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

Percentage Accurate: 95.7% → 97.9%

Time: 11.8s

Alternatives: 13

Speedup: 0.4×

• 42.2% 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: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-def 98.0%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-def 97.3%

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

   5. fma-def 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 3: 96.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-def 97.3%

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

   5. fma-def 97.7%

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

3. Simplified 97.7%

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

   1. fma-udef 97.2%

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

   2. fma-def 96.9%

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

   3. associate-+r+ 96.9%

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

6. Applied egg-rr 96.9%

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

7. Final simplification 96.9%

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

Alternative 4: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* x y) (* c i))))
   (if (<= (* a b) -5.2e+153)
     (* a b)
     (if (<= (* a b) -1.4e-89)
       t_1
       (if (<= (* a b) 2.8e-134)
         t_2
         (if (<= (* a b) 7e-61)
           t_1
           (if (<= (* a b) 7.2e+133) t_2 (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -5.2e+153) {
		tmp = a * b;
	} else if ((a * b) <= -1.4e-89) {
		tmp = t_1;
	} else if ((a * b) <= 2.8e-134) {
		tmp = t_2;
	} else if ((a * b) <= 7e-61) {
		tmp = t_1;
	} else if ((a * b) <= 7.2e+133) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (x * y) + (c * i)
    if ((a * b) <= (-5.2d+153)) then
        tmp = a * b
    else if ((a * b) <= (-1.4d-89)) then
        tmp = t_1
    else if ((a * b) <= 2.8d-134) then
        tmp = t_2
    else if ((a * b) <= 7d-61) then
        tmp = t_1
    else if ((a * b) <= 7.2d+133) then
        tmp = t_2
    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 t_1 = (c * i) + (z * t);
	double t_2 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -5.2e+153) {
		tmp = a * b;
	} else if ((a * b) <= -1.4e-89) {
		tmp = t_1;
	} else if ((a * b) <= 2.8e-134) {
		tmp = t_2;
	} else if ((a * b) <= 7e-61) {
		tmp = t_1;
	} else if ((a * b) <= 7.2e+133) {
		tmp = t_2;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (c * i)
	tmp = 0
	if (a * b) <= -5.2e+153:
		tmp = a * b
	elif (a * b) <= -1.4e-89:
		tmp = t_1
	elif (a * b) <= 2.8e-134:
		tmp = t_2
	elif (a * b) <= 7e-61:
		tmp = t_1
	elif (a * b) <= 7.2e+133:
		tmp = t_2
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -5.2e+153)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.4e-89)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.8e-134)
		tmp = t_2;
	elseif (Float64(a * b) <= 7e-61)
		tmp = t_1;
	elseif (Float64(a * b) <= 7.2e+133)
		tmp = t_2;
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (x * y) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -5.2e+153)
		tmp = a * b;
	elseif ((a * b) <= -1.4e-89)
		tmp = t_1;
	elseif ((a * b) <= 2.8e-134)
		tmp = t_2;
	elseif ((a * b) <= 7e-61)
		tmp = t_1;
	elseif ((a * b) <= 7.2e+133)
		tmp = t_2;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5.2e+153], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.4e-89], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.8e-134], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 7e-61], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 7.2e+133], t$95$2, N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.1999999999999998e153 or 7.19999999999999956e133 < (*.f64 a b)

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf 81.2%

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

   if -5.1999999999999998e153 < (*.f64 a b) < -1.3999999999999999e-89 or 2.7999999999999999e-134 < (*.f64 a b) < 7.0000000000000006e-61

   1. Initial program 94.2%

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

   3. Taylor expanded in a around 0 83.0%

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

   4. Taylor expanded in x around 0 64.8%

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

   if -1.3999999999999999e-89 < (*.f64 a b) < 2.7999999999999999e-134 or 7.0000000000000006e-61 < (*.f64 a b) < 7.19999999999999956e133

