SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 6

Speedup: 1.0×

• 21.1% 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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(z - x\right) \]
4. Add Preprocessing

Alternative 2: 59.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+158}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -220000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -0.0066:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+15} \lor \neg \left(y \leq 2.85 \cdot 10^{+116}\right) \land y \leq 9 \cdot 10^{+167}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.9e+158)
     (* y z)
     (if (<= y -220000000000.0)
       t_0
       (if (<= y -0.0066)
         (* y z)
         (if (<= y 1.16e-125)
           x
           (if (or (<= y 7e+15) (and (not (<= y 2.85e+116)) (<= y 9e+167)))
             (* y z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.9e+158) {
		tmp = y * z;
	} else if (y <= -220000000000.0) {
		tmp = t_0;
	} else if (y <= -0.0066) {
		tmp = y * z;
	} else if (y <= 1.16e-125) {
		tmp = x;
	} else if ((y <= 7e+15) || (!(y <= 2.85e+116) && (y <= 9e+167))) {
		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 <= (-1.9d+158)) then
        tmp = y * z
    else if (y <= (-220000000000.0d0)) then
        tmp = t_0
    else if (y <= (-0.0066d0)) then
        tmp = y * z
    else if (y <= 1.16d-125) then
        tmp = x
    else if ((y <= 7d+15) .or. (.not. (y <= 2.85d+116)) .and. (y <= 9d+167)) 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 <= -1.9e+158) {
		tmp = y * z;
	} else if (y <= -220000000000.0) {
		tmp = t_0;
	} else if (y <= -0.0066) {
		tmp = y * z;
	} else if (y <= 1.16e-125) {
		tmp = x;
	} else if ((y <= 7e+15) || (!(y <= 2.85e+116) && (y <= 9e+167))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -1.9e+158:
		tmp = y * z
	elif y <= -220000000000.0:
		tmp = t_0
	elif y <= -0.0066:
		tmp = y * z
	elif y <= 1.16e-125:
		tmp = x
	elif (y <= 7e+15) or (not (y <= 2.85e+116) and (y <= 9e+167)):
		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 <= -1.9e+158)
		tmp = Float64(y * z);
	elseif (y <= -220000000000.0)
		tmp = t_0;
	elseif (y <= -0.0066)
		tmp = Float64(y * z);
	elseif (y <= 1.16e-125)
		tmp = x;
	elseif ((y <= 7e+15) || (!(y <= 2.85e+116) && (y <= 9e+167)))
		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 <= -1.9e+158)
		tmp = y * z;
	elseif (y <= -220000000000.0)
		tmp = t_0;
	elseif (y <= -0.0066)
		tmp = y * z;
	elseif (y <= 1.16e-125)
		tmp = x;
	elseif ((y <= 7e+15) || (~((y <= 2.85e+116)) && (y <= 9e+167)))
		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, -1.9e+158], N[(y * z), $MachinePrecision], If[LessEqual[y, -220000000000.0], t$95$0, If[LessEqual[y, -0.0066], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.16e-125], x, If[Or[LessEqual[y, 7e+15], And[N[Not[LessEqual[y, 2.85e+116]], $MachinePrecision], LessEqual[y, 9e+167]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999999e158 or -2.2e11 < y < -0.0066 or 1.15999999999999995e-125 < y < 7e15 or 2.84999999999999991e116 < y < 8.9999999999999998e167

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.4%

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

   4. Taylor expanded in x around 0 67.7%

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

   if -1.8999999999999999e158 < y < -2.2e11 or 7e15 < y < 2.84999999999999991e116 or 8.9999999999999998e167 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-lft-neg-out 68.3%

