SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 8

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, 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-def 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. Final simplification 100.0%

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

Alternative 2: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3.05 \cdot 10^{+165}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+275}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -3.05e+165)
     (* y z)
     (if (<= y -9e+95)
       t_0
       (if (<= y -2.2e-51)
         (* y z)
         (if (<= y 13000.0) x (if (<= y 3.8e+275) t_0 (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3.05e+165) {
		tmp = y * z;
	} else if (y <= -9e+95) {
		tmp = t_0;
	} else if (y <= -2.2e-51) {
		tmp = y * z;
	} else if (y <= 13000.0) {
		tmp = x;
	} else if (y <= 3.8e+275) {
		tmp = t_0;
	} 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) :: tmp
    t_0 = y * -x
    if (y <= (-3.05d+165)) then
        tmp = y * z
    else if (y <= (-9d+95)) then
        tmp = t_0
    else if (y <= (-2.2d-51)) then
        tmp = y * z
    else if (y <= 13000.0d0) then
        tmp = x
    else if (y <= 3.8d+275) then
        tmp = t_0
    else
        tmp = y * z
    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 <= -3.05e+165) {
		tmp = y * z;
	} else if (y <= -9e+95) {
		tmp = t_0;
	} else if (y <= -2.2e-51) {
		tmp = y * z;
	} else if (y <= 13000.0) {
		tmp = x;
	} else if (y <= 3.8e+275) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -3.05e+165:
		tmp = y * z
	elif y <= -9e+95:
		tmp = t_0
	elif y <= -2.2e-51:
		tmp = y * z
	elif y <= 13000.0:
		tmp = x
	elif y <= 3.8e+275:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -3.05e+165)
		tmp = Float64(y * z);
	elseif (y <= -9e+95)
		tmp = t_0;
	elseif (y <= -2.2e-51)
		tmp = Float64(y * z);
	elseif (y <= 13000.0)
		tmp = x;
	elseif (y <= 3.8e+275)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -3.05e+165)
		tmp = y * z;
	elseif (y <= -9e+95)
		tmp = t_0;
	elseif (y <= -2.2e-51)
		tmp = y * z;
	elseif (y <= 13000.0)
		tmp = x;
	elseif (y <= 3.8e+275)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -3.05e+165], N[(y * z), $MachinePrecision], If[LessEqual[y, -9e+95], t$95$0, If[LessEqual[y, -2.2e-51], N[(y * z), $MachinePrecision], If[LessEqual[y, 13000.0], x, If[LessEqual[y, 3.8e+275], t$95$0, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.04999999999999983e165 or -9.00000000000000033e95 < y < -2.2e-51 or 3.80000000000000012e275 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 74.0%

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

   3. Taylor expanded in x around 0 66.9%

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

   if -3.04999999999999983e165 < y < -9.00000000000000033e95 or 13000 < y < 3.80000000000000012e275

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in y around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-rgt-neg-in 67.4%

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

   7. Simplified 67.4%

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

   if -2.2e-51 < y < 13000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+165}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+86} \lor \neg \left(x \leq 5.8 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e+86) (not (<= x 5.8e+73))) (* x (- 1.0 y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+86) || !(x <= 5.8e+73)) {
		tmp = x * (1.0 - 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 <= (-2.4d+86)) .or. (.not. (x <= 5.8d+73))) then
        tmp = x * (1.0d0 - 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 <= -2.4e+86) || !(x <= 5.8e+73)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e+86) or not (x <= 5.8e+73):
		tmp = x * (1.0 - y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e+86) || !(x <= 5.8e+73))
		tmp = Float64(x * Float64(1.0 - 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 <= -2.4e+86) || ~((x <= 5.8e+73)))
		tmp = x * (1.0 - y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e+86], N[Not[LessEqual[x, 5.8e+73]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e86 or 5.8000000000000005e73 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 91.5%

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

      1. *-commutative 91.5%

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

      2. mul-1-neg 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in x around 0 91.5%

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

   if -2.4e86 < x < 5.8000000000000005e73

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 87.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+86} \lor \neg \left(x \leq 5.8 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 135000000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e+122)
   (* y z)
   (if (<= z 135000000000.0) (* x (- 1.0 y)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+122) {
		tmp = y * z;
	} else if (z <= 135000000000.0) {
		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 (z <= (-1.6d+122)) then
        tmp = y * z
    else if (z <= 135000000000.0d0) 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 (z <= -1.6e+122) {
		tmp = y * z;
	} else if (z <= 135000000000.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e+122:
		tmp = y * z
	elif z <= 135000000000.0:
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e+122)
		tmp = Float64(y * z);
	elseif (z <= 135000000000.0)
		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 (z <= -1.6e+122)
		tmp = y * z;
	elseif (z <= 135000000000.0)
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e+122], N[(y * z), $MachinePrecision], If[LessEqual[z, 135000000000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000006e122 or 1.35e11 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 90.8%

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

   3. Taylor expanded in x around 0 71.6%

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

   if -1.60000000000000006e122 < z < 1.35e11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in x around 0 78.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 135000000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+88}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e+88)
   (- x (* y x))
   (if (<= x 4.6e+73) (+ x (* y z)) (* x (- 1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+88) {
		tmp = x - (y * x);
	} else if (x <= 4.6e+73) {
		tmp = x + (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 (x <= (-1.4d+88)) then
        tmp = x - (y * x)
    else if (x <= 4.6d+73) then
        tmp = x + (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 (x <= -1.4e+88) {
		tmp = x - (y * x);
	} else if (x <= 4.6e+73) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e+88:
		tmp = x - (y * x)
	elif x <= 4.6e+73:
		tmp = x + (y * z)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e+88)
		tmp = Float64(x - Float64(y * x));
	elseif (x <= 4.6e+73)
		tmp = Float64(x + 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 (x <= -1.4e+88)
		tmp = x - (y * x);
	elseif (x <= 4.6e+73)
		tmp = x + (y * z);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e+88], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+73], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.39999999999999994e88

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.7%

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

      1. +-commutative 92.7%

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

      2. distribute-rgt1-in 92.7%

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

      3. mul-1-neg 92.7%

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

      4. cancel-sign-sub-inv 92.7%

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

   4. Simplified 92.7%

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

   if -1.39999999999999994e88 < x < 4.6e73

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 87.1%

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

   if 4.6e73 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. mul-1-neg 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in x around 0 90.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+88}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 6: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e-50) (* y z) (if (<= y 1e-5) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e-50) {
		tmp = y * z;
	} else if (y <= 1e-5) {
		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 <= (-2.5d-50)) then
        tmp = y * z
    else if (y <= 1d-5) 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 <= -2.5e-50) {
		tmp = y * z;
	} else if (y <= 1e-5) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e-50:
		tmp = y * z
	elif y <= 1e-5:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e-50)
		tmp = Float64(y * z);
	elseif (y <= 1e-5)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.5e-50)
		tmp = y * z;
	elseif (y <= 1e-5)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e-50], N[(y * z), $MachinePrecision], If[LessEqual[y, 1e-5], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999984e-50 or 1.00000000000000008e-5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.5%

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

   3. Taylor expanded in x around 0 54.3%

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

   if -2.49999999999999984e-50 < y < 1.00000000000000008e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 8: 35.8% 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 y around 0 38.3%

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

3. Final simplification 38.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))