   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 0 76.6%

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

      1. fma-def 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in a around 0 71.3%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{-89}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{-134}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{-61}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7 \cdot 10^{-80}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2.9 \cdot 10^{-274}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{-225}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.4 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.75e+108)
   (* c i)
   (if (<= (* c i) -7e-80)
     (* z t)
     (if (<= (* c i) -2.9e-274)
       (* a b)
       (if (<= (* c i) 4.8e-225)
         (* z t)
         (if (<= (* c i) 5.4e+103) (* 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) <= -1.75e+108) {
		tmp = c * i;
	} else if ((c * i) <= -7e-80) {
		tmp = z * t;
	} else if ((c * i) <= -2.9e-274) {
		tmp = a * b;
	} else if ((c * i) <= 4.8e-225) {
		tmp = z * t;
	} else if ((c * i) <= 5.4e+103) {
		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) <= (-1.75d+108)) then
        tmp = c * i
    else if ((c * i) <= (-7d-80)) then
        tmp = z * t
    else if ((c * i) <= (-2.9d-274)) then
        tmp = a * b
    else if ((c * i) <= 4.8d-225) then
        tmp = z * t
    else if ((c * i) <= 5.4d+103) 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) <= -1.75e+108) {
		tmp = c * i;
	} else if ((c * i) <= -7e-80) {
		tmp = z * t;
	} else if ((c * i) <= -2.9e-274) {
		tmp = a * b;
	} else if ((c * i) <= 4.8e-225) {
		tmp = z * t;
	} else if ((c * i) <= 5.4e+103) {
		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) <= -1.75e+108:
		tmp = c * i
	elif (c * i) <= -7e-80:
		tmp = z * t
	elif (c * i) <= -2.9e-274:
		tmp = a * b
	elif (c * i) <= 4.8e-225:
		tmp = z * t
	elif (c * i) <= 5.4e+103:
		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) <= -1.75e+108)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -7e-80)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -2.9e-274)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.8e-225)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 5.4e+103)
		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) <= -1.75e+108)
		tmp = c * i;
	elseif ((c * i) <= -7e-80)
		tmp = z * t;
	elseif ((c * i) <= -2.9e-274)
		tmp = a * b;
	elseif ((c * i) <= 4.8e-225)
		tmp = z * t;
	elseif ((c * i) <= 5.4e+103)
		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], -1.75e+108], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -7e-80], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.9e-274], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.8e-225], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.4e+103], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.7500000000000001e108 or 5.39999999999999985e103 < (*.f64 c i)

   1. Initial program 89.0%

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

   3. Taylor expanded in c around inf 66.6%

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

   if -1.7500000000000001e108 < (*.f64 c i) < -7.00000000000000029e-80 or -2.89999999999999976e-274 < (*.f64 c i) < 4.79999999999999992e-225

   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 z around inf 46.9%

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

   if -7.00000000000000029e-80 < (*.f64 c i) < -2.89999999999999976e-274 or 4.79999999999999992e-225 < (*.f64 c i) < 5.39999999999999985e103

   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 a around inf 48.6%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7 \cdot 10^{-80}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2.9 \cdot 10^{-274}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{-225}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.4 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.95 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 6.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* a b) -5e+153)
     (* a b)
     (if (<= (* a b) -1.95e-87)
       t_1
       (if (<= (* a b) 6.5e-116)
         (+ (* x y) (* c i))
         (if (<= (* a b) 1.35e+133) t_1 (* 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);
	double tmp;
	if ((a * b) <= -5e+153) {
		tmp = a * b;
	} else if ((a * b) <= -1.95e-87) {
		tmp = t_1;
	} else if ((a * b) <= 6.5e-116) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 1.35e+133) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a * b) <= (-5d+153)) then
        tmp = a * b
    else if ((a * b) <= (-1.95d-87)) then
        tmp = t_1
    else if ((a * b) <= 6.5d-116) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 1.35d+133) then
        tmp = t_1
    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 t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -5e+153) {
		tmp = a * b;
	} else if ((a * b) <= -1.95e-87) {
		tmp = t_1;
	} else if ((a * b) <= 6.5e-116) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 1.35e+133) {
		tmp = t_1;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -5e+153:
		tmp = a * b
	elif (a * b) <= -1.95e-87:
		tmp = t_1
	elif (a * b) <= 6.5e-116:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 1.35e+133:
		tmp = t_1
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+153)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.95e-87)
		tmp = t_1;
	elseif (Float64(a * b) <= 6.5e-116)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 1.35e+133)
		tmp = t_1;
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+153)
		tmp = a * b;
	elseif ((a * b) <= -1.95e-87)
		tmp = t_1;
	elseif ((a * b) <= 6.5e-116)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 1.35e+133)
		tmp = t_1;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+153], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.95e-87], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 6.5e-116], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.35e+133], t$95$1, N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000018e153 or 1.3500000000000001e133 < (*.f64 a b)

