SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 8

Speedup: 1.0×

• 21.4% 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: 59.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -34000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -7.5e+145)
     (* y z)
     (if (<= y -34000000000000.0)
       t_0
       (if (<= y -1.65e-118)
         (* y z)
         (if (<= y 8e-22) x (if (<= y 8.5e+141) (* y z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -7.5e+145) {
		tmp = y * z;
	} else if (y <= -34000000000000.0) {
		tmp = t_0;
	} else if (y <= -1.65e-118) {
		tmp = y * z;
	} else if (y <= 8e-22) {
		tmp = x;
	} else if (y <= 8.5e+141) {
		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 <= (-7.5d+145)) then
        tmp = y * z
    else if (y <= (-34000000000000.0d0)) then
        tmp = t_0
    else if (y <= (-1.65d-118)) then
        tmp = y * z
    else if (y <= 8d-22) then
        tmp = x
    else if (y <= 8.5d+141) 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 <= -7.5e+145) {
		tmp = y * z;
	} else if (y <= -34000000000000.0) {
		tmp = t_0;
	} else if (y <= -1.65e-118) {
		tmp = y * z;
	} else if (y <= 8e-22) {
		tmp = x;
	} else if (y <= 8.5e+141) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -7.5e+145:
		tmp = y * z
	elif y <= -34000000000000.0:
		tmp = t_0
	elif y <= -1.65e-118:
		tmp = y * z
	elif y <= 8e-22:
		tmp = x
	elif y <= 8.5e+141:
		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 <= -7.5e+145)
		tmp = Float64(y * z);
	elseif (y <= -34000000000000.0)
		tmp = t_0;
	elseif (y <= -1.65e-118)
		tmp = Float64(y * z);
	elseif (y <= 8e-22)
		tmp = x;
	elseif (y <= 8.5e+141)
		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 <= -7.5e+145)
		tmp = y * z;
	elseif (y <= -34000000000000.0)
		tmp = t_0;
	elseif (y <= -1.65e-118)
		tmp = y * z;
	elseif (y <= 8e-22)
		tmp = x;
	elseif (y <= 8.5e+141)
		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, -7.5e+145], N[(y * z), $MachinePrecision], If[LessEqual[y, -34000000000000.0], t$95$0, If[LessEqual[y, -1.65e-118], N[(y * z), $MachinePrecision], If[LessEqual[y, 8e-22], x, If[LessEqual[y, 8.5e+141], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000006e145 or -3.4e13 < y < -1.65e-118 or 8.0000000000000004e-22 < y < 8.4999999999999996e141

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.0%

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

   4. Taylor expanded in z around inf 64.9%

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

   if -7.50000000000000006e145 < y < -3.4e13 or 8.4999999999999996e141 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in y around inf 64.3%

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

      1. neg-mul-1 64.3%

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

      2. distribute-rgt-neg-in 64.3%

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

   8. Simplified 64.3%

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

   if -1.65e-118 < y < 8.0000000000000004e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -34000000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160 \lor \neg \left(y \leq 0.55\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -160.0) (not (<= y 0.55))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -160.0) || !(y <= 0.55)) {
		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 <= (-160.0d0)) .or. (.not. (y <= 0.55d0))) 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 <= -160.0) || !(y <= 0.55)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -160.0) or not (y <= 0.55):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -160.0) || !(y <= 0.55))
		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 <= -160.0) || ~((y <= 0.55)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -160.0], N[Not[LessEqual[y, 0.55]], $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 < -160 or 0.55000000000000004 < 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 99.1%

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

   if -160 < y < 0.55000000000000004

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160 \lor \neg \left(y \leq 0.55\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-118} \lor \neg \left(y \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e-118) (not (<= y 4e-21))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e-118) || !(y <= 4e-21)) {
		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 <= (-1.65d-118)) .or. (.not. (y <= 4d-21))) 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 <= -1.65e-118) || !(y <= 4e-21)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e-118) or not (y <= 4e-21):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e-118) || !(y <= 4e-21))
		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 <= -1.65e-118) || ~((y <= 4e-21)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e-118], N[Not[LessEqual[y, 4e-21]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-118 or 3.99999999999999963e-21 < 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 93.6%

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

   if -1.65e-118 < y < 3.99999999999999963e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-118} \lor \neg \left(y \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+65} \lor \neg \left(z \leq 5500\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e+65) (not (<= z 5500.0))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+65) || !(z <= 5500.0)) {
		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 <= (-4.8d+65)) .or. (.not. (z <= 5500.0d0))) 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 <= -4.8e+65) || !(z <= 5500.0)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e+65) or not (z <= 5500.0):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e+65) || !(z <= 5500.0))
		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 <= -4.8e+65) || ~((z <= 5500.0)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e+65], N[Not[LessEqual[z, 5500.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000003e65 or 5500 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 94.0%

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

   4. Taylor expanded in z around inf 78.9%

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

   if -4.8000000000000003e65 < z < 5500

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+65} \lor \neg \left(z \leq 5500\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-118} \lor \neg \left(y \leq 4.4 \cdot 10^{-21}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.2e-118) (not (<= y 4.4e-21))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e-118) || !(y <= 4.4e-21)) {
		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 <= (-1.2d-118)) .or. (.not. (y <= 4.4d-21))) 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 <= -1.2e-118) || !(y <= 4.4e-21)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.2e-118) or not (y <= 4.4e-21):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.2e-118) || !(y <= 4.4e-21))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.2e-118) || ~((y <= 4.4e-21)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.2e-118], N[Not[LessEqual[y, 4.4e-21]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e-118 or 4.4000000000000001e-21 < 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 54.5%

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

   if -1.2000000000000001e-118 < y < 4.4000000000000001e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-118} \lor \neg \left(y \leq 4.4 \cdot 10^{-21}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 35.6% 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 31.4%

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

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))