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

Percentage Accurate: 95.9% → 98.2%

Time: 8.3s

Alternatives: 10

Speedup: 0.5×

• 41.4% 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: 95.9% 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: 98.2% accurate, 0.5× speedup

Math

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

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 a b (fma c i (* x y))))))

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(a, b, fma(c, i, (x * y)));
	}
	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(a, b, fma(c, i, Float64(x * y)));
	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[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 50.0

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

   5. Simplified 50.0%

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

Alternative 2: 42.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.6 \cdot 10^{+170}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -51000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -9.8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 6.8 \cdot 10^{+100}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.6e+170)
   (* c i)
   (if (<= (* c i) -51000000.0)
     (* a b)
     (if (<= (* c i) -9.8e-307)
       (* x y)
       (if (<= (* c i) 4.5e-80)
         (* a b)
         (if (<= (* c i) 6.8e+100) (* 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) <= -4.6e+170) {
		tmp = c * i;
	} else if ((c * i) <= -51000000.0) {
		tmp = a * b;
	} else if ((c * i) <= -9.8e-307) {
		tmp = x * y;
	} else if ((c * i) <= 4.5e-80) {
		tmp = a * b;
	} else if ((c * i) <= 6.8e+100) {
		tmp = z * t;
	} 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) <= (-4.6d+170)) then
        tmp = c * i
    else if ((c * i) <= (-51000000.0d0)) then
        tmp = a * b
    else if ((c * i) <= (-9.8d-307)) then
        tmp = x * y
    else if ((c * i) <= 4.5d-80) then
        tmp = a * b
    else if ((c * i) <= 6.8d+100) then
        tmp = z * t
    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) <= -4.6e+170) {
		tmp = c * i;
	} else if ((c * i) <= -51000000.0) {
		tmp = a * b;
	} else if ((c * i) <= -9.8e-307) {
		tmp = x * y;
	} else if ((c * i) <= 4.5e-80) {
		tmp = a * b;
	} else if ((c * i) <= 6.8e+100) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.6e+170:
		tmp = c * i
	elif (c * i) <= -51000000.0:
		tmp = a * b
	elif (c * i) <= -9.8e-307:
		tmp = x * y
	elif (c * i) <= 4.5e-80:
		tmp = a * b
	elif (c * i) <= 6.8e+100:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.6e+170)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -51000000.0)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= -9.8e-307)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 4.5e-80)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 6.8e+100)
		tmp = Float64(z * t);
	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) <= -4.6e+170)
		tmp = c * i;
	elseif ((c * i) <= -51000000.0)
		tmp = a * b;
	elseif ((c * i) <= -9.8e-307)
		tmp = x * y;
	elseif ((c * i) <= 4.5e-80)
		tmp = a * b;
	elseif ((c * i) <= 6.8e+100)
		tmp = z * t;
	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], -4.6e+170], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -51000000.0], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -9.8e-307], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.5e-80], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.8e+100], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.6000000000000001e170 or 6.79999999999999988e100 < (*.f64 c i)

   1. Initial program 91.3%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

   if -4.6000000000000001e170 < (*.f64 c i) < -5.1e7 or -9.8000000000000005e-307 < (*.f64 c i) < 4.5000000000000003e-80

   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 a around inf

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

      1. *-lowering-*.f64 48.0

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

   5. Simplified 48.0%

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

   if -5.1e7 < (*.f64 c i) < -9.8000000000000005e-307

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 45.4

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

   5. Simplified 45.4%

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

   if 4.5000000000000003e-80 < (*.f64 c i) < 6.79999999999999988e100

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 51.9

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

   5. Simplified 51.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.6 \cdot 10^{+170}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -51000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -9.8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 6.8 \cdot 10^{+100}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, i, \mathsf{fma}\left(t, z, x \cdot y\right)\right)\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma c i (fma t z (* x y)))))
   (if (<= (* z t) -1e+196)
     t_1
     (if (<= (* z t) 5e-21) (fma a b (fma c i (* x y))) 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(c, i, fma(t, z, (x * y)));
	double tmp;
	if ((z * t) <= -1e+196) {
		tmp = t_1;
	} else if ((z * t) <= 5e-21) {
		tmp = fma(a, b, fma(c, i, (x * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(c, i, fma(t, z, Float64(x * y)))
	tmp = 0.0
	if (Float64(z * t) <= -1e+196)
		tmp = t_1;
	elseif (Float64(z * t) <= 5e-21)
		tmp = fma(a, b, fma(c, i, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * i + N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+196], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5e-21], N[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.9999999999999995e195 or 4.99999999999999973e-21 < (*.f64 z t)

