SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 7

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: 60.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+78}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+72} \lor \neg \left(y \leq 1.48 \cdot 10^{+165}\right) \land y \leq 4.2 \cdot 10^{+219}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -6.6e+78)
     (* y z)
     (if (<= y -4.5e+43)
       t_0
       (if (<= y -3.7e-15)
         (* y z)
         (if (<= y 3e-184)
           x
           (if (<= y 9.2e-156)
             (* y z)
             (if (<= y 6e-51)
               x
               (if (or (<= y 3.4e+72)
                       (and (not (<= y 1.48e+165)) (<= y 4.2e+219)))
                 (* y z)
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -6.6e+78) {
		tmp = y * z;
	} else if (y <= -4.5e+43) {
		tmp = t_0;
	} else if (y <= -3.7e-15) {
		tmp = y * z;
	} else if (y <= 3e-184) {
		tmp = x;
	} else if (y <= 9.2e-156) {
		tmp = y * z;
	} else if (y <= 6e-51) {
		tmp = x;
	} else if ((y <= 3.4e+72) || (!(y <= 1.48e+165) && (y <= 4.2e+219))) {
		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 <= (-6.6d+78)) then
        tmp = y * z
    else if (y <= (-4.5d+43)) then
        tmp = t_0
    else if (y <= (-3.7d-15)) then
        tmp = y * z
    else if (y <= 3d-184) then
        tmp = x
    else if (y <= 9.2d-156) then
        tmp = y * z
    else if (y <= 6d-51) then
        tmp = x
    else if ((y <= 3.4d+72) .or. (.not. (y <= 1.48d+165)) .and. (y <= 4.2d+219)) 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 <= -6.6e+78) {
		tmp = y * z;
	} else if (y <= -4.5e+43) {
		tmp = t_0;
	} else if (y <= -3.7e-15) {
		tmp = y * z;
	} else if (y <= 3e-184) {
		tmp = x;
	} else if (y <= 9.2e-156) {
		tmp = y * z;
	} else if (y <= 6e-51) {
		tmp = x;
	} else if ((y <= 3.4e+72) || (!(y <= 1.48e+165) && (y <= 4.2e+219))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -6.6e+78:
		tmp = y * z
	elif y <= -4.5e+43:
		tmp = t_0
	elif y <= -3.7e-15:
		tmp = y * z
	elif y <= 3e-184:
		tmp = x
	elif y <= 9.2e-156:
		tmp = y * z
	elif y <= 6e-51:
		tmp = x
	elif (y <= 3.4e+72) or (not (y <= 1.48e+165) and (y <= 4.2e+219)):
		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 <= -6.6e+78)
		tmp = Float64(y * z);
	elseif (y <= -4.5e+43)
		tmp = t_0;
	elseif (y <= -3.7e-15)
		tmp = Float64(y * z);
	elseif (y <= 3e-184)
		tmp = x;
	elseif (y <= 9.2e-156)
		tmp = Float64(y * z);
	elseif (y <= 6e-51)
		tmp = x;
	elseif ((y <= 3.4e+72) || (!(y <= 1.48e+165) && (y <= 4.2e+219)))
		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 <= -6.6e+78)
		tmp = y * z;
	elseif (y <= -4.5e+43)
		tmp = t_0;
	elseif (y <= -3.7e-15)
		tmp = y * z;
	elseif (y <= 3e-184)
		tmp = x;
	elseif (y <= 9.2e-156)
		tmp = y * z;
	elseif (y <= 6e-51)
		tmp = x;
	elseif ((y <= 3.4e+72) || (~((y <= 1.48e+165)) && (y <= 4.2e+219)))
		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, -6.6e+78], N[(y * z), $MachinePrecision], If[LessEqual[y, -4.5e+43], t$95$0, If[LessEqual[y, -3.7e-15], N[(y * z), $MachinePrecision], If[LessEqual[y, 3e-184], x, If[LessEqual[y, 9.2e-156], N[(y * z), $MachinePrecision], If[LessEqual[y, 6e-51], x, If[Or[LessEqual[y, 3.4e+72], And[N[Not[LessEqual[y, 1.48e+165]], $MachinePrecision], LessEqual[y, 4.2e+219]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6e78 or -4.5e43 < y < -3.70000000000000017e-15 or 2.99999999999999991e-184 < y < 9.1999999999999998e-156 or 6.00000000000000005e-51 < y < 3.3999999999999998e72 or 1.48e165 < y < 4.19999999999999976e219

