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

Percentage Accurate: 96.1% → 97.3%

Time: 10.4s

Alternatives: 10

Speedup: 0.4×

• 40.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 96.1% 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: 97.3% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
   (if (<= t_1 INFINITY) t_1 (* 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)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * t;
	}
	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 = z * t;
	}
	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 = z * t
	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(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)) + (a * b)) + (c * i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * t;
	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[(z * t), $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

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 54.7%

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

4. Final simplification 98.0%

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

Alternative 2: 41.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+169}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{+76}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-294}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+192}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2.05e+169)
   (* x y)
   (if (<= (* x y) -2.45e+76)
     (* c i)
     (if (<= (* x y) 2.2e-294)
       (* z t)
       (if (<= (* x y) 1.15e-122)
         (* a b)
         (if (<= (* x y) 4.5e+192) (* c i) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2.05e+169) {
		tmp = x * y;
	} else if ((x * y) <= -2.45e+76) {
		tmp = c * i;
	} else if ((x * y) <= 2.2e-294) {
		tmp = z * t;
	} else if ((x * y) <= 1.15e-122) {
		tmp = a * b;
	} else if ((x * y) <= 4.5e+192) {
		tmp = c * i;
	} 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) :: tmp
    if ((x * y) <= (-2.05d+169)) then
        tmp = x * y
    else if ((x * y) <= (-2.45d+76)) then
        tmp = c * i
    else if ((x * y) <= 2.2d-294) then
        tmp = z * t
    else if ((x * y) <= 1.15d-122) then
        tmp = a * b
    else if ((x * y) <= 4.5d+192) then
        tmp = c * i
    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 tmp;
	if ((x * y) <= -2.05e+169) {
		tmp = x * y;
	} else if ((x * y) <= -2.45e+76) {
		tmp = c * i;
	} else if ((x * y) <= 2.2e-294) {
		tmp = z * t;
	} else if ((x * y) <= 1.15e-122) {
		tmp = a * b;
	} else if ((x * y) <= 4.5e+192) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2.05e+169:
		tmp = x * y
	elif (x * y) <= -2.45e+76:
		tmp = c * i
	elif (x * y) <= 2.2e-294:
		tmp = z * t
	elif (x * y) <= 1.15e-122:
		tmp = a * b
	elif (x * y) <= 4.5e+192:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2.05e+169)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.45e+76)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= 2.2e-294)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.15e-122)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 4.5e+192)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2.05e+169)
		tmp = x * y;
	elseif ((x * y) <= -2.45e+76)
		tmp = c * i;
	elseif ((x * y) <= 2.2e-294)
		tmp = z * t;
	elseif ((x * y) <= 1.15e-122)
		tmp = a * b;
	elseif ((x * y) <= 4.5e+192)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.05e+169], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.45e+76], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-294], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.15e-122], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.5e+192], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.0500000000000002e169 or 4.5e192 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 80.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 80.8%

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

   if -2.0500000000000002e169 < (*.f64 x y) < -2.45000000000000013e76 or 1.15000000000000003e-122 < (*.f64 x y) < 4.5e192

   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 inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 46.7%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 46.7%

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

   if -2.45000000000000013e76 < (*.f64 x y) < 2.2e-294

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 45.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 45.0%

