SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.0×

• 21.5% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, z - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, z - x, x\right) \]
6. Add Preprocessing

Alternative 2: 62.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+214}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+32} \lor \neg \left(y \leq 1.65 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -3.2e+214)
     (* y z)
     (if (<= y -8.2e+48)
       t_0
       (if (<= y -5.6e-15)
         (* y z)
         (if (<= y 1.5e-88)
           x
           (if (<= y 1.22e-79)
             (* y z)
             (if (<= y 1.6e-33)
               x
               (if (or (<= y 2.8e+32) (not (<= y 1.65e+236)))
                 (* y z)
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3.2e+214) {
		tmp = y * z;
	} else if (y <= -8.2e+48) {
		tmp = t_0;
	} else if (y <= -5.6e-15) {
		tmp = y * z;
	} else if (y <= 1.5e-88) {
		tmp = x;
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 1.6e-33) {
		tmp = x;
	} else if ((y <= 2.8e+32) || !(y <= 1.65e+236)) {
		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 <= (-3.2d+214)) then
        tmp = y * z
    else if (y <= (-8.2d+48)) then
        tmp = t_0
    else if (y <= (-5.6d-15)) then
        tmp = y * z
    else if (y <= 1.5d-88) then
        tmp = x
    else if (y <= 1.22d-79) then
        tmp = y * z
    else if (y <= 1.6d-33) then
        tmp = x
    else if ((y <= 2.8d+32) .or. (.not. (y <= 1.65d+236))) 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 <= -3.2e+214) {
		tmp = y * z;
	} else if (y <= -8.2e+48) {
		tmp = t_0;
	} else if (y <= -5.6e-15) {
		tmp = y * z;
	} else if (y <= 1.5e-88) {
		tmp = x;
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 1.6e-33) {
		tmp = x;
	} else if ((y <= 2.8e+32) || !(y <= 1.65e+236)) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -3.2e+214:
		tmp = y * z
	elif y <= -8.2e+48:
		tmp = t_0
	elif y <= -5.6e-15:
		tmp = y * z
	elif y <= 1.5e-88:
		tmp = x
	elif y <= 1.22e-79:
		tmp = y * z
	elif y <= 1.6e-33:
		tmp = x
	elif (y <= 2.8e+32) or not (y <= 1.65e+236):
		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 <= -3.2e+214)
		tmp = Float64(y * z);
	elseif (y <= -8.2e+48)
		tmp = t_0;
	elseif (y <= -5.6e-15)
		tmp = Float64(y * z);
	elseif (y <= 1.5e-88)
		tmp = x;
	elseif (y <= 1.22e-79)
		tmp = Float64(y * z);
	elseif (y <= 1.6e-33)
		tmp = x;
	elseif ((y <= 2.8e+32) || !(y <= 1.65e+236))
		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 <= -3.2e+214)
		tmp = y * z;
	elseif (y <= -8.2e+48)
		tmp = t_0;
	elseif (y <= -5.6e-15)
		tmp = y * z;
	elseif (y <= 1.5e-88)
		tmp = x;
	elseif (y <= 1.22e-79)
		tmp = y * z;
	elseif (y <= 1.6e-33)
		tmp = x;
	elseif ((y <= 2.8e+32) || ~((y <= 1.65e+236)))
		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, -3.2e+214], N[(y * z), $MachinePrecision], If[LessEqual[y, -8.2e+48], t$95$0, If[LessEqual[y, -5.6e-15], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.5e-88], x, If[LessEqual[y, 1.22e-79], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.6e-33], x, If[Or[LessEqual[y, 2.8e+32], N[Not[LessEqual[y, 1.65e+236]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.19999999999999995e214 or -8.2000000000000005e48 < y < -5.60000000000000028e-15 or 1.5e-88 < y < 1.22e-79 or 1.59999999999999988e-33 < y < 2.8e32 or 1.6499999999999999e236 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 72.4%

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

   4. Taylor expanded in z around inf 75.6%

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

   5. Taylor expanded in z around inf 67.6%

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

   if -3.19999999999999995e214 < y < -8.2000000000000005e48 or 2.8e32 < y < 1.6499999999999999e236

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in z around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-lft-neg-out 66.3%

