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

Percentage Accurate: 95.7% → 97.5%

Time: 8.7s

Alternatives: 10

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% 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: 97.5% accurate, 0.5× speedup

Math

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

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 (fma 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 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(x, y, (a * b));
	}
	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 = fma(x, y, Float64(a * b));
	end
	return 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[(x * y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 50.0

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

   5. Simplified 50.0%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 50.8

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

   8. Simplified 50.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{a \cdot b}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 43.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 10^{-264}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 1000000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -2e+132)
   (* z t)
   (if (<= (* z t) -1e-176)
     (* a b)
     (if (<= (* z t) 1e-264)
       (* x y)
       (if (<= (* z t) 1000000000000.0) (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -2e+132) {
		tmp = z * t;
	} else if ((z * t) <= -1e-176) {
		tmp = a * b;
	} else if ((z * t) <= 1e-264) {
		tmp = x * y;
	} else if ((z * t) <= 1000000000000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-2d+132)) then
        tmp = z * t
    else if ((z * t) <= (-1d-176)) then
        tmp = a * b
    else if ((z * t) <= 1d-264) then
        tmp = x * y
    else if ((z * t) <= 1000000000000.0d0) then
        tmp = a * b
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -2e+132) {
		tmp = z * t;
	} else if ((z * t) <= -1e-176) {
		tmp = a * b;
	} else if ((z * t) <= 1e-264) {
		tmp = x * y;
	} else if ((z * t) <= 1000000000000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -2e+132:
		tmp = z * t
	elif (z * t) <= -1e-176:
		tmp = a * b
	elif (z * t) <= 1e-264:
		tmp = x * y
	elif (z * t) <= 1000000000000.0:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -2e+132)
		tmp = Float64(z * t);
	elseif (Float64(z * t) <= -1e-176)
		tmp = Float64(a * b);
	elseif (Float64(z * t) <= 1e-264)
		tmp = Float64(x * y);
	elseif (Float64(z * t) <= 1000000000000.0)
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -2e+132)
		tmp = z * t;
	elseif ((z * t) <= -1e-176)
		tmp = a * b;
	elseif ((z * t) <= 1e-264)
		tmp = x * y;
	elseif ((z * t) <= 1000000000000.0)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+132], N[(z * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -1e-176], N[(a * b), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-264], N[(x * y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1000000000000.0], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.99999999999999998e132 or 1e12 < (*.f64 z t)

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 68.2

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

   5. Simplified 68.2%

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

   if -1.99999999999999998e132 < (*.f64 z t) < -1e-176 or 1e-264 < (*.f64 z t) < 1e12

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 52.8

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

   5. Simplified 52.8%

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

   if -1e-176 < (*.f64 z t) < 1e-264

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 45.4

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

   5. Simplified 45.4%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 10^{-264}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 1000000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y, z \cdot t\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma x y (* z t))) (t_2 (+ (* x y) (* z t))))
   (if (<= t_2 -5e+150) t_1 (if (<= t_2 5e+129) (fma i c (* 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 = fma(x, y, (z * t));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -5e+150) {
		tmp = t_1;
	} else if (t_2 <= 5e+129) {
		tmp = fma(i, c, (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(x, y, Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+150)
		tmp = t_1;
	elseif (t_2 <= 5e+129)
		tmp = fma(i, c, Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+150], t$95$1, If[LessEqual[t$95$2, 5e+129], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -5.00000000000000009e150 or 5.0000000000000003e129 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 96.3%

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

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 92.6

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

   5. Simplified 92.6%

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

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{t \cdot z}\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 82.2

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

   8. Simplified 82.2%

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

   if -5.00000000000000009e150 < (+.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000003e129

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 80.7

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

   5. Simplified 80.7%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 81.6

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

   7. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, c, a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq -5 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot t\right)\\ \mathbf{elif}\;x \cdot y + z \cdot t \leq 5 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y, a \cdot b\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -10000000:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(a, b, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma x y (* a b))))
   (if (<= (* x y) -2e+121)
     t_1
     (if (<= (* x y) -10000000.0)
       (fma i c (* a b))
       (if (<= (* x y) 2e+110) (fma 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 = fma(x, y, (a * b));
	double tmp;
	if ((x * y) <= -2e+121) {
		tmp = t_1;
	} else if ((x * y) <= -10000000.0) {
		tmp = fma(i, c, (a * b));
	} else if ((x * y) <= 2e+110) {
		tmp = fma(a, b, (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(x, y, Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -2e+121)
		tmp = t_1;
	elseif (Float64(x * y) <= -10000000.0)
		tmp = fma(i, c, Float64(a * b));
	elseif (Float64(x * y) <= 2e+110)
		tmp = fma(a, b, Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * y + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+121], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -10000000.0], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+110], N[(a * b + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000007e121 or 2e110 < (*.f64 x y)

