SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 8

Speedup: 1.0×

• 20.5% 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-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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 60.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0016:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+216} \lor \neg \left(y \leq 2.3 \cdot 10^{+286}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.16e-8)
     t_0
     (if (<= y 0.0016)
       x
       (if (or (<= y 2.6e+216) (not (<= y 2.3e+286))) (* y z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.16e-8) {
		tmp = t_0;
	} else if (y <= 0.0016) {
		tmp = x;
	} else if ((y <= 2.6e+216) || !(y <= 2.3e+286)) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (y <= (-1.16d-8)) then
        tmp = t_0
    else if (y <= 0.0016d0) then
        tmp = x
    else if ((y <= 2.6d+216) .or. (.not. (y <= 2.3d+286))) then
        tmp = y * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.16e-8) {
		tmp = t_0;
	} else if (y <= 0.0016) {
		tmp = x;
	} else if ((y <= 2.6e+216) || !(y <= 2.3e+286)) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -1.16e-8:
		tmp = t_0
	elif y <= 0.0016:
		tmp = x
	elif (y <= 2.6e+216) or not (y <= 2.3e+286):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.16e-8)
		tmp = t_0;
	elseif (y <= 0.0016)
		tmp = x;
	elseif ((y <= 2.6e+216) || !(y <= 2.3e+286))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -1.16e-8)
		tmp = t_0;
	elseif (y <= 0.0016)
		tmp = x;
	elseif ((y <= 2.6e+216) || ~((y <= 2.3e+286)))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.16e-8], t$95$0, If[LessEqual[y, 0.0016], x, If[Or[LessEqual[y, 2.6e+216], N[Not[LessEqual[y, 2.3e+286]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15999999999999996e-8 or 2.5999999999999999e216 < y < 2.3000000000000001e286

   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 96.9%

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

      3. fma-def 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in x around 0 96.9%

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

      1. fma-def 98.4%

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

      2. mul-1-neg 98.4%

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

      3. sub-neg 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in y around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   10. Simplified 99.5%

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

   11. Taylor expanded in z around 0 66.8%

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

       1. mul-1-neg 66.8%

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

       2. distribute-lft-neg-out 66.8%

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

       3. *-commutative 66.8%

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

   13. Simplified 66.8%

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

   if -1.15999999999999996e-8 < y < 0.00160000000000000008

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.3%

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

   if 0.00160000000000000008 < y < 2.5999999999999999e216 or 2.3000000000000001e286 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 61.7%

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

   4. Taylor expanded in x around 0 62.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 0.0016:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+216} \lor \neg \left(y \leq 2.3 \cdot 10^{+286}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+28} \lor \neg \left(x \leq 6.8 \cdot 10^{-57}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+28) (not (<= x 6.8e-57))) (* x (- 1.0 y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+28) || !(x <= 6.8e-57)) {
		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 <= (-2.8d+28)) .or. (.not. (x <= 6.8d-57))) 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 <= -2.8e+28) || !(x <= 6.8e-57)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e+28) or not (x <= 6.8e-57):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e+28) || !(x <= 6.8e-57))
		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 <= -2.8e+28) || ~((x <= 6.8e-57)))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e+28], N[Not[LessEqual[x, 6.8e-57]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e28 or 6.80000000000000032e-57 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   if -2.8000000000000001e28 < x < 6.80000000000000032e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.2%

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

   4. Taylor expanded in x around 0 67.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+28} \lor \neg \left(x \leq 6.8 \cdot 10^{-57}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+32} \lor \neg \left(x \leq 3.5 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.56e+32) (not (<= x 3.5e-12))) (* x (- 1.0 y)) (* y (- z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.56e+32) || !(x <= 3.5e-12)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (z - 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 ((x <= (-1.56d+32)) .or. (.not. (x <= 3.5d-12))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.56e+32) || !(x <= 3.5e-12)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.56e+32) or not (x <= 3.5e-12):
		tmp = x * (1.0 - y)
	else:
		tmp = y * (z - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.56e+32) || !(x <= 3.5e-12))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.56e+32) || ~((x <= 3.5e-12)))
		tmp = x * (1.0 - y);
	else
		tmp = y * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.56e+32], N[Not[LessEqual[x, 3.5e-12]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.56e32 or 3.5e-12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 92.3%

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

      1. mul-1-neg 92.3%

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

      2. unsub-neg 92.3%

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

   5. Simplified 92.3%

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

   if -1.56e32 < x < 3.5e-12

   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 99.9%

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

      3. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

   10. Simplified 77.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+32} \lor \neg \left(x \leq 3.5 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0085\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.0085))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.0085)) {
		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 <= 0.0085d0))) 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 <= 0.0085)) {
		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 <= 0.0085):
		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 <= 0.0085))
		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 <= 0.0085)))
		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, 0.0085]], $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 0.0085000000000000006 < 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 98.1%

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

      3. fma-def 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in x around 0 98.1%

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

      1. fma-def 99.1%

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

      2. mul-1-neg 99.1%

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

      3. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in y around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. unsub-neg 98.4%

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

   10. Simplified 98.4%

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

   if -1 < y < 0.0085000000000000006

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0085\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-9} \lor \neg \left(y \leq 0.00192\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-9) (not (<= y 0.00192))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-9) || !(y <= 0.00192)) {
		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-9)) .or. (.not. (y <= 0.00192d0))) 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-9) || !(y <= 0.00192)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-9) or not (y <= 0.00192):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-9) || !(y <= 0.00192))
		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-9) || ~((y <= 0.00192)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-9], N[Not[LessEqual[y, 0.00192]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000025e-9 or 0.00192000000000000005 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 46.5%

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

   4. Taylor expanded in x around 0 46.1%

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

   if -4.00000000000000025e-9 < y < 0.00192000000000000005

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.3%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-9} \lor \neg \left(y \leq 0.00192\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 36.1% 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 41.2%

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

4. Final simplification 41.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))