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

   if 2.2e-294 < (*.f64 x y) < 1.15000000000000003e-122

   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 a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 57.2%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+169}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{+76}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-294}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+192}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.6 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.25e+123)
     t_2
     (if (<= (* c i) -2.35e-7)
       t_1
       (if (<= (* c i) 1.35e-75)
         (+ (* a b) (* z t))
         (if (<= (* c i) 8.6e+140) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.25e+123) {
		tmp = t_2;
	} else if ((c * i) <= -2.35e-7) {
		tmp = t_1;
	} else if ((c * i) <= 1.35e-75) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 8.6e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (x * y) + (a * b)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-1.25d+123)) then
        tmp = t_2
    else if ((c * i) <= (-2.35d-7)) then
        tmp = t_1
    else if ((c * i) <= 1.35d-75) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 8.6d+140) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.25e+123) {
		tmp = t_2;
	} else if ((c * i) <= -2.35e-7) {
		tmp = t_1;
	} else if ((c * i) <= 1.35e-75) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 8.6e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.25e+123:
		tmp = t_2
	elif (c * i) <= -2.35e-7:
		tmp = t_1
	elif (c * i) <= 1.35e-75:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 8.6e+140:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.25e+123)
		tmp = t_2;
	elseif (Float64(c * i) <= -2.35e-7)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.35e-75)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 8.6e+140)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (a * b);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.25e+123)
		tmp = t_2;
	elseif ((c * i) <= -2.35e-7)
		tmp = t_1;
	elseif ((c * i) <= 1.35e-75)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 8.6e+140)
		tmp = t_1;
	else
		tmp = t_2;
	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[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.25e+123], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -2.35e-7], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.35e-75], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.6e+140], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.24999999999999994e123 or 8.60000000000000004e140 < (*.f64 c i)

   1. Initial program 88.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]

   if -1.24999999999999994e123 < (*.f64 c i) < -2.35e-7 or 1.3499999999999999e-75 < (*.f64 c i) < 8.60000000000000004e140

   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 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 87.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 87.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 73.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 73.1%

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

   if -2.35e-7 < (*.f64 c i) < 1.3499999999999999e-75

   1. Initial program 98.3%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 96.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 96.6%

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

   6. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right) \]

      3. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 74.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+123}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.6 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+107}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.2 \cdot 10^{-234}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8 \cdot 10^{-300}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+79}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.6e+107)
   (* c i)
   (if (<= (* c i) -3.2e-234)
     (* a b)
     (if (<= (* c i) 8e-300)
       (* z t)
       (if (<= (* c i) 1e+79) (* 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) <= -1.6e+107) {
		tmp = c * i;
	} else if ((c * i) <= -3.2e-234) {
		tmp = a * b;
	} else if ((c * i) <= 8e-300) {
		tmp = z * t;
	} else if ((c * i) <= 1e+79) {
		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) <= (-1.6d+107)) then
        tmp = c * i
    else if ((c * i) <= (-3.2d-234)) then
        tmp = a * b
    else if ((c * i) <= 8d-300) then
        tmp = z * t
    else if ((c * i) <= 1d+79) 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) <= -1.6e+107) {
		tmp = c * i;
	} else if ((c * i) <= -3.2e-234) {
		tmp = a * b;
	} else if ((c * i) <= 8e-300) {
		tmp = z * t;
	} else if ((c * i) <= 1e+79) {
		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) <= -1.6e+107:
		tmp = c * i
	elif (c * i) <= -3.2e-234:
		tmp = a * b
	elif (c * i) <= 8e-300:
		tmp = z * t
	elif (c * i) <= 1e+79:
		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) <= -1.6e+107)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -3.2e-234)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 8e-300)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1e+79)
		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) <= -1.6e+107)
		tmp = c * i;
	elseif ((c * i) <= -3.2e-234)
		tmp = a * b;
	elseif ((c * i) <= 8e-300)
		tmp = z * t;
	elseif ((c * i) <= 1e+79)
		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], -1.6e+107], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -3.2e-234], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8e-300], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+79], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.60000000000000015e107 or 9.99999999999999967e78 < (*.f64 c i)

   1. Initial program 90.0%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 68.9%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 68.9%

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

   if -1.60000000000000015e107 < (*.f64 c i) < -3.1999999999999999e-234 or 8.0000000000000002e-300 < (*.f64 c i) < 9.99999999999999967e78

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 39.5%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 39.5%

