SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 6

Speedup: 1.0×

• 20.9% 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: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+188}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -6.5e+189)
     t_0
     (if (<= y -1.6e+122)
       (* y z)
       (if (<= y -1.95e+68)
         t_0
         (if (<= y -2.8e-18)
           (* y z)
           (if (<= y 1.35e-16) x (if (<= y 9.8e+188) (* y z) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -6.5e+189) {
		tmp = t_0;
	} else if (y <= -1.6e+122) {
		tmp = y * z;
	} else if (y <= -1.95e+68) {
		tmp = t_0;
	} else if (y <= -2.8e-18) {
		tmp = y * z;
	} else if (y <= 1.35e-16) {
		tmp = x;
	} else if (y <= 9.8e+188) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	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 <= (-6.5d+189)) then
        tmp = t_0
    else if (y <= (-1.6d+122)) then
        tmp = y * z
    else if (y <= (-1.95d+68)) then
        tmp = t_0
    else if (y <= (-2.8d-18)) then
        tmp = y * z
    else if (y <= 1.35d-16) then
        tmp = x
    else if (y <= 9.8d+188) then
        tmp = y * z
    else
        tmp = t_0
    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 <= -6.5e+189) {
		tmp = t_0;
	} else if (y <= -1.6e+122) {
		tmp = y * z;
	} else if (y <= -1.95e+68) {
		tmp = t_0;
	} else if (y <= -2.8e-18) {
		tmp = y * z;
	} else if (y <= 1.35e-16) {
		tmp = x;
	} else if (y <= 9.8e+188) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -6.5e+189:
		tmp = t_0
	elif y <= -1.6e+122:
		tmp = y * z
	elif y <= -1.95e+68:
		tmp = t_0
	elif y <= -2.8e-18:
		tmp = y * z
	elif y <= 1.35e-16:
		tmp = x
	elif y <= 9.8e+188:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -6.5e+189)
		tmp = t_0;
	elseif (y <= -1.6e+122)
		tmp = Float64(y * z);
	elseif (y <= -1.95e+68)
		tmp = t_0;
	elseif (y <= -2.8e-18)
		tmp = Float64(y * z);
	elseif (y <= 1.35e-16)
		tmp = x;
	elseif (y <= 9.8e+188)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -6.5e+189)
		tmp = t_0;
	elseif (y <= -1.6e+122)
		tmp = y * z;
	elseif (y <= -1.95e+68)
		tmp = t_0;
	elseif (y <= -2.8e-18)
		tmp = y * z;
	elseif (y <= 1.35e-16)
		tmp = x;
	elseif (y <= 9.8e+188)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -6.5e+189], t$95$0, If[LessEqual[y, -1.6e+122], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.95e+68], t$95$0, If[LessEqual[y, -2.8e-18], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.35e-16], x, If[LessEqual[y, 9.8e+188], N[(y * z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000027e189 or -1.60000000000000006e122 < y < -1.95000000000000009e68 or 9.8e188 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. distribute-lft-neg-out 66.1%

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

      3. *-commutative 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in y around inf 66.1%

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

      1. associate-*r* 66.1%

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

      2. mul-1-neg 66.1%

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

   7. Simplified 66.1%

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

   if -6.50000000000000027e189 < y < -1.60000000000000006e122 or -1.95000000000000009e68 < y < -2.80000000000000012e-18 or 1.35e-16 < y < 9.8e188

