SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 6

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \left(z - x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))

C

double code(double x, double y, double z) {
	return x + (y * (z - x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (z - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (z - x));
}

Python

def code(x, y, z):
	return x + (y * (z - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (z - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z - x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))

C

double code(double x, double y, double z) {
	return x + (y * (z - x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (z - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (z - x));
}

Python

def code(x, y, z):
	return x + (y * (z - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (z - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z - x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))

C

double code(double x, double y, double z) {
	return x + (y * (z - x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (z - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (z - x));
}

Python

def code(x, y, z):
	return x + (y * (z - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (z - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]

2. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(z - x\right) \]

Alternative 2: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 14000000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+78} \lor \neg \left(y \leq 2.15 \cdot 10^{+251}\right) \land y \leq 1.12 \cdot 10^{+292}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -2.3e+81)
     t_0
     (if (<= y 14000000000000.0)
       (+ x (* y z))
       (if (or (<= y 1.8e+78) (and (not (<= y 2.15e+251)) (<= y 1.12e+292)))
         t_0
         (* y z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -2.3e+81) {
		tmp = t_0;
	} else if (y <= 14000000000000.0) {
		tmp = x + (y * z);
	} else if ((y <= 1.8e+78) || (!(y <= 2.15e+251) && (y <= 1.12e+292))) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (y <= (-2.3d+81)) then
        tmp = t_0
    else if (y <= 14000000000000.0d0) then
        tmp = x + (y * z)
    else if ((y <= 1.8d+78) .or. (.not. (y <= 2.15d+251)) .and. (y <= 1.12d+292)) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -2.3e+81) {
		tmp = t_0;
	} else if (y <= 14000000000000.0) {
		tmp = x + (y * z);
	} else if ((y <= 1.8e+78) || (!(y <= 2.15e+251) && (y <= 1.12e+292))) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -2.3e+81:
		tmp = t_0
	elif y <= 14000000000000.0:
		tmp = x + (y * z)
	elif (y <= 1.8e+78) or (not (y <= 2.15e+251) and (y <= 1.12e+292)):
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -2.3e+81)
		tmp = t_0;
	elseif (y <= 14000000000000.0)
		tmp = Float64(x + Float64(y * z));
	elseif ((y <= 1.8e+78) || (!(y <= 2.15e+251) && (y <= 1.12e+292)))
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -2.3e+81)
		tmp = t_0;
	elseif (y <= 14000000000000.0)
		tmp = x + (y * z);
	elseif ((y <= 1.8e+78) || (~((y <= 2.15e+251)) && (y <= 1.12e+292)))
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -2.3e+81], t$95$0, If[LessEqual[y, 14000000000000.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.8e+78], And[N[Not[LessEqual[y, 2.15e+251]], $MachinePrecision], LessEqual[y, 1.12e+292]]], t$95$0, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999999e81 or 1.4e13 < y < 1.8000000000000001e78 or 2.15e251 < y < 1.12000000000000004e292

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around 0 72.2%

      \[\leadsto x + \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 72.2%

         \[\leadsto x + \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 72.2%

         \[\leadsto x + \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 72.2%

         \[\leadsto x + \color{blue}{y \cdot \left(-x\right)} \]

   4. Simplified 72.2%

      \[\leadsto x + \color{blue}{y \cdot \left(-x\right)} \]

   5. Taylor expanded in y around inf 72.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-out 72.0%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -2.2999999999999999e81 < y < 1.4e13

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 93.9%

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

   if 1.8000000000000001e78 < y < 2.15e251 or 1.12000000000000004e292 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 67.0%

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

   3. Taylor expanded in x around 0 67.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 14000000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+78} \lor \neg \left(y \leq 2.15 \cdot 10^{+251}\right) \land y \leq 1.12 \cdot 10^{+292}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+250}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 10^{+292}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -3.9e+63)
     t_0
     (if (<= y -1.4e-6)
       (* y z)
       (if (<= y 1.9e-26)
         x
         (if (<= y 1.26e+250) (* y z) (if (<= y 1e+292) t_0 (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3.9e+63) {
		tmp = t_0;
	} else if (y <= -1.4e-6) {
		tmp = y * z;
	} else if (y <= 1.9e-26) {
		tmp = x;
	} else if (y <= 1.26e+250) {
		tmp = y * z;
	} else if (y <= 1e+292) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (y <= (-3.9d+63)) then
        tmp = t_0
    else if (y <= (-1.4d-6)) then
        tmp = y * z
    else if (y <= 1.9d-26) then
        tmp = x
    else if (y <= 1.26d+250) then
        tmp = y * z
    else if (y <= 1d+292) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3.9e+63) {
		tmp = t_0;
	} else if (y <= -1.4e-6) {
		tmp = y * z;
	} else if (y <= 1.9e-26) {
		tmp = x;
	} else if (y <= 1.26e+250) {
		tmp = y * z;
	} else if (y <= 1e+292) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -3.9e+63:
		tmp = t_0
	elif y <= -1.4e-6:
		tmp = y * z
	elif y <= 1.9e-26:
		tmp = x
	elif y <= 1.26e+250:
		tmp = y * z
	elif y <= 1e+292:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -3.9e+63)
		tmp = t_0;
	elseif (y <= -1.4e-6)
		tmp = Float64(y * z);
	elseif (y <= 1.9e-26)
		tmp = x;
	elseif (y <= 1.26e+250)
		tmp = Float64(y * z);
	elseif (y <= 1e+292)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -3.9e+63)
		tmp = t_0;
	elseif (y <= -1.4e-6)
		tmp = y * z;
	elseif (y <= 1.9e-26)
		tmp = x;
	elseif (y <= 1.26e+250)
		tmp = y * z;
	elseif (y <= 1e+292)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -3.9e+63], t$95$0, If[LessEqual[y, -1.4e-6], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.9e-26], x, If[LessEqual[y, 1.26e+250], N[(y * z), $MachinePrecision], If[LessEqual[y, 1e+292], t$95$0, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e63 or 1.26000000000000006e250 < y < 1e292