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

   if -3.1999999999999999e-234 < (*.f64 c i) < 8.0000000000000002e-300

   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

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 46.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 46.0%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+107}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.2 \cdot 10^{-234}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8 \cdot 10^{-300}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+79}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -2.7 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -0.32:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))))
   (if (<= (* c i) -2.7e+111)
     t_1
     (if (<= (* c i) -0.32)
       (+ (* x y) (* a b))
       (if (<= (* c i) 8.2e-51) (+ (* a b) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((c * i) <= -2.7e+111) {
		tmp = t_1;
	} else if ((c * i) <= -0.32) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 8.2e-51) {
		tmp = (a * b) + (z * t);
	} 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 = (x * y) + (c * i)
    if ((c * i) <= (-2.7d+111)) then
        tmp = t_1
    else if ((c * i) <= (-0.32d0)) then
        tmp = (x * y) + (a * b)
    else if ((c * i) <= 8.2d-51) then
        tmp = (a * b) + (z * t)
    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 = (x * y) + (c * i);
	double tmp;
	if ((c * i) <= -2.7e+111) {
		tmp = t_1;
	} else if ((c * i) <= -0.32) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 8.2e-51) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	tmp = 0
	if (c * i) <= -2.7e+111:
		tmp = t_1
	elif (c * i) <= -0.32:
		tmp = (x * y) + (a * b)
	elif (c * i) <= 8.2e-51:
		tmp = (a * b) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -2.7e+111)
		tmp = t_1;
	elseif (Float64(c * i) <= -0.32)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(c * i) <= 8.2e-51)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -2.7e+111)
		tmp = t_1;
	elseif ((c * i) <= -0.32)
		tmp = (x * y) + (a * b);
	elseif ((c * i) <= 8.2e-51)
		tmp = (a * b) + (z * t);
	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[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.7e+111], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -0.32], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.2e-51], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.6999999999999999e111 or 8.19999999999999947e-51 < (*.f64 c i)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.3%

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

   if -2.6999999999999999e111 < (*.f64 c i) < -0.320000000000000007

   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 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 93.7%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 81.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 81.0%

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

   if -0.320000000000000007 < (*.f64 c i) < 8.19999999999999947e-51

   1. Initial program 98.3%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 96.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 96.8%

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

   6. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right) \]

      3. *-lowering-*.f64 74.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 74.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.7 \cdot 10^{+111}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -0.32:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -2.8 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 5.6 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))))
   (if (<= (* c i) -2.8e+131)
     t_1
     (if (<= (* c i) 5.6e+108) (+ (* x y) (+ (* a b) (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((c * i) <= -2.8e+131) {
		tmp = t_1;
	} else if ((c * i) <= 5.6e+108) {
		tmp = (x * y) + ((a * b) + (z * t));
	} 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 = (x * y) + (c * i)
    if ((c * i) <= (-2.8d+131)) then
        tmp = t_1
    else if ((c * i) <= 5.6d+108) then
        tmp = (x * y) + ((a * b) + (z * t))
    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 = (x * y) + (c * i);
	double tmp;
	if ((c * i) <= -2.8e+131) {
		tmp = t_1;
	} else if ((c * i) <= 5.6e+108) {
		tmp = (x * y) + ((a * b) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	tmp = 0
	if (c * i) <= -2.8e+131:
		tmp = t_1
	elif (c * i) <= 5.6e+108:
		tmp = (x * y) + ((a * b) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -2.8e+131)
		tmp = t_1;
	elseif (Float64(c * i) <= 5.6e+108)
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -2.8e+131)
		tmp = t_1;
	elseif ((c * i) <= 5.6e+108)
		tmp = (x * y) + ((a * b) + (z * t));
	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[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.8e+131], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 5.6e+108], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.8000000000000001e131 or 5.5999999999999996e108 < (*.f64 c i)

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 85.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 85.6%

