SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 6

Speedup: 1.0×

• 20.9% 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, 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 2: 62.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+124}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-9}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 270000000000 \lor \neg \left(y \leq 2.6 \cdot 10^{+242}\right) \land y \leq 1.15 \cdot 10^{+303}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -3.6e+124)
     (* y z)
     (if (<= y -6.3e+29)
       t_0
       (if (<= y -1e-9)
         (* y z)
         (if (<= y 1.7e-10)
           x
           (if (or (<= y 270000000000.0)
                   (and (not (<= y 2.6e+242)) (<= y 1.15e+303)))
             (* y z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3.6e+124) {
		tmp = y * z;
	} else if (y <= -6.3e+29) {
		tmp = t_0;
	} else if (y <= -1e-9) {
		tmp = y * z;
	} else if (y <= 1.7e-10) {
		tmp = x;
	} else if ((y <= 270000000000.0) || (!(y <= 2.6e+242) && (y <= 1.15e+303))) {
		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 <= (-3.6d+124)) then
        tmp = y * z
    else if (y <= (-6.3d+29)) then
        tmp = t_0
    else if (y <= (-1d-9)) then
        tmp = y * z
    else if (y <= 1.7d-10) then
        tmp = x
    else if ((y <= 270000000000.0d0) .or. (.not. (y <= 2.6d+242)) .and. (y <= 1.15d+303)) 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 <= -3.6e+124) {
		tmp = y * z;
	} else if (y <= -6.3e+29) {
		tmp = t_0;
	} else if (y <= -1e-9) {
		tmp = y * z;
	} else if (y <= 1.7e-10) {
		tmp = x;
	} else if ((y <= 270000000000.0) || (!(y <= 2.6e+242) && (y <= 1.15e+303))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -3.6e+124:
		tmp = y * z
	elif y <= -6.3e+29:
		tmp = t_0
	elif y <= -1e-9:
		tmp = y * z
	elif y <= 1.7e-10:
		tmp = x
	elif (y <= 270000000000.0) or (not (y <= 2.6e+242) and (y <= 1.15e+303)):
		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 <= -3.6e+124)
		tmp = Float64(y * z);
	elseif (y <= -6.3e+29)
		tmp = t_0;
	elseif (y <= -1e-9)
		tmp = Float64(y * z);
	elseif (y <= 1.7e-10)
		tmp = x;
	elseif ((y <= 270000000000.0) || (!(y <= 2.6e+242) && (y <= 1.15e+303)))
		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 <= -3.6e+124)
		tmp = y * z;
	elseif (y <= -6.3e+29)
		tmp = t_0;
	elseif (y <= -1e-9)
		tmp = y * z;
	elseif (y <= 1.7e-10)
		tmp = x;
	elseif ((y <= 270000000000.0) || (~((y <= 2.6e+242)) && (y <= 1.15e+303)))
		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, -3.6e+124], N[(y * z), $MachinePrecision], If[LessEqual[y, -6.3e+29], t$95$0, If[LessEqual[y, -1e-9], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.7e-10], x, If[Or[LessEqual[y, 270000000000.0], And[N[Not[LessEqual[y, 2.6e+242]], $MachinePrecision], LessEqual[y, 1.15e+303]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999986e124 or -6.2999999999999998e29 < y < -1.00000000000000006e-9 or 1.70000000000000007e-10 < y < 2.7e11 or 2.5999999999999998e242 < y < 1.15e303

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 76.1%

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

   4. Taylor expanded in x around 0 74.0%

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

   if -3.59999999999999986e124 < y < -6.2999999999999998e29 or 2.7e11 < y < 2.5999999999999998e242 or 1.15e303 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-lft-neg-out 69.9%

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

      3. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 69.5%

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

      1. associate-*r* 69.5%

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

      2. mul-1-neg 69.5%

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

   8. Simplified 69.5%

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

   if -1.00000000000000006e-9 < y < 1.70000000000000007e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.5%

