SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 8

Speedup: 1.0×

• 20.8% 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: 61.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.55 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+65} \lor \neg \left(y \leq 7.6 \cdot 10^{+183}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.42e+184)
     t_0
     (if (<= y -4.55e-10)
       (* y z)
       (if (<= y 3.6e-58)
         x
         (if (or (<= y 1.9e+65) (not (<= y 7.6e+183))) (* y z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.42e+184) {
		tmp = t_0;
	} else if (y <= -4.55e-10) {
		tmp = y * z;
	} else if (y <= 3.6e-58) {
		tmp = x;
	} else if ((y <= 1.9e+65) || !(y <= 7.6e+183)) {
		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 <= (-1.42d+184)) then
        tmp = t_0
    else if (y <= (-4.55d-10)) then
        tmp = y * z
    else if (y <= 3.6d-58) then
        tmp = x
    else if ((y <= 1.9d+65) .or. (.not. (y <= 7.6d+183))) 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 <= -1.42e+184) {
		tmp = t_0;
	} else if (y <= -4.55e-10) {
		tmp = y * z;
	} else if (y <= 3.6e-58) {
		tmp = x;
	} else if ((y <= 1.9e+65) || !(y <= 7.6e+183)) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -1.42e+184:
		tmp = t_0
	elif y <= -4.55e-10:
		tmp = y * z
	elif y <= 3.6e-58:
		tmp = x
	elif (y <= 1.9e+65) or not (y <= 7.6e+183):
		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 <= -1.42e+184)
		tmp = t_0;
	elseif (y <= -4.55e-10)
		tmp = Float64(y * z);
	elseif (y <= 3.6e-58)
		tmp = x;
	elseif ((y <= 1.9e+65) || !(y <= 7.6e+183))
		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 <= -1.42e+184)
		tmp = t_0;
	elseif (y <= -4.55e-10)
		tmp = y * z;
	elseif (y <= 3.6e-58)
		tmp = x;
	elseif ((y <= 1.9e+65) || ~((y <= 7.6e+183)))
		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, -1.42e+184], t$95$0, If[LessEqual[y, -4.55e-10], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.6e-58], x, If[Or[LessEqual[y, 1.9e+65], N[Not[LessEqual[y, 7.6e+183]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42000000000000002e184 or 1.90000000000000006e65 < y < 7.60000000000000002e183

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in y around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-rgt-neg-out 71.6%

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

   8. Simplified 71.6%

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

   if -1.42000000000000002e184 < y < -4.5499999999999998e-10 or 3.60000000000000009e-58 < y < 1.90000000000000006e65 or 7.60000000000000002e183 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 62.9%

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

   if -4.5499999999999998e-10 < y < 3.60000000000000009e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -4.55 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+65} \lor \neg \left(y \leq 7.6 \cdot 10^{+183}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+16} \lor \neg \left(x \leq 1.3 \cdot 10^{-136}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e+16) (not (<= x 1.3e-136))) (* x (- 1.0 y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e+16) || !(x <= 1.3e-136)) {
		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 <= (-1.8d+16)) .or. (.not. (x <= 1.3d-136))) 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 <= -1.8e+16) || !(x <= 1.3e-136)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e+16) or not (x <= 1.3e-136):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e+16) || !(x <= 1.3e-136))
		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 <= -1.8e+16) || ~((x <= 1.3e-136)))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e+16], N[Not[LessEqual[x, 1.3e-136]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e16 or 1.29999999999999998e-136 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   5. Simplified 85.6%

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

   if -1.8e16 < x < 1.29999999999999998e-136

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+16} \lor \neg \left(x \leq 1.3 \cdot 10^{-136}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14} \lor \neg \left(y \leq 3.2 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+14) (not (<= y 3.2e-58))) (* y (- z x)) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+14) || !(y <= 3.2e-58)) {
		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 <= (-4.4d+14)) .or. (.not. (y <= 3.2d-58))) 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 <= -4.4e+14) || !(y <= 3.2e-58)) {
		tmp = y * (z - x);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e+14) or not (y <= 3.2e-58):
		tmp = y * (z - x)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e+14) || !(y <= 3.2e-58))
		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 <= -4.4e+14) || ~((y <= 3.2e-58)))
		tmp = y * (z - x);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e+14], N[Not[LessEqual[y, 3.2e-58]], $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 < -4.4e14 or 3.2000000000000001e-58 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.5%

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

   if -4.4e14 < y < 3.2000000000000001e-58

   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 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14} \lor \neg \left(y \leq 3.2 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14} \lor \neg \left(y \leq 3.6 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+14) (not (<= y 3.6e-58))) (* y (- z x)) (- x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+14) || !(y <= 3.6e-58)) {
		tmp = y * (z - x);
	} else {
		tmp = x - (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 <= (-4.4d+14)) .or. (.not. (y <= 3.6d-58))) then
        tmp = y * (z - x)
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+14) || !(y <= 3.6e-58)) {
		tmp = y * (z - x);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e+14) or not (y <= 3.6e-58):
		tmp = y * (z - x)
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e+14) || !(y <= 3.6e-58))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.4e+14) || ~((y <= 3.6e-58)))
		tmp = y * (z - x);
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e+14], N[Not[LessEqual[y, 3.6e-58]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e14 or 3.60000000000000009e-58 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.5%

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

   if -4.4e14 < y < 3.60000000000000009e-58

   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%

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

      1. sub-neg 80.7%

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

      2. distribute-rgt-in 80.7%

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

      3. *-un-lft-identity 80.7%

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

   7. Applied egg-rr 80.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14} \lor \neg \left(y \leq 3.6 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-9} \lor \neg \left(y \leq 1.65 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.75e-9) (not (<= y 1.65e-58))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.75e-9) || !(y <= 1.65e-58)) {
		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 <= (-1.75d-9)) .or. (.not. (y <= 1.65d-58))) 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 <= -1.75e-9) || !(y <= 1.65e-58)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.75e-9) or not (y <= 1.65e-58):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.75e-9) || !(y <= 1.65e-58))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.75e-9) || ~((y <= 1.65e-58)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.75e-9], N[Not[LessEqual[y, 1.65e-58]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e-9 or 1.65000000000000013e-58 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.5%

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

   if -1.75e-9 < y < 1.65000000000000013e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-9} \lor \neg \left(y \leq 1.65 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 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. Add Preprocessing

3. Taylor expanded in y around 0 39.7%

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

4. Final simplification 39.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))