   1. Initial program 93.9%

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

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 90.6

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

   5. Simplified 90.6%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 84.2

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

   8. Simplified 84.2%

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

   if -2.00000000000000007e121 < (*.f64 x y) < -1e7

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 66.0

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

   5. Simplified 66.0%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 66.0

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

   7. Applied egg-rr 66.0%

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

   if -1e7 < (*.f64 x y) < 2e110

   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

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 76.0

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

   5. Simplified 76.0%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 73.3

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

   8. Simplified 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, b, t \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(x, y, a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq -10000000:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(a, b, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, c \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2e+232)
   (fma i c (* a b))
   (if (<= (* c i) 5e+215) (fma x y (fma a b (* z t))) (fma z t (* 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) <= -2e+232) {
		tmp = fma(i, c, (a * b));
	} else if ((c * i) <= 5e+215) {
		tmp = fma(x, y, fma(a, b, (z * t)));
	} else {
		tmp = fma(z, t, (c * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2e+232)
		tmp = fma(i, c, Float64(a * b));
	elseif (Float64(c * i) <= 5e+215)
		tmp = fma(x, y, fma(a, b, Float64(z * t)));
	else
		tmp = fma(z, t, Float64(c * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2e+232], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+215], N[(x * y + N[(a * b + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.00000000000000011e232

   1. Initial program 92.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 78.8

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

   5. Simplified 78.8%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 82.6

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

   7. Applied egg-rr 82.6%

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

   if -2.00000000000000011e232 < (*.f64 c i) < 5.0000000000000001e215

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 89.9

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

   5. Simplified 89.9%

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

   if 5.0000000000000001e215 < (*.f64 c i)

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 96.2

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

   5. Simplified 96.2%

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 96.2

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

   7. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t, c \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, c \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, b, z \cdot t\right)\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 50000000000000:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma a b (* z t))))
   (if (<= (* z t) -2e+82)
     t_1
     (if (<= (* z t) 50000000000000.0) (fma i c (* 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 = fma(a, b, (z * t));
	double tmp;
	if ((z * t) <= -2e+82) {
		tmp = t_1;
	} else if ((z * t) <= 50000000000000.0) {
		tmp = fma(i, c, (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(a, b, Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -2e+82)
		tmp = t_1;
	elseif (Float64(z * t) <= 50000000000000.0)
		tmp = fma(i, c, Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * b + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+82], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 50000000000000.0], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.9999999999999999e82 or 5e13 < (*.f64 z t)

   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 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

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 88.7

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

   5. Simplified 88.7%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 75.9

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

   8. Simplified 75.9%

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

   if -1.9999999999999999e82 < (*.f64 z t) < 5e13

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 69.0

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

   5. Simplified 69.0%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 69.7

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

   7. Applied egg-rr 69.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, c, a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(a, b, z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 50000000000000:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.95 \cdot 10^{+206}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(a, b, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2.95e+206)
   (* x y)
   (if (<= (* x y) 6e+217) (fma a b (* z t)) (* 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) <= -2.95e+206) {
		tmp = x * y;
	} else if ((x * y) <= 6e+217) {
		tmp = fma(a, b, (z * t));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2.95e+206)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 6e+217)
		tmp = fma(a, b, Float64(z * t));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.95e+206], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e+217], N[(a * b + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.95e206 or 5.99999999999999952e217 < (*.f64 x y)

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 81.3

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

   5. Simplified 81.3%

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

   if -2.95e206 < (*.f64 x y) < 5.99999999999999952e217

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 75.3

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

   5. Simplified 75.3%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 67.9

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

   8. Simplified 67.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.95 \cdot 10^{+206}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(a, b, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 1000000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -2e+132)
   (* z t)
   (if (<= (* z t) 1000000000000.0) (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -2e+132) {
		tmp = z * t;
	} else if ((z * t) <= 1000000000000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-2d+132)) then
        tmp = z * t
    else if ((z * t) <= 1000000000000.0d0) then
        tmp = a * b
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -2e+132) {
		tmp = z * t;
	} else if ((z * t) <= 1000000000000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -2e+132:
		tmp = z * t
	elif (z * t) <= 1000000000000.0:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -2e+132)
		tmp = Float64(z * t);
	elseif (Float64(z * t) <= 1000000000000.0)
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -2e+132)
		tmp = z * t;
	elseif ((z * t) <= 1000000000000.0)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+132], N[(z * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1000000000000.0], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.99999999999999998e132 or 1e12 < (*.f64 z t)

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 68.2

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

   5. Simplified 68.2%

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

   if -1.99999999999999998e132 < (*.f64 z t) < 1e12

   1. Initial program 96.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 43.8

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

   5. Simplified 43.8%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 1000000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+56}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.6e+56) (* a b) (if (<= (* a b) 8.6e+90) (* c i) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.6e+56) {
		tmp = a * b;
	} else if ((a * b) <= 8.6e+90) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-2.6d+56)) then
        tmp = a * b
    else if ((a * b) <= 8.6d+90) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.6e+56) {
		tmp = a * b;
	} else if ((a * b) <= 8.6e+90) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -2.6e+56:
		tmp = a * b
	elif (a * b) <= 8.6e+90:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -2.6e+56)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 8.6e+90)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -2.6e+56)
		tmp = a * b;
	elseif ((a * b) <= 8.6e+90)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.6e+56], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.6e+90], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.60000000000000011e56 or 8.5999999999999994e90 < (*.f64 a b)

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 70.6

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

   5. Simplified 70.6%

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

   if -2.60000000000000011e56 < (*.f64 a b) < 8.5999999999999994e90

   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 inf

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

      1. lower-*.f64 32.3

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

   5. Simplified 32.3%

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

Alternative 10: 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

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

   1. lower-*.f64 31.2

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

5. Simplified 31.2%

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

Reproduce

herbie shell --seed 2024207 
(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)))