SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 7

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-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: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1800000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1800000.0) (not (<= y 1.0))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1800000.0) || !(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 <= (-1800000.0d0)) .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 <= -1800000.0) || !(y <= 1.0)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1800000.0) 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 <= -1800000.0) || !(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 <= -1800000.0) || ~((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, -1800000.0], 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 < -1.8e6 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around inf 99.0%

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

   if -1.8e6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1800000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-51} \lor \neg \left(y \leq 1.06 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.1e-51) (not (<= y 1.06e-17))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e-51) || !(y <= 1.06e-17)) {
		tmp = y * (z - x);
	} 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 <= (-4.1d-51)) .or. (.not. (y <= 1.06d-17))) then
        tmp = y * (z - x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e-51) || !(y <= 1.06e-17)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.1e-51) or not (y <= 1.06e-17):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.1e-51) || !(y <= 1.06e-17))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.1e-51) || ~((y <= 1.06e-17)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.1e-51], N[Not[LessEqual[y, 1.06e-17]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.09999999999999973e-51 or 1.06000000000000006e-17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.4%

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

   4. Taylor expanded in z around inf 95.3%

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

   if -4.09999999999999973e-51 < y < 1.06000000000000006e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-51} \lor \neg \left(y \leq 1.06 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+21} \lor \neg \left(z \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.9e+21) (not (<= z 4.8e+110))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.9e+21) || !(z <= 4.8e+110)) {
		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 <= (-2.9d+21)) .or. (.not. (z <= 4.8d+110))) 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 <= -2.9e+21) || !(z <= 4.8e+110)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.9e+21) or not (z <= 4.8e+110):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.9e+21) || !(z <= 4.8e+110))
		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 <= -2.9e+21) || ~((z <= 4.8e+110)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.9e+21], N[Not[LessEqual[z, 4.8e+110]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e21 or 4.80000000000000025e110 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.4%

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

      1. +-commutative 96.4%

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

      2. mul-1-neg 96.4%

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

      3. unsub-neg 96.4%

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

      4. div-sub 96.4%

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

      5. unsub-neg 96.4%

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

      6. mul-1-neg 96.4%

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

      7. mul-1-neg 96.4%

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

      8. unsub-neg 96.4%

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

      9. *-lft-identity 96.4%

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

      10. *-commutative 96.4%

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

      11. distribute-rgt-out-- 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in z around inf 76.6%

      \[\leadsto \color{blue}{y \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if -2.9e21 < z < 4.80000000000000025e110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+21} \lor \neg \left(z \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-52} \lor \neg \left(y \leq 2.2 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-52) (not (<= y 2.2e-16))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-52) || !(y <= 2.2e-16)) {
		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 <= (-3.4d-52)) .or. (.not. (y <= 2.2d-16))) 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 <= -3.4e-52) || !(y <= 2.2e-16)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-52) or not (y <= 2.2e-16):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-52) || !(y <= 2.2e-16))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-52) || ~((y <= 2.2e-16)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-52], N[Not[LessEqual[y, 2.2e-16]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000017e-52 or 2.2e-16 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.5%

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

      1. +-commutative 86.5%

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

      2. mul-1-neg 86.5%

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

      3. unsub-neg 86.5%

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

      4. div-sub 87.9%

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

      5. unsub-neg 87.9%

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

      6. mul-1-neg 87.9%

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

      7. mul-1-neg 87.9%

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

      8. unsub-neg 87.9%

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

      9. *-lft-identity 87.9%

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

      10. *-commutative 87.9%

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

      11. distribute-rgt-out-- 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in z around inf 58.8%

      \[\leadsto \color{blue}{y \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative 58.8%

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

   8. Simplified 58.8%

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

   if -3.40000000000000017e-52 < y < 2.2e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-52} \lor \neg \left(y \leq 2.2 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 7: 36.3% 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 34.8%

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

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))