SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 8

Speedup: 1.0×

• 21.2% 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. Add Preprocessing

Alternative 2: 61.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-41}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.0065:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e-41)
   (* y z)
   (if (<= y 0.0065) x (if (<= y 7.2e+65) (* y z) (* y (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e-41) {
		tmp = y * z;
	} else if (y <= 0.0065) {
		tmp = x;
	} else if (y <= 7.2e+65) {
		tmp = y * z;
	} else {
		tmp = y * -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 <= (-6.8d-41)) then
        tmp = y * z
    else if (y <= 0.0065d0) then
        tmp = x
    else if (y <= 7.2d+65) then
        tmp = y * z
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e-41) {
		tmp = y * z;
	} else if (y <= 0.0065) {
		tmp = x;
	} else if (y <= 7.2e+65) {
		tmp = y * z;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e-41:
		tmp = y * z
	elif y <= 0.0065:
		tmp = x
	elif y <= 7.2e+65:
		tmp = y * z
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e-41)
		tmp = Float64(y * z);
	elseif (y <= 0.0065)
		tmp = x;
	elseif (y <= 7.2e+65)
		tmp = Float64(y * z);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e-41)
		tmp = y * z;
	elseif (y <= 0.0065)
		tmp = x;
	elseif (y <= 7.2e+65)
		tmp = y * z;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e-41], N[(y * z), $MachinePrecision], If[LessEqual[y, 0.0065], x, If[LessEqual[y, 7.2e+65], N[(y * z), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999997e-41 or 0.0064999999999999997 < y < 7.19999999999999957e65

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. fma-define 98.6%

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

      2. +-commutative 98.6%

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

      3. mul-1-neg 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in x around 0 55.8%

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

   if -6.7999999999999997e-41 < y < 0.0064999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.0%

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

   if 7.19999999999999957e65 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.6%

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

      1. fma-define 96.7%

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

      2. +-commutative 96.7%

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

      3. mul-1-neg 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. sub-neg 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around 0 70.0%

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

       1. mul-1-neg 70.0%

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

       2. distribute-lft-neg-out 70.0%

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

       3. *-commutative 70.0%

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

   11. Simplified 70.0%

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

Alternative 3: 98.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) 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 <= -1.0) || !(y <= 1.0)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $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 < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.4%

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

      1. fma-define 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around inf 98.5%

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

      1. neg-mul-1 98.5%

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

      2. sub-neg 98.5%

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

   8. Simplified 98.5%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.2%

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

4. Final simplification 98.3%

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

Alternative 4: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00023 \lor \neg \left(y \leq 0.25\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00023) (not (<= y 0.25))) (* y (- z x)) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00023) || !(y <= 0.25)) {
		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 ((y <= (-0.00023d0)) .or. (.not. (y <= 0.25d0))) 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 ((y <= -0.00023) || !(y <= 0.25)) {
		tmp = y * (z - x);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00023) or not (y <= 0.25):
		tmp = y * (z - x)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00023) || !(y <= 0.25))
		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 ((y <= -0.00023) || ~((y <= 0.25)))
		tmp = y * (z - x);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00023], N[Not[LessEqual[y, 0.25]], $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 y < -2.3000000000000001e-4 or 0.25 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.5%

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

      1. fma-define 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around inf 98.5%

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

      1. neg-mul-1 98.5%

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

      2. sub-neg 98.5%

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

   8. Simplified 98.5%

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

   if -2.3000000000000001e-4 < y < 0.25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.0%

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

      1. mul-1-neg 73.0%

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

      2. unsub-neg 73.0%

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

   5. Simplified 73.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00023 \lor \neg \left(y \leq 0.25\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+64} \lor \neg \left(z \leq 6.8 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.22e+64) (not (<= z 6.8e+167))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.22e+64) || !(z <= 6.8e+167)) {
		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 <= (-1.22d+64)) .or. (.not. (z <= 6.8d+167))) 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 <= -1.22e+64) || !(z <= 6.8e+167)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.22e+64) or not (z <= 6.8e+167):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.22e+64) || !(z <= 6.8e+167))
		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 <= -1.22e+64) || ~((z <= 6.8e+167)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.22e+64], N[Not[LessEqual[z, 6.8e+167]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.21999999999999994e64 or 6.8000000000000001e167 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.2%

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

      1. fma-define 97.7%

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

      2. +-commutative 97.7%

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

      3. mul-1-neg 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x around 0 72.1%

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

   if -1.21999999999999994e64 < z < 6.8000000000000001e167

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

   5. Simplified 80.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+64} \lor \neg \left(z \leq 6.8 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-41} \lor \neg \left(y \leq 0.006\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-41) (not (<= y 0.006))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-41) || !(y <= 0.006)) {
		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 <= (-4d-41)) .or. (.not. (y <= 0.006d0))) 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 <= -4e-41) || !(y <= 0.006)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-41) or not (y <= 0.006):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-41) || !(y <= 0.006))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e-41) || ~((y <= 0.006)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-41], N[Not[LessEqual[y, 0.006]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000002e-41 or 0.0060000000000000001 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.8%

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

      1. fma-define 97.8%

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

      2. +-commutative 97.8%

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

      3. mul-1-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around 0 48.2%

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

   if -4.00000000000000002e-41 < y < 0.0060000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.0%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-41} \lor \neg \left(y \leq 0.006\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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. Add Preprocessing

Alternative 8: 36.6% 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 37.3%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))