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 71.2%

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

   4. Taylor expanded in x around 0 66.0%

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

   if -6.6e78 < y < -4.5e43 or 3.3999999999999998e72 < y < 1.48e165 or 4.19999999999999976e219 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in y around inf 69.3%

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

      1. associate-*r* 69.3%

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

      2. mul-1-neg 69.3%

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

   8. Simplified 69.3%

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

   if -3.70000000000000017e-15 < y < 2.99999999999999991e-184 or 9.1999999999999998e-156 < y < 6.00000000000000005e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+78}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+72} \lor \neg \left(y \leq 1.48 \cdot 10^{+165}\right) \land y \leq 4.2 \cdot 10^{+219}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-14} \lor \neg \left(y \leq 3 \cdot 10^{-184}\right) \land \left(y \leq 9 \cdot 10^{-156} \lor \neg \left(y \leq 3.1 \cdot 10^{-55}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.55e-14)
         (and (not (<= y 3e-184)) (or (<= y 9e-156) (not (<= y 3.1e-55)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e-14) || (!(y <= 3e-184) && ((y <= 9e-156) || !(y <= 3.1e-55)))) {
		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 <= (-2.55d-14)) .or. (.not. (y <= 3d-184)) .and. (y <= 9d-156) .or. (.not. (y <= 3.1d-55))) 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 <= -2.55e-14) || (!(y <= 3e-184) && ((y <= 9e-156) || !(y <= 3.1e-55)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.55e-14) or (not (y <= 3e-184) and ((y <= 9e-156) or not (y <= 3.1e-55))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.55e-14) || (!(y <= 3e-184) && ((y <= 9e-156) || !(y <= 3.1e-55))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.55e-14) || (~((y <= 3e-184)) && ((y <= 9e-156) || ~((y <= 3.1e-55)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.55e-14], And[N[Not[LessEqual[y, 3e-184]], $MachinePrecision], Or[LessEqual[y, 9e-156], N[Not[LessEqual[y, 3.1e-55]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.5499999999999999e-14 or 2.99999999999999991e-184 < y < 8.99999999999999971e-156 or 3.09999999999999997e-55 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 61.4%

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

   4. Taylor expanded in x around 0 57.8%

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

   if -2.5499999999999999e-14 < y < 2.99999999999999991e-184 or 8.99999999999999971e-156 < y < 3.09999999999999997e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-14} \lor \neg \left(y \leq 3 \cdot 10^{-184}\right) \land \left(y \leq 9 \cdot 10^{-156} \lor \neg \left(y \leq 3.1 \cdot 10^{-55}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+70} \lor \neg \left(z \leq 10^{+44}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5e+70) (not (<= z 1e+44))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e+70) || !(z <= 1e+44)) {
		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 <= (-5.5d+70)) .or. (.not. (z <= 1d+44))) 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 <= -5.5e+70) || !(z <= 1e+44)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5e+70) or not (z <= 1e+44):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5e+70) || !(z <= 1e+44))
		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 <= -5.5e+70) || ~((z <= 1e+44)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5e+70], N[Not[LessEqual[z, 1e+44]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999986e70 or 1.0000000000000001e44 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.1%

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

   4. Taylor expanded in x around 0 75.4%

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

   if -5.49999999999999986e70 < z < 1.0000000000000001e44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+70} \lor \neg \left(z \leq 10^{+44}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16} \lor \neg \left(z \leq 9.8 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-16) (not (<= z 9.8e+31))) (+ x (* y z)) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-16) || !(z <= 9.8e+31)) {
		tmp = x + (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 <= (-8.5d-16)) .or. (.not. (z <= 9.8d+31))) then
        tmp = x + (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 <= -8.5e-16) || !(z <= 9.8e+31)) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-16) or not (z <= 9.8e+31):
		tmp = x + (y * z)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-16) || !(z <= 9.8e+31))
		tmp = Float64(x + 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 <= -8.5e-16) || ~((z <= 9.8e+31)))
		tmp = x + (y * z);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-16], N[Not[LessEqual[z, 9.8e+31]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e-16 or 9.79999999999999991e31 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.7%

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

   if -8.5000000000000001e-16 < z < 9.79999999999999991e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16} \lor \neg \left(z \leq 9.8 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
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. Final simplification 100.0%

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

Alternative 7: 36.7% 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 37.2%

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

4. Final simplification 37.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))