   1. Initial program 95.1%

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

   3. Taylor expanded in a around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 84.0

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

   5. Simplified 84.0%

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

   if -9.9999999999999995e195 < (*.f64 z t) < 4.99999999999999973e-21

   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 z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 92.8

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

   5. Simplified 92.8%

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

Alternative 4: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+213}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i c (* z t))))
   (if (<= (* z t) -1e+196)
     t_1
     (if (<= (* z t) 5e+213) (fma a b (fma c i (* x y))) 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(i, c, (z * t));
	double tmp;
	if ((z * t) <= -1e+196) {
		tmp = t_1;
	} else if ((z * t) <= 5e+213) {
		tmp = fma(a, b, fma(c, i, (x * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, c, Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -1e+196)
		tmp = t_1;
	elseif (Float64(z * t) <= 5e+213)
		tmp = fma(a, b, fma(c, i, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * c + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+196], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5e+213], N[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.9999999999999995e195 or 4.9999999999999998e213 < (*.f64 z t)

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 86.4

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

   5. Simplified 86.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 86.4

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

   7. Applied egg-rr 86.4%

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

   if -9.9999999999999995e195 < (*.f64 z t) < 4.9999999999999998e213

   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 z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 88.1

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

   5. Simplified 88.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+213}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+164}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.9 \cdot 10^{+99}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5.5e+164)
   (* c i)
   (if (<= (* c i) 6.2e-80)
     (* a b)
     (if (<= (* c i) 3.9e+99) (* 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) <= -5.5e+164) {
		tmp = c * i;
	} else if ((c * i) <= 6.2e-80) {
		tmp = a * b;
	} else if ((c * i) <= 3.9e+99) {
		tmp = z * t;
	} 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) <= (-5.5d+164)) then
        tmp = c * i
    else if ((c * i) <= 6.2d-80) then
        tmp = a * b
    else if ((c * i) <= 3.9d+99) then
        tmp = z * t
    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) <= -5.5e+164) {
		tmp = c * i;
	} else if ((c * i) <= 6.2e-80) {
		tmp = a * b;
	} else if ((c * i) <= 3.9e+99) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5.5e+164:
		tmp = c * i
	elif (c * i) <= 6.2e-80:
		tmp = a * b
	elif (c * i) <= 3.9e+99:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5.5e+164)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 6.2e-80)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.9e+99)
		tmp = Float64(z * t);
	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) <= -5.5e+164)
		tmp = c * i;
	elseif ((c * i) <= 6.2e-80)
		tmp = a * b;
	elseif ((c * i) <= 3.9e+99)
		tmp = z * t;
	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], -5.5e+164], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.2e-80], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.9e+99], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.4999999999999998e164 or 3.89999999999999995e99 < (*.f64 c i)

   1. Initial program 91.3%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

   if -5.4999999999999998e164 < (*.f64 c i) < 6.20000000000000032e-80

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 40.9

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

   5. Simplified 40.9%

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

   if 6.20000000000000032e-80 < (*.f64 c i) < 3.89999999999999995e99

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 51.9

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

   5. Simplified 51.9%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+164}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.9 \cdot 10^{+99}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(c, i, x \cdot y\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(x, y, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+191)
   (fma c i (* x y))
   (if (<= (* c i) 5e-82) (fma x y (* a b)) (fma i c (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+191) {
		tmp = fma(c, i, (x * y));
	} else if ((c * i) <= 5e-82) {
		tmp = fma(x, y, (a * b));
	} else {
		tmp = fma(i, c, (z * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+191)
		tmp = fma(c, i, Float64(x * y));
	elseif (Float64(c * i) <= 5e-82)
		tmp = fma(x, y, Float64(a * b));
	else
		tmp = fma(i, c, Float64(z * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1e+191], N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e-82], N[(x * y + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(i * c + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.00000000000000007e191

