SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Alternatives: 6

Speedup: 1.0×

• 20.7% 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. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(z - x\right) \]

Alternative 2: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+121}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+65} \lor \neg \left(y \leq 3.8 \cdot 10^{+156}\right) \land y \leq 3.8 \cdot 10^{+197}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -3e+121)
     (* y z)
     (if (<= y -1.45e+31)
       t_0
       (if (<= y -8.5e-19)
         (* y z)
         (if (<= y 5.8e-18)
           x
           (if (or (<= y 2.2e+65) (and (not (<= y 3.8e+156)) (<= y 3.8e+197)))
             (* y z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -3e+121) {
		tmp = y * z;
	} else if (y <= -1.45e+31) {
		tmp = t_0;
	} else if (y <= -8.5e-19) {
		tmp = y * z;
	} else if (y <= 5.8e-18) {
		tmp = x;
	} else if ((y <= 2.2e+65) || (!(y <= 3.8e+156) && (y <= 3.8e+197))) {
		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 = x * -y
    if (y <= (-3d+121)) then
        tmp = y * z
    else if (y <= (-1.45d+31)) then
        tmp = t_0
    else if (y <= (-8.5d-19)) then
        tmp = y * z
    else if (y <= 5.8d-18) then
        tmp = x
    else if ((y <= 2.2d+65) .or. (.not. (y <= 3.8d+156)) .and. (y <= 3.8d+197)) 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 = x * -y;
	double tmp;
	if (y <= -3e+121) {
		tmp = y * z;
	} else if (y <= -1.45e+31) {
		tmp = t_0;
	} else if (y <= -8.5e-19) {
		tmp = y * z;
	} else if (y <= 5.8e-18) {
		tmp = x;
	} else if ((y <= 2.2e+65) || (!(y <= 3.8e+156) && (y <= 3.8e+197))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if y <= -3e+121:
		tmp = y * z
	elif y <= -1.45e+31:
		tmp = t_0
	elif y <= -8.5e-19:
		tmp = y * z
	elif y <= 5.8e-18:
		tmp = x
	elif (y <= 2.2e+65) or (not (y <= 3.8e+156) and (y <= 3.8e+197)):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -3e+121)
		tmp = Float64(y * z);
	elseif (y <= -1.45e+31)
		tmp = t_0;
	elseif (y <= -8.5e-19)
		tmp = Float64(y * z);
	elseif (y <= 5.8e-18)
		tmp = x;
	elseif ((y <= 2.2e+65) || (!(y <= 3.8e+156) && (y <= 3.8e+197)))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (y <= -3e+121)
		tmp = y * z;
	elseif (y <= -1.45e+31)
		tmp = t_0;
	elseif (y <= -8.5e-19)
		tmp = y * z;
	elseif (y <= 5.8e-18)
		tmp = x;
	elseif ((y <= 2.2e+65) || (~((y <= 3.8e+156)) && (y <= 3.8e+197)))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -3e+121], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.45e+31], t$95$0, If[LessEqual[y, -8.5e-19], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.8e-18], x, If[Or[LessEqual[y, 2.2e+65], And[N[Not[LessEqual[y, 3.8e+156]], $MachinePrecision], LessEqual[y, 3.8e+197]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000002e121 or -1.45e31 < y < -8.50000000000000003e-19 or 5.8e-18 < y < 2.1999999999999998e65 or 3.80000000000000024e156 < y < 3.8000000000000001e197

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 70.3%

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

   3. Taylor expanded in x around 0 66.6%

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

   if -3.0000000000000002e121 < y < -1.45e31 or 2.1999999999999998e65 < y < 3.80000000000000024e156 or 3.8000000000000001e197 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-lft-neg-out 75.3%

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

      3. *-commutative 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in y around inf 75.3%

