0.0) {
		tmp = (t * z) + (x * y);
	} else if ((a * b) <= 1e-45) {
		tmp = (t * z) + (c * i);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1e+64:
		tmp = (a * b) + (c * i)
	elif (a * b) <= -5e-215:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 0.0:
		tmp = (t * z) + (x * y)
	elif (a * b) <= 1e-45:
		tmp = (t * z) + (c * i)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1e+64)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= -5e-215)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(Float64(t * z) + Float64(x * y));
	elseif (Float64(a * b) <= 1e-45)
		tmp = Float64(Float64(t * z) + Float64(c * i));
	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 ((a * b) <= -1e+64)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= -5e-215)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 0.0)
		tmp = (t * z) + (x * y);
	elseif ((a * b) <= 1e-45)
		tmp = (t * z) + (c * i);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+64], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-215], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-45], N[(N[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -1.00000000000000002e64

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.00000000000000002e64 < (*.f64 a b) < -4.99999999999999956e-215

   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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.99999999999999956e-215 < (*.f64 a b) < 0.0

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 0.0 < (*.f64 a b) < 9.99999999999999984e-46

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 9.99999999999999984e-46 < (*.f64 a b)

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+71}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;t \cdot z + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* t z) (* c i))))
   (if (<= (* a b) -1e+71)
     (+ (* a b) (* c i))
     (if (<= (* a b) -5e-215)
       t_1
       (if (<= (* a b) 0.0)
         (+ (* t z) (* x y))
         (if (<= (* a b) 1e-45) t_1 (+ (* x y) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * z) + (c * i);
	double tmp;
	if ((a * b) <= -1e+71) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = t_1;
	} else if ((a * b) <= 0.0) {
		tmp = (t * z) + (x * y);
	} else if ((a * b) <= 1e-45) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t * z) + (c * i)
    if ((a * b) <= (-1d+71)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= (-5d-215)) then
        tmp = t_1
    else if ((a * b) <= 0.0d0) then
        tmp = (t * z) + (x * y)
    else if ((a * b) <= 1d-45) then
        tmp = t_1
    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 t_1 = (t * z) + (c * i);
	double tmp;
	if ((a * b) <= -1e+71) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = t_1;
	} else if ((a * b) <= 0.0) {
		tmp = (t * z) + (x * y);
	} else if ((a * b) <= 1e-45) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t * z) + (c * i)
	tmp = 0
	if (a * b) <= -1e+71:
		tmp = (a * b) + (c * i)
	elif (a * b) <= -5e-215:
		tmp = t_1
	elif (a * b) <= 0.0:
		tmp = (t * z) + (x * y)
	elif (a * b) <= 1e-45:
		tmp = t_1
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t * z) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -1e+71)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= -5e-215)
		tmp = t_1;
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(Float64(t * z) + Float64(x * y));
	elseif (Float64(a * b) <= 1e-45)
		tmp = t_1;
	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)
	t_1 = (t * z) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -1e+71)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= -5e-215)
		tmp = t_1;
	elseif ((a * b) <= 0.0)
		tmp = (t * z) + (x * y);
	elseif ((a * b) <= 1e-45)
		tmp = t_1;
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+71], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-215], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-45], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1e71

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1e71 < (*.f64 a b) < -4.99999999999999956e-215 or 0.0 < (*.f64 a b) < 9.99999999999999984e-46

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.99999999999999956e-215 < (*.f64 a b) < 0.0

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 9.99999999999999984e-46 < (*.f64 a b)