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf 81.2%

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

   if -5.00000000000000018e153 < (*.f64 a b) < -1.9499999999999999e-87 or 6.5000000000000001e-116 < (*.f64 a b) < 1.3500000000000001e133

   1. Initial program 94.3%

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

   3. Taylor expanded in a around 0 81.3%

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

   4. Taylor expanded in c around 0 64.6%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if -1.9499999999999999e-87 < (*.f64 a b) < 6.5000000000000001e-116

   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 78.6%

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

      1. fma-def 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in a around 0 78.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.95 \cdot 10^{-87}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + \left(a \cdot b + t\_1\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) (+ (* a b) t_1))))
   (if (<= t_2 INFINITY) t_2 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) + (z * t);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (c * i) + ((a * b) + t_1)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(Float64(a * b) + t_1))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	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) + (z * t);
	t_2 = (c * i) + ((a * b) + t_1);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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 a around 0 23.1%

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

   4. Taylor expanded in c around 0 46.6%

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

4. Final simplification 97.3%

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

Alternative 8: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+17} \lor \neg \left(c \cdot i \leq 1.12 \cdot 10^{+104}\right):\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* c i) -2e+17) (not (<= (* c i) 1.12e+104)))
     (+ (* c i) t_1)
     (+ (* 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 = (x * y) + (z * t);
	double tmp;
	if (((c * i) <= -2e+17) || !((c * i) <= 1.12e+104)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + 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) + (z * t)
    if (((c * i) <= (-2d+17)) .or. (.not. ((c * i) <= 1.12d+104))) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + 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) + (z * t);
	double tmp;
	if (((c * i) <= -2e+17) || !((c * i) <= 1.12e+104)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((c * i) <= -2e+17) or not ((c * i) <= 1.12e+104):
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((Float64(c * i) <= -2e+17) || !(Float64(c * i) <= 1.12e+104))
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((c * i) <= -2e+17) || ~(((c * i) <= 1.12e+104)))
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + 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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(c * i), $MachinePrecision], -2e+17], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.12e+104]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2e17 or 1.12000000000000003e104 < (*.f64 c i)

   1. Initial program 89.7%

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

   3. Taylor expanded in a around 0 82.8%

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

   if -2e17 < (*.f64 c i) < 1.12000000000000003e104

   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 c around 0 93.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+17} \lor \neg \left(c \cdot i \leq 1.12 \cdot 10^{+104}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+203}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.45 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6.5e+203)
   (+ (* c i) (* z t))
   (if (<= (* c i) 1.45e+110)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* x y) (* 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) <= -6.5e+203) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1.45e+110) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (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) <= (-6.5d+203)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 1.45d+110) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (x * y) + (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) <= -6.5e+203) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1.45e+110) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -6.5e+203:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 1.45e+110:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -6.5e+203)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 1.45e+110)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + 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) <= -6.5e+203)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 1.45e+110)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -6.5e+203], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.45e+110], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.5000000000000003e203

   1. Initial program 86.7%

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

   3. Taylor expanded in a around 0 83.5%

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

   4. Taylor expanded in x around 0 76.9%

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

   if -6.5000000000000003e203 < (*.f64 c i) < 1.45e110

   1. Initial program 97.9%

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

   3. Taylor expanded in c around 0 89.7%

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

   if 1.45e110 < (*.f64 c i)