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

      1. associate-*r* 75.3%

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

      2. mul-1-neg 75.3%

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

   7. Simplified 75.3%

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

   if -8.50000000000000003e-19 < y < 5.8e-18

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in x around inf 78.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+121}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+65} \lor \neg \left(y \leq 3.8 \cdot 10^{+156}\right) \land y \leq 3.8 \cdot 10^{+197}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot z\\ t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+156} \lor \neg \left(y \leq 3 \cdot 10^{+197}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y z))) (t_1 (* x (- y))))
   (if (<= y -9e+120)
     t_0
     (if (<= y -1.5e+31)
       t_1
       (if (<= y 5.7e+63)
         t_0
         (if (or (<= y 3.7e+156) (not (<= y 3e+197))) t_1 (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double t_1 = x * -y;
	double tmp;
	if (y <= -9e+120) {
		tmp = t_0;
	} else if (y <= -1.5e+31) {
		tmp = t_1;
	} else if (y <= 5.7e+63) {
		tmp = t_0;
	} else if ((y <= 3.7e+156) || !(y <= 3e+197)) {
		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 = x * -y
    if (y <= (-9d+120)) then
        tmp = t_0
    else if (y <= (-1.5d+31)) then
        tmp = t_1
    else if (y <= 5.7d+63) then
        tmp = t_0
    else if ((y <= 3.7d+156) .or. (.not. (y <= 3d+197))) 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 = x * -y;
	double tmp;
	if (y <= -9e+120) {
		tmp = t_0;
	} else if (y <= -1.5e+31) {
		tmp = t_1;
	} else if (y <= 5.7e+63) {
		tmp = t_0;
	} else if ((y <= 3.7e+156) || !(y <= 3e+197)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * z)
	t_1 = x * -y
	tmp = 0
	if y <= -9e+120:
		tmp = t_0
	elif y <= -1.5e+31:
		tmp = t_1
	elif y <= 5.7e+63:
		tmp = t_0
	elif (y <= 3.7e+156) or not (y <= 3e+197):
		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(x * Float64(-y))
	tmp = 0.0
	if (y <= -9e+120)
		tmp = t_0;
	elseif (y <= -1.5e+31)
		tmp = t_1;
	elseif (y <= 5.7e+63)
		tmp = t_0;
	elseif ((y <= 3.7e+156) || !(y <= 3e+197))
		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 = x * -y;
	tmp = 0.0;
	if (y <= -9e+120)
		tmp = t_0;
	elseif (y <= -1.5e+31)
		tmp = t_1;
	elseif (y <= 5.7e+63)
		tmp = t_0;
	elseif ((y <= 3.7e+156) || ~((y <= 3e+197)))
		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[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -9e+120], t$95$0, If[LessEqual[y, -1.5e+31], t$95$1, If[LessEqual[y, 5.7e+63], t$95$0, If[Or[LessEqual[y, 3.7e+156], N[Not[LessEqual[y, 3e+197]], $MachinePrecision]], t$95$1, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999953e120 or -1.49999999999999995e31 < y < 5.7000000000000002e63

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 89.2%

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

   if -8.99999999999999953e120 < y < -1.49999999999999995e31 or 5.7000000000000002e63 < y < 3.70000000000000001e156 or 3.0000000000000002e197 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-lft-neg-out 75.3%

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

      3. *-commutative 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in y around inf 75.3%

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

      1. associate-*r* 75.3%

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

      2. mul-1-neg 75.3%

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

   7. Simplified 75.3%

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

   if 3.70000000000000001e156 < y < 3.0000000000000002e197

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 70.9%

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

   3. Taylor expanded in x around 0 71.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+120}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+63}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+156} \lor \neg \left(y \leq 3 \cdot 10^{+197}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+18} \lor \neg \left(x \leq 7 \cdot 10^{-39}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e+18) (not (<= x 7e-39))) (- x (* x y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+18) || !(x <= 7e-39)) {
		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 <= (-8.2d+18)) .or. (.not. (x <= 7d-39))) 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 <= -8.2e+18) || !(x <= 7e-39)) {
		tmp = x - (x * y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e+18) or not (x <= 7e-39):
		tmp = x - (x * y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e+18) || !(x <= 7e-39))
		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 <= -8.2e+18) || ~((x <= 7e-39)))
		tmp = x - (x * y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e+18], N[Not[LessEqual[x, 7e-39]], $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 < -8.2e18 or 6.99999999999999999e-39 < x

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around 0 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-lft-neg-out 92.2%

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

      3. *-commutative 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in x around 0 92.2%

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

      1. neg-mul-1 92.2%

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

      2. distribute-rgt-in 92.2%

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

      3. *-lft-identity 92.2%

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

      4. cancel-sign-sub-inv 92.2%

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

   7. Simplified 92.2%

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

   if -8.2e18 < x < 6.99999999999999999e-39

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 86.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+18} \lor \neg \left(x \leq 7 \cdot 10^{-39}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.4e-19) (* y z) (if (<= y 9e-18) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.4e-19) {
		tmp = y * z;
	} else if (y <= 9e-18) {
		tmp = x;
	} 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 (y <= (-8.4d-19)) then
        tmp = y * z
    else if (y <= 9d-18) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.4e-19) {
		tmp = y * z;
	} else if (y <= 9e-18) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.4e-19:
		tmp = y * z
	elif y <= 9e-18:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.4e-19)
		tmp = Float64(y * z);
	elseif (y <= 9e-18)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.4e-19)
		tmp = y * z;
	elseif (y <= 9e-18)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.4e-19], N[(y * z), $MachinePrecision], If[LessEqual[y, 9e-18], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.3999999999999996e-19 or 8.99999999999999987e-18 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 54.6%

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

   3. Taylor expanded in x around 0 52.2%

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

   if -8.3999999999999996e-19 < y < 8.99999999999999987e-18

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in x around inf 78.0%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 37.3% 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. Taylor expanded in z around inf 75.9%

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

3. Taylor expanded in x around inf 39.0%

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

4. Final simplification 39.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))