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-51}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -5e+139)
     (* x y)
     (if (<= (* x y) 8.5e-182)
       t_1
       (if (<= (* x y) 1.25e-51)
         (* t z)
         (if (<= (* x y) 2.4e+103) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -5e+139) {
		tmp = x * y;
	} else if ((x * y) <= 8.5e-182) {
		tmp = t_1;
	} else if ((x * y) <= 1.25e-51) {
		tmp = t * z;
	} else if ((x * y) <= 2.4e+103) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	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) + (c * i)
    if ((x * y) <= (-5d+139)) then
        tmp = x * y
    else if ((x * y) <= 8.5d-182) then
        tmp = t_1
    else if ((x * y) <= 1.25d-51) then
        tmp = t * z
    else if ((x * y) <= 2.4d+103) then
        tmp = t_1
    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 i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -5e+139) {
		tmp = x * y;
	} else if ((x * y) <= 8.5e-182) {
		tmp = t_1;
	} else if ((x * y) <= 1.25e-51) {
		tmp = t * z;
	} else if ((x * y) <= 2.4e+103) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -5e+139:
		tmp = x * y
	elif (x * y) <= 8.5e-182:
		tmp = t_1
	elif (x * y) <= 1.25e-51:
		tmp = t * z
	elif (x * y) <= 2.4e+103:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -5e+139)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 8.5e-182)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.25e-51)
		tmp = Float64(t * z);
	elseif (Float64(x * y) <= 2.4e+103)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -5e+139)
		tmp = x * y;
	elseif ((x * y) <= 8.5e-182)
		tmp = t_1;
	elseif ((x * y) <= 1.25e-51)
		tmp = t * z;
	elseif ((x * y) <= 2.4e+103)
		tmp = t_1;
	else
		tmp = x * y;
	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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+139], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.5e-182], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.25e-51], N[(t * z), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.4e+103], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000003e139 or 2.3999999999999998e103 < (*.f64 x y)

   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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.0000000000000003e139 < (*.f64 x y) < 8.5000000000000001e-182 or 1.25000000000000001e-51 < (*.f64 x y) < 2.3999999999999998e103

   1. Initial program 98.8%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 8.5000000000000001e-182 < (*.f64 x y) < 1.25000000000000001e-51

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right) + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot z + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot z + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4e+114)
   (+ (* a (+ b (/ (* x y) a))) (* c i))
   (if (<= (* c i) 2e+38)
     (+ (* t z) (+ (* x y) (* a b)))
     (+ (* t z) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4e+114) {
		tmp = (a * (b + ((x * y) / a))) + (c * i);
	} else if ((c * i) <= 2e+38) {
		tmp = (t * z) + ((x * y) + (a * b));
	} else {
		tmp = (t * z) + (c * i);
	}
	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) <= (-4d+114)) then
        tmp = (a * (b + ((x * y) / a))) + (c * i)
    else if ((c * i) <= 2d+38) then
        tmp = (t * z) + ((x * y) + (a * b))
    else
        tmp = (t * z) + (c * i)
    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) <= -4e+114) {
		tmp = (a * (b + ((x * y) / a))) + (c * i);
	} else if ((c * i) <= 2e+38) {
		tmp = (t * z) + ((x * y) + (a * b));
	} else {
		tmp = (t * z) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4e+114:
		tmp = (a * (b + ((x * y) / a))) + (c * i)
	elif (c * i) <= 2e+38:
		tmp = (t * z) + ((x * y) + (a * b))
	else:
		tmp = (t * z) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4e+114)
		tmp = Float64(Float64(a * Float64(b + Float64(Float64(x * y) / a))) + Float64(c * i));
	elseif (Float64(c * i) <= 2e+38)
		tmp = Float64(Float64(t * z) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = Float64(Float64(t * z) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4e+114)
		tmp = (a * (b + ((x * y) / a))) + (c * i);
	elseif ((c * i) <= 2e+38)
		tmp = (t * z) + ((x * y) + (a * b));
	else
		tmp = (t * z) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4e+114], N[(N[(a * N[(b + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+38], N[(N[(t * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4e114

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around -inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4e114 < (*.f64 c i) < 1.99999999999999995e38

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.99999999999999995e38 < (*.f64 c i)

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot z + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* t z) (* c i))))
   (if (<= (* c i) -4e+114)
     t_1
     (if (<= (* c i) 2e+38) (+ (* t z) (+ (* x y) (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * z) + (c * i);
	double tmp;
	if ((c * i) <= -4e+114) {
		tmp = t_1;
	} else if ((c * i) <= 2e+38) {
		tmp = (t * z) + ((x * y) + (a * b));
	} 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 = (t * z) + (c * i)
    if ((c * i) <= (-4d+114)) then
        tmp = t_1
    else if ((c * i) <= 2d+38) then
        tmp = (t * z) + ((x * y) + (a * b))
    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 = (t * z) + (c * i);
	double tmp;
	if ((c * i) <= -4e+114) {
		tmp = t_1;
	} else if ((c * i) <= 2e+38) {
		tmp = (t * z) + ((x * y) + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t * z) + (c * i)
	tmp = 0
	if (c * i) <= -4e+114:
		tmp = t_1
	elif (c * i) <= 2e+38:
		tmp = (t * z) + ((x * y) + (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t * z) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -4e+114)
		tmp = t_1;
	elseif (Float64(c * i) <= 2e+38)
		tmp = Float64(Float64(t * z) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t * z) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -4e+114)
		tmp = t_1;
	elseif ((c * i) <= 2e+38)
		tmp = (t * z) + ((x * y) + (a * b));
	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[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -4e+114], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2e+38], N[(N[(t * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4e114 or 1.99999999999999995e38 < (*.f64 c i)