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 72.5%

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

   3. Taylor expanded in x around 0 71.0%

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

   if -2.80000000000000012e-18 < y < 1.35e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in x around inf 77.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+189}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+188}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+189} \lor \neg \left(y \leq -5.6 \cdot 10^{+122}\right) \land \left(y \leq -1.9 \cdot 10^{+70} \lor \neg \left(y \leq 5.5 \cdot 10^{+182}\right)\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.5e+189)
         (and (not (<= y -5.6e+122))
              (or (<= y -1.9e+70) (not (<= y 5.5e+182)))))
   (* y (- x))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5e+189) || (!(y <= -5.6e+122) && ((y <= -1.9e+70) || !(y <= 5.5e+182)))) {
		tmp = y * -x;
	} else {
		tmp = x + (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 <= (-8.5d+189)) .or. (.not. (y <= (-5.6d+122))) .and. (y <= (-1.9d+70)) .or. (.not. (y <= 5.5d+182))) then
        tmp = y * -x
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5e+189) || (!(y <= -5.6e+122) && ((y <= -1.9e+70) || !(y <= 5.5e+182)))) {
		tmp = y * -x;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.5e+189) or (not (y <= -5.6e+122) and ((y <= -1.9e+70) or not (y <= 5.5e+182))):
		tmp = y * -x
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.5e+189) || (!(y <= -5.6e+122) && ((y <= -1.9e+70) || !(y <= 5.5e+182))))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.5e+189) || (~((y <= -5.6e+122)) && ((y <= -1.9e+70) || ~((y <= 5.5e+182)))))
		tmp = y * -x;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.5e+189], And[N[Not[LessEqual[y, -5.6e+122]], $MachinePrecision], Or[LessEqual[y, -1.9e+70], N[Not[LessEqual[y, 5.5e+182]], $MachinePrecision]]]], N[(y * (-x)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999998e189 or -5.5999999999999999e122 < y < -1.8999999999999999e70 or 5.49999999999999977e182 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. distribute-lft-neg-out 65.7%

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

      3. *-commutative 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in y around inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. mul-1-neg 65.7%

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

   7. Simplified 65.7%

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

   if -8.4999999999999998e189 < y < -5.5999999999999999e122 or -1.8999999999999999e70 < y < 5.49999999999999977e182

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 89.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+189} \lor \neg \left(y \leq -5.6 \cdot 10^{+122}\right) \land \left(y \leq -1.9 \cdot 10^{+70} \lor \neg \left(y \leq 5.5 \cdot 10^{+182}\right)\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-84} \lor \neg \left(z \leq 6.5 \cdot 10^{-20}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95e-84) (not (<= z 6.5e-20))) (+ x (* y z)) (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-84) || !(z <= 6.5e-20)) {
		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 <= (-1.95d-84)) .or. (.not. (z <= 6.5d-20))) 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 <= -1.95e-84) || !(z <= 6.5e-20)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95e-84) or not (z <= 6.5e-20):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95e-84) || !(z <= 6.5e-20))
		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 <= -1.95e-84) || ~((z <= 6.5e-20)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95e-84], N[Not[LessEqual[z, 6.5e-20]], $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 < -1.95000000000000011e-84 or 6.50000000000000032e-20 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 93.3%

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

   if -1.95000000000000011e-84 < z < 6.50000000000000032e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-lft-neg-out 90.2%

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

      3. *-commutative 90.2%

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

   4. Simplified 90.2%

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

      1. *-commutative 90.2%

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

      2. distribute-lft-neg-out 90.2%

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

      3. unsub-neg 90.2%

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

   6. Applied egg-rr 90.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-84} \lor \neg \left(z \leq 6.5 \cdot 10^{-20}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 5: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-17} \lor \neg \left(y \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e-17) (not (<= y 5e-20))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-17) || !(y <= 5e-20)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	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 <= (-1.5d-17)) .or. (.not. (y <= 5d-20))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-17) || !(y <= 5e-20)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e-17) or not (y <= 5e-20):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e-17) || !(y <= 5e-20))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5e-17) || ~((y <= 5e-20)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e-17], N[Not[LessEqual[y, 5e-20]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000003e-17 or 4.9999999999999999e-20 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 56.2%

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

   3. Taylor expanded in x around 0 55.2%

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

   if -1.50000000000000003e-17 < y < 4.9999999999999999e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in x around inf 77.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-17} \lor \neg \left(y \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 75.4%

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

3. Taylor expanded in x around inf 36.0%

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

4. Final simplification 36.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023306 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))