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 86.7%

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

      1. fma-def 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in a around 0 84.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+203}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.45 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.6 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.52 \cdot 10^{-89}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5.6e+153)
   (* a b)
   (if (<= (* a b) -1.52e-89)
     (* z t)
     (if (<= (* a b) 6.8e+105) (* 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) <= -5.6e+153) {
		tmp = a * b;
	} else if ((a * b) <= -1.52e-89) {
		tmp = z * t;
	} else if ((a * b) <= 6.8e+105) {
		tmp = x * y;
	} 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) <= (-5.6d+153)) then
        tmp = a * b
    else if ((a * b) <= (-1.52d-89)) then
        tmp = z * t
    else if ((a * b) <= 6.8d+105) then
        tmp = x * y
    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) <= -5.6e+153) {
		tmp = a * b;
	} else if ((a * b) <= -1.52e-89) {
		tmp = z * t;
	} else if ((a * b) <= 6.8e+105) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5.6e+153:
		tmp = a * b
	elif (a * b) <= -1.52e-89:
		tmp = z * t
	elif (a * b) <= 6.8e+105:
		tmp = 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) <= -5.6e+153)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.52e-89)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 6.8e+105)
		tmp = Float64(x * y);
	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) <= -5.6e+153)
		tmp = a * b;
	elseif ((a * b) <= -1.52e-89)
		tmp = z * t;
	elseif ((a * b) <= 6.8e+105)
		tmp = x * y;
	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], -5.6e+153], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.52e-89], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.8e+105], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.5999999999999997e153 or 6.7999999999999999e105 < (*.f64 a b)

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf 76.2%

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

   if -5.5999999999999997e153 < (*.f64 a b) < -1.52e-89

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf 43.2%

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

   if -1.52e-89 < (*.f64 a b) < 6.7999999999999999e105

   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 x around inf 43.6%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.6 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.52 \cdot 10^{-89}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+124} \lor \neg \left(x \cdot y \leq 3.4 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+124) (not (<= (* x y) 3.4e+138)))
   (* x y)
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+124) || !((x * y) <= 3.4e+138)) {
		tmp = x * y;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2d+124)) .or. (.not. ((x * y) <= 3.4d+138))) then
        tmp = x * y
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+124) || !((x * y) <= 3.4e+138)) {
		tmp = x * y;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+124) or not ((x * y) <= 3.4e+138):
		tmp = x * y
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+124) || !(Float64(x * y) <= 3.4e+138))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+124) || ~(((x * y) <= 3.4e+138)))
		tmp = x * y;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+124], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.4e+138]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e124 or 3.40000000000000011e138 < (*.f64 x y)

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 71.6%

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

   if -1.9999999999999999e124 < (*.f64 x y) < 3.40000000000000011e138

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0 66.4%

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

   4. Taylor expanded in x around 0 59.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+124} \lor \neg \left(x \cdot y \leq 3.4 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+17} \lor \neg \left(c \cdot i \leq 2.4 \cdot 10^{+103}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2e+17) (not (<= (* c i) 2.4e+103))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2e+17) || !((c * i) <= 2.4e+103)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-2d+17)) .or. (.not. ((c * i) <= 2.4d+103))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2e+17) || !((c * i) <= 2.4e+103)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2e+17) or not ((c * i) <= 2.4e+103):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2e+17) || !(Float64(c * i) <= 2.4e+103))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -2e+17) || ~(((c * i) <= 2.4e+103)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2e+17], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.4e+103]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2e17 or 2.3999999999999998e103 < (*.f64 c i)

   1. Initial program 89.7%

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

   3. Taylor expanded in c around inf 60.4%

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

   if -2e17 < (*.f64 c i) < 2.3999999999999998e103

   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 38.4%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+17} \lor \neg \left(c \cdot i \leq 2.4 \cdot 10^{+103}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 94.9%

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

3. Taylor expanded in a around inf 30.4%

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

4. Final simplification 30.4%

   \[\leadsto a \cdot b \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024029 
(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)))