SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

Alternatives: 6

Speedup: 1.0×

• 21.0% 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: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+263}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+166}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+144} \lor \neg \left(y \leq 4.2 \cdot 10^{+176}\right) \land y \leq 3 \cdot 10^{+269}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -2.8e+263)
     (* y z)
     (if (<= y -4.3e+198)
       t_0
       (if (<= y -2.3e+166)
         (* y z)
         (if (<= y -1.0)
           t_0
           (if (<= y 2.4e-124)
             x
             (if (or (<= y 7e+144) (and (not (<= y 4.2e+176)) (<= y 3e+269)))
               (* y z)
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -2.8e+263) {
		tmp = y * z;
	} else if (y <= -4.3e+198) {
		tmp = t_0;
	} else if (y <= -2.3e+166) {
		tmp = y * z;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.4e-124) {
		tmp = x;
	} else if ((y <= 7e+144) || (!(y <= 4.2e+176) && (y <= 3e+269))) {
		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 <= (-2.8d+263)) then
        tmp = y * z
    else if (y <= (-4.3d+198)) then
        tmp = t_0
    else if (y <= (-2.3d+166)) then
        tmp = y * z
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 2.4d-124) then
        tmp = x
    else if ((y <= 7d+144) .or. (.not. (y <= 4.2d+176)) .and. (y <= 3d+269)) 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 <= -2.8e+263) {
		tmp = y * z;
	} else if (y <= -4.3e+198) {
		tmp = t_0;
	} else if (y <= -2.3e+166) {
		tmp = y * z;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.4e-124) {
		tmp = x;
	} else if ((y <= 7e+144) || (!(y <= 4.2e+176) && (y <= 3e+269))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -2.8e+263:
		tmp = y * z
	elif y <= -4.3e+198:
		tmp = t_0
	elif y <= -2.3e+166:
		tmp = y * z
	elif y <= -1.0:
		tmp = t_0
	elif y <= 2.4e-124:
		tmp = x
	elif (y <= 7e+144) or (not (y <= 4.2e+176) and (y <= 3e+269)):
		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 <= -2.8e+263)
		tmp = Float64(y * z);
	elseif (y <= -4.3e+198)
		tmp = t_0;
	elseif (y <= -2.3e+166)
		tmp = Float64(y * z);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.4e-124)
		tmp = x;
	elseif ((y <= 7e+144) || (!(y <= 4.2e+176) && (y <= 3e+269)))
		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 <= -2.8e+263)
		tmp = y * z;
	elseif (y <= -4.3e+198)
		tmp = t_0;
	elseif (y <= -2.3e+166)
		tmp = y * z;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.4e-124)
		tmp = x;
	elseif ((y <= 7e+144) || (~((y <= 4.2e+176)) && (y <= 3e+269)))
		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, -2.8e+263], N[(y * z), $MachinePrecision], If[LessEqual[y, -4.3e+198], t$95$0, If[LessEqual[y, -2.3e+166], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 2.4e-124], x, If[Or[LessEqual[y, 7e+144], And[N[Not[LessEqual[y, 4.2e+176]], $MachinePrecision], LessEqual[y, 3e+269]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e263 or -4.29999999999999982e198 < y < -2.30000000000000008e166 or 2.39999999999999992e-124 < y < 6.9999999999999996e144 or 4.1999999999999998e176 < y < 3.0000000000000001e269

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 84.1%

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

   3. Taylor expanded in x around 0 77.5%

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

   if -2.7999999999999998e263 < y < -4.29999999999999982e198 or -2.30000000000000008e166 < y < -1 or 6.9999999999999996e144 < y < 4.1999999999999998e176 or 3.0000000000000001e269 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 67.0%

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

      1. mul-1-neg 67.0%

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

      2. distribute-lft-neg-out 67.0%

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

      3. *-commutative 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in y around inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. mul-1-neg 66.9%

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

   7. Simplified 66.9%

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

   if -1 < y < 2.39999999999999992e-124

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.3%

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

   3. Taylor expanded in x around inf 80.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+263}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+166}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+144} \lor \neg \left(y \leq 4.2 \cdot 10^{+176}\right) \land y \leq 3 \cdot 10^{+269}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-26} \lor \neg \left(z \leq 9500000000\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e-26) (not (<= z 9500000000.0)))
   (+ x (* y z))
   (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-26) || !(z <= 9500000000.0)) {
		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 <= (-4.6d-26)) .or. (.not. (z <= 9500000000.0d0))) 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 <= -4.6e-26) || !(z <= 9500000000.0)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e-26) or not (z <= 9500000000.0):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.6e-26) || !(z <= 9500000000.0))
		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 <= -4.6e-26) || ~((z <= 9500000000.0)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e-26], N[Not[LessEqual[z, 9500000000.0]], $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 < -4.60000000000000018e-26 or 9.5e9 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 91.9%

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

   if -4.60000000000000018e-26 < z < 9.5e9

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. distribute-lft-neg-out 91.4%

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

      3. *-commutative 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in x around 0 91.4%

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

      1. neg-mul-1 91.4%

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

      2. distribute-rgt-in 91.4%

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

      3. *-lft-identity 91.4%

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

      4. cancel-sign-sub-inv 91.4%

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

   7. Simplified 91.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-26} \lor \neg \left(z \leq 9500000000\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 4: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e-16) (* y z) (if (<= y 2.3e-124) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e-16) {
		tmp = y * z;
	} else if (y <= 2.3e-124) {
		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 <= (-1.65d-16)) then
        tmp = y * z
    else if (y <= 2.3d-124) 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 <= -1.65e-16) {
		tmp = y * z;
	} else if (y <= 2.3e-124) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e-16:
		tmp = y * z
	elif y <= 2.3e-124:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e-16)
		tmp = Float64(y * z);
	elseif (y <= 2.3e-124)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e-16)
		tmp = y * z;
	elseif (y <= 2.3e-124)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e-16], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.3e-124], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999994e-16 or 2.30000000000000012e-124 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 62.3%

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

   3. Taylor expanded in x around 0 58.4%

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

   if -1.64999999999999994e-16 < y < 2.30000000000000012e-124

   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 81.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+116) (* y (- x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+116) {
		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 (x <= (-1d+116)) 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 (x <= -1e+116) {
		tmp = y * -x;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+116:
		tmp = y * -x
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+116)
		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 (x <= -1e+116)
		tmp = y * -x;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+116], N[(y * (-x)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000002e116

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-lft-neg-out 97.8%

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

      3. *-commutative 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in y around inf 63.1%

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

      1. associate-*r* 63.1%

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

      2. mul-1-neg 63.1%

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

   7. Simplified 63.1%

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

   if -1.00000000000000002e116 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 36.3% 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 75.7%

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

3. Taylor expanded in x around inf 33.1%

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

4. Final simplification 33.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023285 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))