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4e114 < (*.f64 c i) < 1.99999999999999995e38

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 44.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+114}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-253}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 10^{+62}:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4e+114)
   (* a b)
   (if (<= (* a b) -1e-253) (* c i) (if (<= (* a b) 1e+62) (* t z) (* 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) <= -4e+114) {
		tmp = a * b;
	} else if ((a * b) <= -1e-253) {
		tmp = c * i;
	} else if ((a * b) <= 1e+62) {
		tmp = t * z;
	} 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) <= (-4d+114)) then
        tmp = a * b
    else if ((a * b) <= (-1d-253)) then
        tmp = c * i
    else if ((a * b) <= 1d+62) then
        tmp = t * z
    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) <= -4e+114) {
		tmp = a * b;
	} else if ((a * b) <= -1e-253) {
		tmp = c * i;
	} else if ((a * b) <= 1e+62) {
		tmp = t * z;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4e+114:
		tmp = a * b
	elif (a * b) <= -1e-253:
		tmp = c * i
	elif (a * b) <= 1e+62:
		tmp = t * z
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4e+114)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1e-253)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1e+62)
		tmp = Float64(t * z);
	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) <= -4e+114)
		tmp = a * b;
	elseif ((a * b) <= -1e-253)
		tmp = c * i;
	elseif ((a * b) <= 1e+62)
		tmp = t * z;
	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], -4e+114], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-253], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+62], N[(t * z), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4e114 or 1.00000000000000004e62 < (*.f64 a b)

   1. Initial program 95.7%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4e114 < (*.f64 a b) < -1.0000000000000001e-253

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0000000000000001e-253 < (*.f64 a b) < 1.00000000000000004e62

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+62}:\\ \;\;\;\;t \cdot z + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* a b) -1e+71)
     t_1
     (if (<= (* a b) 1e+62) (+ (* t z) (* 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) + (c * i);
	double tmp;
	if ((a * b) <= -1e+71) {
		tmp = t_1;
	} else if ((a * b) <= 1e+62) {
		tmp = (t * z) + (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) + (c * i)
    if ((a * b) <= (-1d+71)) then
        tmp = t_1
    else if ((a * b) <= 1d+62) then
        tmp = (t * z) + (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) + (c * i);
	double tmp;
	if ((a * b) <= -1e+71) {
		tmp = t_1;
	} else if ((a * b) <= 1e+62) {
		tmp = (t * z) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -1e+71:
		tmp = t_1
	elif (a * b) <= 1e+62:
		tmp = (t * z) + (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(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -1e+71)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e+62)
		tmp = Float64(Float64(t * z) + 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) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -1e+71)
		tmp = t_1;
	elseif ((a * b) <= 1e+62)
		tmp = (t * z) + (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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+71], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e+62], N[(N[(t * z), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1e71 or 1.00000000000000004e62 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1e71 < (*.f64 a b) < 1.00000000000000004e62

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9.6 \cdot 10^{+110}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 9 \cdot 10^{+48}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -9.6e+110) (* c i) (if (<= (* c i) 9e+48) (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -9.6e+110) {
		tmp = c * i;
	} else if ((c * i) <= 9e+48) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	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) <= (-9.6d+110)) then
        tmp = c * i
    else if ((c * i) <= 9d+48) then
        tmp = a * b
    else
        tmp = c * i
    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) <= -9.6e+110) {
		tmp = c * i;
	} else if ((c * i) <= 9e+48) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -9.6e+110:
		tmp = c * i
	elif (c * i) <= 9e+48:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -9.6e+110)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 9e+48)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -9.6e+110)
		tmp = c * i;
	elseif ((c * i) <= 9e+48)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -9.6e+110], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9e+48], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.60000000000000049e110 or 8.99999999999999991e48 < (*.f64 c i)

   1. Initial program 94.5%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.60000000000000049e110 < (*.f64 c i) < 8.99999999999999991e48

   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 a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 27.7% 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 96.9%

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

3. Taylor expanded in a around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))