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

   if -2.8000000000000001e131 < (*.f64 c i) < 5.5999999999999996e108

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 93.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.8 \cdot 10^{+131}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5.6 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+29}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* c i) -6e+92)
     t_1
     (if (<= (* c i) 4.5e+29) (+ (* a b) (* z t)) 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 ((c * i) <= -6e+92) {
		tmp = t_1;
	} else if ((c * i) <= 4.5e+29) {
		tmp = (a * b) + (z * t);
	} 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 ((c * i) <= (-6d+92)) then
        tmp = t_1
    else if ((c * i) <= 4.5d+29) then
        tmp = (a * b) + (z * t)
    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 ((c * i) <= -6e+92) {
		tmp = t_1;
	} else if ((c * i) <= 4.5e+29) {
		tmp = (a * b) + (z * t);
	} 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 (c * i) <= -6e+92:
		tmp = t_1
	elif (c * i) <= 4.5e+29:
		tmp = (a * b) + (z * t)
	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(c * i) <= -6e+92)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.5e+29)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	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 ((c * i) <= -6e+92)
		tmp = t_1;
	elseif ((c * i) <= 4.5e+29)
		tmp = (a * b) + (z * t);
	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[(c * i), $MachinePrecision], -6e+92], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.5e+29], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -6.00000000000000026e92 or 4.5000000000000002e29 < (*.f64 c i)

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 70.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]

   if -6.00000000000000026e92 < (*.f64 c i) < 4.5000000000000002e29

   1. Initial program 98.7%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 95.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 95.4%

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

   6. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right) \]

      3. *-lowering-*.f64 69.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 69.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6 \cdot 10^{+92}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+29}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.4 \cdot 10^{+177}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+193}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -6.4e+177)
   (* x y)
   (if (<= (* x y) 2.1e+193) (+ (* a b) (* c i)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -6.4e+177) {
		tmp = x * y;
	} else if ((x * y) <= 2.1e+193) {
		tmp = (a * b) + (c * i);
	} 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) :: tmp
    if ((x * y) <= (-6.4d+177)) then
        tmp = x * y
    else if ((x * y) <= 2.1d+193) then
        tmp = (a * b) + (c * i)
    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 tmp;
	if ((x * y) <= -6.4e+177) {
		tmp = x * y;
	} else if ((x * y) <= 2.1e+193) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -6.4e+177:
		tmp = x * y
	elif (x * y) <= 2.1e+193:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -6.4e+177)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.1e+193)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -6.4e+177)
		tmp = x * y;
	elseif ((x * y) <= 2.1e+193)
		tmp = (a * b) + (c * i);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -6.4e+177], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.1e+193], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.4e177 or 2.1e193 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 80.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 80.8%

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

   if -6.4e177 < (*.f64 x y) < 2.1e193

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 63.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 63.1%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 43.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+80}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.7e+108) (* c i) (if (<= (* c i) 2e+80) (* 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) <= -3.7e+108) {
		tmp = c * i;
	} else if ((c * i) <= 2e+80) {
		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) <= (-3.7d+108)) then
        tmp = c * i
    else if ((c * i) <= 2d+80) 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) <= -3.7e+108) {
		tmp = c * i;
	} else if ((c * i) <= 2e+80) {
		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) <= -3.7e+108:
		tmp = c * i
	elif (c * i) <= 2e+80:
		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) <= -3.7e+108)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2e+80)
		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) <= -3.7e+108)
		tmp = c * i;
	elseif ((c * i) <= 2e+80)
		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], -3.7e+108], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+80], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.6999999999999998e108 or 2e80 < (*.f64 c i)

   1. Initial program 90.0%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 68.9%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 68.9%

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

   if -3.6999999999999998e108 < (*.f64 c i) < 2e80

   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

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 36.4%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 36.4%

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

Alternative 10: 27.5% 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 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

   \[\leadsto \color{blue}{a \cdot b} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 27.0%

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

5. Simplified 27.0%

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

Reproduce

herbie shell --seed 2024191 
(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)))