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

   4. Taylor expanded in x around inf 75.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+124}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-9}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 270000000000 \lor \neg \left(y \leq 2.6 \cdot 10^{+242}\right) \land y \leq 1.15 \cdot 10^{+303}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot z\\ t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 950000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+242} \lor \neg \left(y \leq 4.2 \cdot 10^{+301}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y z))) (t_1 (* y (- x))))
   (if (<= y -1.15e+125)
     t_0
     (if (<= y -2.7e+30)
       t_1
       (if (<= y 950000000000.0)
         t_0
         (if (or (<= y 2.75e+242) (not (<= y 4.2e+301))) t_1 (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double t_1 = y * -x;
	double tmp;
	if (y <= -1.15e+125) {
		tmp = t_0;
	} else if (y <= -2.7e+30) {
		tmp = t_1;
	} else if (y <= 950000000000.0) {
		tmp = t_0;
	} else if ((y <= 2.75e+242) || !(y <= 4.2e+301)) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * z)
    t_1 = y * -x
    if (y <= (-1.15d+125)) then
        tmp = t_0
    else if (y <= (-2.7d+30)) then
        tmp = t_1
    else if (y <= 950000000000.0d0) then
        tmp = t_0
    else if ((y <= 2.75d+242) .or. (.not. (y <= 4.2d+301))) then
        tmp = t_1
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double t_1 = y * -x;
	double tmp;
	if (y <= -1.15e+125) {
		tmp = t_0;
	} else if (y <= -2.7e+30) {
		tmp = t_1;
	} else if (y <= 950000000000.0) {
		tmp = t_0;
	} else if ((y <= 2.75e+242) || !(y <= 4.2e+301)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * z)
	t_1 = y * -x
	tmp = 0
	if y <= -1.15e+125:
		tmp = t_0
	elif y <= -2.7e+30:
		tmp = t_1
	elif y <= 950000000000.0:
		tmp = t_0
	elif (y <= 2.75e+242) or not (y <= 4.2e+301):
		tmp = t_1
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * z))
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.15e+125)
		tmp = t_0;
	elseif (y <= -2.7e+30)
		tmp = t_1;
	elseif (y <= 950000000000.0)
		tmp = t_0;
	elseif ((y <= 2.75e+242) || !(y <= 4.2e+301))
		tmp = t_1;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * z);
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -1.15e+125)
		tmp = t_0;
	elseif (y <= -2.7e+30)
		tmp = t_1;
	elseif (y <= 950000000000.0)
		tmp = t_0;
	elseif ((y <= 2.75e+242) || ~((y <= 4.2e+301)))
		tmp = t_1;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.15e+125], t$95$0, If[LessEqual[y, -2.7e+30], t$95$1, If[LessEqual[y, 950000000000.0], t$95$0, If[Or[LessEqual[y, 2.75e+242], N[Not[LessEqual[y, 4.2e+301]], $MachinePrecision]], t$95$1, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000006e125 or -2.6999999999999999e30 < y < 9.5e11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.5%

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

   if -1.15000000000000006e125 < y < -2.6999999999999999e30 or 9.5e11 < y < 2.75000000000000011e242 or 4.1999999999999999e301 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-lft-neg-out 69.9%

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

      3. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 69.5%

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

      1. associate-*r* 69.5%

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

      2. mul-1-neg 69.5%

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

   8. Simplified 69.5%

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

   if 2.75000000000000011e242 < y < 4.1999999999999999e301

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.3%

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

   4. Taylor expanded in x around 0 75.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 950000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+242} \lor \neg \left(y \leq 4.2 \cdot 10^{+301}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+78} \lor \neg \left(x \leq 1.4 \cdot 10^{-70}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.5e+78) (not (<= x 1.4e-70))) (- x (* x y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e+78) || !(x <= 1.4e-70)) {
		tmp = x - (x * y);
	} 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 ((x <= (-7.5d+78)) .or. (.not. (x <= 1.4d-70))) then
        tmp = x - (x * y)
    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 ((x <= -7.5e+78) || !(x <= 1.4e-70)) {
		tmp = x - (x * y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.5e+78) or not (x <= 1.4e-70):
		tmp = x - (x * y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.5e+78) || !(x <= 1.4e-70))
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.5e+78) || ~((x <= 1.4e-70)))
		tmp = x - (x * y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.5e+78], N[Not[LessEqual[x, 1.4e-70]], $MachinePrecision]], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999934e78 or 1.4e-70 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. distribute-lft-neg-out 89.3%

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

      3. *-commutative 89.3%

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

   5. Simplified 89.3%

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

      1. *-commutative 89.3%

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

      2. distribute-lft-neg-out 89.3%

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

      3. unsub-neg 89.3%

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

   7. Applied egg-rr 89.3%

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

   if -7.49999999999999934e78 < x < 1.4e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+78} \lor \neg \left(x \leq 1.4 \cdot 10^{-70}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-10} \lor \neg \left(y \leq 2.45 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e-10) (not (<= y 2.45e-17))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-10) || !(y <= 2.45e-17)) {
		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 <= (-7.5d-10)) .or. (.not. (y <= 2.45d-17))) 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 <= -7.5e-10) || !(y <= 2.45e-17)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e-10) or not (y <= 2.45e-17):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e-10) || !(y <= 2.45e-17))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e-10) || ~((y <= 2.45e-17)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e-10], N[Not[LessEqual[y, 2.45e-17]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999995e-10 or 2.45000000000000006e-17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 50.6%

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

   4. Taylor expanded in x around 0 49.9%

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

   if -7.49999999999999995e-10 < y < 2.45000000000000006e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.5%

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

   4. Taylor expanded in x around inf 75.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-10} \lor \neg \left(y \leq 2.45 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 z around inf 74.7%

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

4. Taylor expanded in x around inf 38.6%

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

5. Final simplification 38.6%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))