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around 0 67.9%

      \[\leadsto x + \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 67.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 67.9%

         \[\leadsto x + \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 67.9%

         \[\leadsto x + \color{blue}{y \cdot \left(-x\right)} \]

   4. Simplified 67.9%

      \[\leadsto x + \color{blue}{y \cdot \left(-x\right)} \]

   5. Taylor expanded in y around inf 67.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 67.9%

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

      2. *-commutative 67.9%

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

      3. distribute-rgt-neg-out 67.9%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   7. Simplified 67.9%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -3.9e63 < y < -1.39999999999999994e-6 or 1.90000000000000007e-26 < y < 1.26000000000000006e250 or 1e292 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 62.1%

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

   3. Taylor expanded in x around 0 59.6%

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

   if -1.39999999999999994e-6 < y < 1.90000000000000007e-26

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 99.5%

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

   3. Taylor expanded in x around inf 74.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+250}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 10^{+292}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-12} \lor \neg \left(z \leq 9 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-12) (not (<= z 9e-34))) (+ x (* y z)) (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-12) || !(z <= 9e-34)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d-12)) .or. (.not. (z <= 9d-34))) then
        tmp = x + (y * z)
    else
        tmp = x - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-12) || !(z <= 9e-34)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-12) or not (z <= 9e-34):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-12) || !(z <= 9e-34))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-12) || ~((z <= 9e-34)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-12], N[Not[LessEqual[z, 9e-34]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999981e-12 or 9.00000000000000085e-34 < z

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 91.0%

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

   if -4.49999999999999981e-12 < z < 9.00000000000000085e-34

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around 0 89.4%

      \[\leadsto x + \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 89.4%

         \[\leadsto x + \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 89.4%

         \[\leadsto x + \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 89.4%

         \[\leadsto x + \color{blue}{y \cdot \left(-x\right)} \]

   4. Simplified 89.4%

      \[\leadsto x + \color{blue}{y \cdot \left(-x\right)} \]

   5. Taylor expanded in x around 0 89.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot y\right)} \]
   6. Step-by-step derivation

      1. +-commutative 89.4%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot y + 1\right)} \]

      2. mul-1-neg 89.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right)} + 1\right) \]

      3. +-commutative 89.4%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right)\right)} \]

      4. distribute-rgt-in 89.4%

         \[\leadsto \color{blue}{1 \cdot x + \left(-y\right) \cdot x} \]

      5. *-lft-identity 89.4%

         \[\leadsto \color{blue}{x} + \left(-y\right) \cdot x \]

      6. cancel-sign-sub-inv 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-12} \lor \neg \left(z \leq 9 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 5: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-6) (* y z) (if (<= y 2.8e-27) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-6) {
		tmp = y * z;
	} else if (y <= 2.8e-27) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.4d-6)) then
        tmp = y * z
    else if (y <= 2.8d-27) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-6) {
		tmp = y * z;
	} else if (y <= 2.8e-27) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-6:
		tmp = y * z
	elif y <= 2.8e-27:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-6)
		tmp = Float64(y * z);
	elseif (y <= 2.8e-27)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e-6)
		tmp = y * z;
	elseif (y <= 2.8e-27)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-6], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.8e-27], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999994e-6 or 2.8e-27 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 54.4%

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

   3. Taylor expanded in x around 0 52.7%

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

   if -1.39999999999999994e-6 < y < 2.8e-27

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 99.5%

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

   3. Taylor expanded in x around inf 74.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 36.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]

2. Taylor expanded in z around inf 75.3%

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

3. Taylor expanded in x around inf 37.1%

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

4. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))