   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 z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 93.3

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

   5. Simplified 93.3%

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

   6. Taylor expanded in a around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. *-lowering-*.f64 87.1

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

   8. Simplified 87.1%

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

   if -1.00000000000000007e191 < (*.f64 c i) < 4.9999999999999998e-82

   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 z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 75.6

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

   5. Simplified 75.6%

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

   6. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 69.2

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

   8. Simplified 69.2%

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

   if 4.9999999999999998e-82 < (*.f64 c i)

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 77.0

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

   5. Simplified 77.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 77.0

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

   7. Applied egg-rr 77.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(c, i, x \cdot y\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(x, y, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+191}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 9.6 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3.5e+191)
   (* a b)
   (if (<= (* a b) 9.6e+173) (fma i c (* z t)) (* 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) <= -3.5e+191) {
		tmp = a * b;
	} else if ((a * b) <= 9.6e+173) {
		tmp = fma(i, c, (z * t));
	} else {
		tmp = a * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -3.5e+191)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 9.6e+173)
		tmp = fma(i, c, Float64(z * t));
	else
		tmp = Float64(a * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -3.5e+191], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9.6e+173], N[(i * c + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.4999999999999997e191 or 9.5999999999999997e173 < (*.f64 a b)

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 80.0

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

   5. Simplified 80.0%

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

   if -3.4999999999999997e191 < (*.f64 a b) < 9.5999999999999997e173

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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. *-lowering-*.f64 63.7

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

   5. Simplified 63.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 63.7

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

   7. Applied egg-rr 63.7%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+191}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 9.6 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.45 \cdot 10^{+121}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 10^{+166}:\\ \;\;\;\;\mathsf{fma}\left(c, i, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.45e+121)
   (* a b)
   (if (<= (* a b) 1e+166) (fma c i (* x y)) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.45e+121) {
		tmp = a * b;
	} else if ((a * b) <= 1e+166) {
		tmp = fma(c, i, (x * y));
	} else {
		tmp = a * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.45e+121)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1e+166)
		tmp = fma(c, i, Float64(x * y));
	else
		tmp = Float64(a * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.45e+121], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+166], N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.45e121 or 9.9999999999999994e165 < (*.f64 a b)

   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 a around inf

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

      1. *-lowering-*.f64 70.4

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

   5. Simplified 70.4%

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

   if -1.45e121 < (*.f64 a b) < 9.9999999999999994e165

   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 z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 73.5

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

   5. Simplified 73.5%

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

   6. Taylor expanded in a around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. *-lowering-*.f64 64.2

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

   8. Simplified 64.2%

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

Alternative 9: 42.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.2 \cdot 10^{+164}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.2e+164)
   (* c i)
   (if (<= (* c i) 5.8e+100) (* 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) <= -4.2e+164) {
		tmp = c * i;
	} else if ((c * i) <= 5.8e+100) {
		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) <= (-4.2d+164)) then
        tmp = c * i
    else if ((c * i) <= 5.8d+100) 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) <= -4.2e+164) {
		tmp = c * i;
	} else if ((c * i) <= 5.8e+100) {
		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) <= -4.2e+164:
		tmp = c * i
	elif (c * i) <= 5.8e+100:
		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) <= -4.2e+164)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 5.8e+100)
		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) <= -4.2e+164)
		tmp = c * i;
	elseif ((c * i) <= 5.8e+100)
		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], -4.2e+164], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.8e+100], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4.1999999999999998e164 or 5.8000000000000001e100 < (*.f64 c i)

   1. Initial program 91.3%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

   if -4.1999999999999998e164 < (*.f64 c i) < 5.8000000000000001e100

   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 a around inf

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

      1. *-lowering-*.f64 38.8

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

   5. Simplified 38.8%

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

Alternative 10: 27.4% 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 96.1%

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

3. Taylor expanded in a around inf

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

   1. *-lowering-*.f64 30.0

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

5. Simplified 30.0%

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

Reproduce

herbie shell --seed 2024199 
(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)))