SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.0×

• 20.6% 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: 59.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+259}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.58 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.00112:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.7e+259)
     (* y z)
     (if (<= y -1.58e+38)
       t_0
       (if (<= y -1e-118) (* y z) (if (<= y 0.00112) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.7e+259) {
		tmp = y * z;
	} else if (y <= -1.58e+38) {
		tmp = t_0;
	} else if (y <= -1e-118) {
		tmp = y * z;
	} else if (y <= 0.00112) {
		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 * -x
    if (y <= (-1.7d+259)) then
        tmp = y * z
    else if (y <= (-1.58d+38)) then
        tmp = t_0
    else if (y <= (-1d-118)) then
        tmp = y * z
    else if (y <= 0.00112d0) 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 * -x;
	double tmp;
	if (y <= -1.7e+259) {
		tmp = y * z;
	} else if (y <= -1.58e+38) {
		tmp = t_0;
	} else if (y <= -1e-118) {
		tmp = y * z;
	} else if (y <= 0.00112) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -1.7e+259:
		tmp = y * z
	elif y <= -1.58e+38:
		tmp = t_0
	elif y <= -1e-118:
		tmp = y * z
	elif y <= 0.00112:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.7e+259)
		tmp = Float64(y * z);
	elseif (y <= -1.58e+38)
		tmp = t_0;
	elseif (y <= -1e-118)
		tmp = Float64(y * z);
	elseif (y <= 0.00112)
		tmp = x;
	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 <= -1.7e+259)
		tmp = y * z;
	elseif (y <= -1.58e+38)
		tmp = t_0;
	elseif (y <= -1e-118)
		tmp = y * z;
	elseif (y <= 0.00112)
		tmp = x;
	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, -1.7e+259], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.58e+38], t$95$0, If[LessEqual[y, -1e-118], N[(y * z), $MachinePrecision], If[LessEqual[y, 0.00112], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999995e259 or -1.58e38 < y < -9.99999999999999985e-119

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 91.4%

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

   4. Applied egg-rr 91.4%

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

      1. associate-+r+ 91.4%

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

      2. distribute-lft-neg-out 91.4%

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

      3. unsub-neg 91.4%

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

      4. +-commutative 91.4%

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

      5. *-commutative 91.4%

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

   6. Applied egg-rr 91.4%

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

   7. Taylor expanded in z around inf 61.2%

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

   if -1.69999999999999995e259 < y < -1.58e38 or 0.0011199999999999999 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

   5. Simplified 60.8%

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

      1. sub-neg 60.8%

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

      2. distribute-rgt-in 60.7%

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

      3. *-un-lft-identity 60.7%

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

      4. distribute-lft-neg-in 60.7%

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

      5. unsub-neg 60.7%

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

   7. Applied egg-rr 60.7%

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

   8. Taylor expanded in y around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. distribute-rgt-neg-out 60.7%

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

   10. Simplified 60.7%

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

   if -9.99999999999999985e-119 < y < 0.0011199999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+259}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.58 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.00112:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-71} \lor \neg \left(z \leq 3.6 \cdot 10^{+107}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e-71) (not (<= z 3.6e+107))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-71) || !(z <= 3.6e+107)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - 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 <= (-2.65d-71)) .or. (.not. (z <= 3.6d+107))) then
        tmp = y * z
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-71) || !(z <= 3.6e+107)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e-71) or not (z <= 3.6e+107):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e-71) || !(z <= 3.6e+107))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e-71) || ~((z <= 3.6e+107)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e-71], N[Not[LessEqual[z, 3.6e+107]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e-71 or 3.5999999999999998e107 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 88.8%

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

   4. Applied egg-rr 88.8%

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

      1. associate-+r+ 88.8%

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

      2. distribute-lft-neg-out 88.8%

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

      3. unsub-neg 88.8%

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

      4. +-commutative 88.8%

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

      5. *-commutative 88.8%

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

   6. Applied egg-rr 88.8%

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

   7. Taylor expanded in z around inf 75.9%

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

   if -2.65e-71 < z < 3.5999999999999998e107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

   5. Simplified 88.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-71} \lor \neg \left(z \leq 3.6 \cdot 10^{+107}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-72} \lor \neg \left(z \leq 8.8 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e-72) (not (<= z 8.8e+97))) (* y (- z x)) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-72) || !(z <= 8.8e+97)) {
		tmp = y * (z - x);
	} else {
		tmp = x * (1.0 - 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 <= (-5.8d-72)) .or. (.not. (z <= 8.8d+97))) then
        tmp = y * (z - x)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-72) || !(z <= 8.8e+97)) {
		tmp = y * (z - x);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e-72) or not (z <= 8.8e+97):
		tmp = y * (z - x)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e-72) || !(z <= 8.8e+97))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.8e-72) || ~((z <= 8.8e+97)))
		tmp = y * (z - x);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e-72], N[Not[LessEqual[z, 8.8e+97]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999995e-72 or 8.8000000000000003e97 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 88.1%

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

   4. Applied egg-rr 88.1%

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

      1. associate-+r+ 88.1%

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

      2. distribute-lft-neg-out 88.1%

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

      3. unsub-neg 88.1%

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

      4. +-commutative 88.1%

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

      5. *-commutative 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around inf 87.1%

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

   if -5.79999999999999995e-72 < z < 8.8000000000000003e97

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. unsub-neg 88.8%

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

   5. Simplified 88.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-72} \lor \neg \left(z \leq 8.8 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -82 \lor \neg \left(y \leq 0.00112\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -82.0) (not (<= y 0.00112))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -82.0) || !(y <= 0.00112)) {
		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 <= (-82.0d0)) .or. (.not. (y <= 0.00112d0))) 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 <= -82.0) || !(y <= 0.00112)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -82.0) or not (y <= 0.00112):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -82.0) || !(y <= 0.00112))
		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 <= -82.0) || ~((y <= 0.00112)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -82.0], N[Not[LessEqual[y, 0.00112]], $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 < -82 or 0.0011199999999999999 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 89.9%

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

   4. Applied egg-rr 89.9%

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

      1. associate-+r+ 89.9%

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

      2. distribute-lft-neg-out 89.9%

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

      3. unsub-neg 89.9%

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

      4. +-commutative 89.9%

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

      5. *-commutative 89.9%

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

   6. Applied egg-rr 89.9%

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

   7. Taylor expanded in y around inf 99.4%

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

   if -82 < y < 0.0011199999999999999

   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 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -82 \lor \neg \left(y \leq 0.00112\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-71} \lor \neg \left(z \leq 5 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-71) (not (<= z 5e+97))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-71) || !(z <= 5e+97)) {
		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 ((z <= (-1.7d-71)) .or. (.not. (z <= 5d+97))) 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 ((z <= -1.7e-71) || !(z <= 5e+97)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-71) or not (z <= 5e+97):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-71) || !(z <= 5e+97))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-71) || ~((z <= 5e+97)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-71], N[Not[LessEqual[z, 5e+97]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000002e-71 or 4.99999999999999999e97 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 88.1%

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

   4. Applied egg-rr 88.1%

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

      1. associate-+r+ 88.1%

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

      2. distribute-lft-neg-out 88.1%

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

      3. unsub-neg 88.1%

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

      4. +-commutative 88.1%

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

      5. *-commutative 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in z around inf 75.5%

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

   if -1.70000000000000002e-71 < z < 4.99999999999999999e97

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 50.6%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-71} \lor \neg \left(z \leq 5 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 36.5% 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 35.4%

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

4. Final simplification 35.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))