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

      3. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. mul-1-neg 68.1%

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

   8. Simplified 68.1%

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

   if -0.0066 < y < 1.15999999999999995e-125

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.7%

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

   4. Taylor expanded in x around inf 77.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+158}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -220000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -0.0066:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+15} \lor \neg \left(y \leq 2.85 \cdot 10^{+116}\right) \land y \leq 9 \cdot 10^{+167}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot z\\ t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -900000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+116} \lor \neg \left(y \leq 1.15 \cdot 10^{+168}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y z))) (t_1 (* y (- x))))
   (if (<= y -7.5e+149)
     t_0
     (if (<= y -900000000000.0)
       t_1
       (if (<= y 6.5e+15)
         t_0
         (if (or (<= y 1.22e+116) (not (<= y 1.15e+168))) t_1 (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double t_1 = y * -x;
	double tmp;
	if (y <= -7.5e+149) {
		tmp = t_0;
	} else if (y <= -900000000000.0) {
		tmp = t_1;
	} else if (y <= 6.5e+15) {
		tmp = t_0;
	} else if ((y <= 1.22e+116) || !(y <= 1.15e+168)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x + (y * z)
    t_1 = y * -x
    if (y <= (-7.5d+149)) then
        tmp = t_0
    else if (y <= (-900000000000.0d0)) then
        tmp = t_1
    else if (y <= 6.5d+15) then
        tmp = t_0
    else if ((y <= 1.22d+116) .or. (.not. (y <= 1.15d+168))) then
        tmp = t_1
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double t_1 = y * -x;
	double tmp;
	if (y <= -7.5e+149) {
		tmp = t_0;
	} else if (y <= -900000000000.0) {
		tmp = t_1;
	} else if (y <= 6.5e+15) {
		tmp = t_0;
	} else if ((y <= 1.22e+116) || !(y <= 1.15e+168)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * z)
	t_1 = y * -x
	tmp = 0
	if y <= -7.5e+149:
		tmp = t_0
	elif y <= -900000000000.0:
		tmp = t_1
	elif y <= 6.5e+15:
		tmp = t_0
	elif (y <= 1.22e+116) or not (y <= 1.15e+168):
		tmp = t_1
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * z))
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -7.5e+149)
		tmp = t_0;
	elseif (y <= -900000000000.0)
		tmp = t_1;
	elseif (y <= 6.5e+15)
		tmp = t_0;
	elseif ((y <= 1.22e+116) || !(y <= 1.15e+168))
		tmp = t_1;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * z);
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -7.5e+149)
		tmp = t_0;
	elseif (y <= -900000000000.0)
		tmp = t_1;
	elseif (y <= 6.5e+15)
		tmp = t_0;
	elseif ((y <= 1.22e+116) || ~((y <= 1.15e+168)))
		tmp = t_1;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -7.5e+149], t$95$0, If[LessEqual[y, -900000000000.0], t$95$1, If[LessEqual[y, 6.5e+15], t$95$0, If[Or[LessEqual[y, 1.22e+116], N[Not[LessEqual[y, 1.15e+168]], $MachinePrecision]], t$95$1, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000031e149 or -9e11 < y < 6.5e15

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.6%

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

   if -7.50000000000000031e149 < y < -9e11 or 6.5e15 < y < 1.21999999999999993e116 or 1.15e168 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-lft-neg-out 68.3%

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

      3. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. mul-1-neg 68.1%

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

   8. Simplified 68.1%

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

   if 1.21999999999999993e116 < y < 1.15e168

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.8%

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

   4. Taylor expanded in x around 0 79.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -900000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+116} \lor \neg \left(y \leq 1.15 \cdot 10^{+168}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-17} \lor \neg \left(x \leq 2.05 \cdot 10^{+108}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.28e-17) (not (<= x 2.05e+108))) (- x (* x y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.28e-17) || !(x <= 2.05e+108)) {
		tmp = x - (x * y);
	} 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 <= (-1.28d-17)) .or. (.not. (x <= 2.05d+108))) then
        tmp = x - (x * y)
    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 <= -1.28e-17) || !(x <= 2.05e+108)) {
		tmp = x - (x * y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.28e-17) or not (x <= 2.05e+108):
		tmp = x - (x * y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.28e-17) || !(x <= 2.05e+108))
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.28e-17) || ~((x <= 2.05e+108)))
		tmp = x - (x * y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.28e-17], N[Not[LessEqual[x, 2.05e+108]], $MachinePrecision]], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.28e-17 or 2.05e108 < x

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.3%

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

      1. mul-1-neg 92.3%

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

      2. distribute-lft-neg-out 92.3%

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

      3. *-commutative 92.3%

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

   5. Simplified 92.3%

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

      1. *-commutative 92.3%

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

      2. distribute-lft-neg-out 92.3%

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

      3. unsub-neg 92.3%

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

   7. Applied egg-rr 92.3%

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

   if -1.28e-17 < x < 2.05e108

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-17} \lor \neg \left(x \leq 2.05 \cdot 10^{+108}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0066 \lor \neg \left(y \leq 1.16 \cdot 10^{-125}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0066) (not (<= y 1.16e-125))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0066) || !(y <= 1.16e-125)) {
		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 <= (-0.0066d0)) .or. (.not. (y <= 1.16d-125))) 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 <= -0.0066) || !(y <= 1.16e-125)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0066) or not (y <= 1.16e-125):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0066) || !(y <= 1.16e-125))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0066) || ~((y <= 1.16e-125)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0066], N[Not[LessEqual[y, 1.16e-125]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.0066 or 1.15999999999999995e-125 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 57.2%

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

   4. Taylor expanded in x around 0 51.4%

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

   if -0.0066 < y < 1.15999999999999995e-125

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.7%

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

   4. Taylor expanded in x around inf 77.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0066 \lor \neg \left(y \leq 1.16 \cdot 10^{-125}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.2% 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. Add Preprocessing

3. Taylor expanded in z around inf 71.8%

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

4. Taylor expanded in x around inf 32.4%

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

5. Final simplification 32.4%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024041 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))