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

      3. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -5.60000000000000028e-15 < y < 1.5e-88 or 1.22e-79 < y < 1.59999999999999988e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.4%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+214}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+32} \lor \neg \left(y \leq 1.65 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -2.9e-26)
     t_0
     (if (<= y 9e-89)
       x
       (if (<= y 1.22e-79) (* y z) (if (<= y 5.5e-34) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -2.9e-26) {
		tmp = t_0;
	} else if (y <= 9e-89) {
		tmp = x;
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 5.5e-34) {
		tmp = x;
	} 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 * (z - x)
    if (y <= (-2.9d-26)) then
        tmp = t_0
    else if (y <= 9d-89) then
        tmp = x
    else if (y <= 1.22d-79) then
        tmp = y * z
    else if (y <= 5.5d-34) then
        tmp = x
    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 * (z - x);
	double tmp;
	if (y <= -2.9e-26) {
		tmp = t_0;
	} else if (y <= 9e-89) {
		tmp = x;
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 5.5e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -2.9e-26:
		tmp = t_0
	elif y <= 9e-89:
		tmp = x
	elif y <= 1.22e-79:
		tmp = y * z
	elif y <= 5.5e-34:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -2.9e-26)
		tmp = t_0;
	elseif (y <= 9e-89)
		tmp = x;
	elseif (y <= 1.22e-79)
		tmp = Float64(y * z);
	elseif (y <= 5.5e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z - x);
	tmp = 0.0;
	if (y <= -2.9e-26)
		tmp = t_0;
	elseif (y <= 9e-89)
		tmp = x;
	elseif (y <= 1.22e-79)
		tmp = y * z;
	elseif (y <= 5.5e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e-26], t$95$0, If[LessEqual[y, 9e-89], x, If[LessEqual[y, 1.22e-79], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.5e-34], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999998e-26 or 5.50000000000000014e-34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in z around inf 95.1%

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

   if -2.8999999999999998e-26 < y < 8.9999999999999998e-89 or 1.22e-79 < y < 5.50000000000000014e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.3%

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

   if 8.9999999999999998e-89 < y < 1.22e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-14} \lor \neg \left(y \leq 9 \cdot 10^{-89}\right) \land \left(y \leq 1.3 \cdot 10^{-79} \lor \neg \left(y \leq 6 \cdot 10^{-33}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e-14)
         (and (not (<= y 9e-89)) (or (<= y 1.3e-79) (not (<= y 6e-33)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-14) || (!(y <= 9e-89) && ((y <= 1.3e-79) || !(y <= 6e-33)))) {
		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 <= (-5d-14)) .or. (.not. (y <= 9d-89)) .and. (y <= 1.3d-79) .or. (.not. (y <= 6d-33))) 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 <= -5e-14) || (!(y <= 9e-89) && ((y <= 1.3e-79) || !(y <= 6e-33)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e-14) or (not (y <= 9e-89) and ((y <= 1.3e-79) or not (y <= 6e-33))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e-14) || (!(y <= 9e-89) && ((y <= 1.3e-79) || !(y <= 6e-33))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e-14) || (~((y <= 9e-89)) && ((y <= 1.3e-79) || ~((y <= 6e-33)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e-14], And[N[Not[LessEqual[y, 9e-89]], $MachinePrecision], Or[LessEqual[y, 1.3e-79], N[Not[LessEqual[y, 6e-33]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e-14 or 8.9999999999999998e-89 < y < 1.29999999999999997e-79 or 6.0000000000000003e-33 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 54.5%

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

   4. Taylor expanded in z around inf 58.4%

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

   5. Taylor expanded in z around inf 52.4%

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

   if -5.0000000000000002e-14 < y < 8.9999999999999998e-89 or 1.29999999999999997e-79 < y < 6.0000000000000003e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-14} \lor \neg \left(y \leq 9 \cdot 10^{-89}\right) \land \left(y \leq 1.3 \cdot 10^{-79} \lor \neg \left(y \leq 6 \cdot 10^{-33}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-112} \lor \neg \left(x \leq 6.5 \cdot 10^{-102}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.15e-112) (not (<= x 6.5e-102))) (* x (- 1.0 y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.15e-112) || !(x <= 6.5e-102)) {
		tmp = x * (1.0 - y);
	} 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 ((x <= (-3.15d-112)) .or. (.not. (x <= 6.5d-102))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.15e-112) || !(x <= 6.5e-102)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.15e-112) or not (x <= 6.5e-102):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.15e-112) || !(x <= 6.5e-102))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.15e-112) || ~((x <= 6.5e-102)))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.15e-112], N[Not[LessEqual[x, 6.5e-102]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.15000000000000008e-112 or 6.5000000000000003e-102 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

   5. Simplified 81.0%

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

   if -3.15000000000000008e-112 < x < 6.5000000000000003e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.5%

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

   4. Taylor expanded in z around inf 94.5%

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

   5. Taylor expanded in z around inf 75.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-112} \lor \neg \left(x \leq 6.5 \cdot 10^{-102}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -540.0) (not (<= y 0.0065))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.0065)) {
		tmp = y * (z - 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 <= (-540.0d0)) .or. (.not. (y <= 0.0065d0))) then
        tmp = y * (z - 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 <= -540.0) || !(y <= 0.0065)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -540.0) or not (y <= 0.0065):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -540.0) || !(y <= 0.0065))
		tmp = Float64(y * Float64(z - 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 <= -540.0) || ~((y <= 0.0065)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -540.0], N[Not[LessEqual[y, 0.0065]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -540 or 0.0064999999999999997 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around inf 98.9%

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

   if -540 < y < 0.0064999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 36.2% 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 y around 0 38.1%

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

4. Final simplification 38.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))