Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 16.0s

Alternatives: 8

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x + z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma y (+ x z) x))

C

double code(double x, double y, double z) {
	return fma(y, (x + z), x);
}

Julia

function code(x, y, z)
	return fma(y, Float64(x + z), x)
end

Wolfram

code[x_, y_, z_] := N[(y * N[(x + z), $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. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{x + z}, x\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x + z, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2e-5))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2e-5)) {
		tmp = y * (x + z);
	} 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 <= (-1.0d0)) .or. (.not. (y <= 2d-5))) then
        tmp = y * (x + z)
    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 <= -1.0) || !(y <= 2e-5)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 2e-5):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 2e-5))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 2e-5)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 2e-5]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.00000000000000016e-5 < 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%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf 98.8%

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

   if -1 < y < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1600000000 \lor \neg \left(y \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1600000000.0) (not (<= y 1.1e-5)))
   (* y (+ x z))
   (+ x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1600000000.0) || !(y <= 1.1e-5)) {
		tmp = y * (x + z);
	} 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 <= (-1600000000.0d0)) .or. (.not. (y <= 1.1d-5))) then
        tmp = y * (x + z)
    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 <= -1600000000.0) || !(y <= 1.1e-5)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1600000000.0) or not (y <= 1.1e-5):
		tmp = y * (x + z)
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1600000000.0) || !(y <= 1.1e-5))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1600000000.0) || ~((y <= 1.1e-5)))
		tmp = y * (x + z);
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1600000000.0], N[Not[LessEqual[y, 1.1e-5]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e9 or 1.1e-5 < 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%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf 100.0%

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

   if -1.6e9 < y < 1.1e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 68.7%

      \[\leadsto x + \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1600000000 \lor \neg \left(y \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-11} \lor \neg \left(y \leq 9.5 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.9e-11) (not (<= y 9.5e-7))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.9e-11) || !(y <= 9.5e-7)) {
		tmp = y * (x + 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 <= (-4.9d-11)) .or. (.not. (y <= 9.5d-7))) then
        tmp = y * (x + 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 <= -4.9e-11) || !(y <= 9.5e-7)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.9e-11) or not (y <= 9.5e-7):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.9e-11) || !(y <= 9.5e-7))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.9e-11) || ~((y <= 9.5e-7)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.9e-11], N[Not[LessEqual[y, 9.5e-7]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.8999999999999999e-11 or 9.5000000000000001e-7 < 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%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf 97.4%

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

   if -4.8999999999999999e-11 < y < 9.5000000000000001e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. clear-num 78.2%

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

      2. inv-pow 78.2%

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

   5. Applied egg-rr 78.2%

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

      1. unpow-1 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in y around 0 67.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-11} \lor \neg \left(y \leq 9.5 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * 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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * 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 <= -1.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. associate-+r+ 81.0%

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

      2. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in y around inf 94.5%

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

      1. associate-*r* 94.4%

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

   8. Simplified 94.4%

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

   9. Taylor expanded in z around 0 54.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.2%

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

      1. clear-num 79.0%

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

      2. inv-pow 79.0%

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

   5. Applied egg-rr 79.0%

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

      1. unpow-1 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in y around 0 65.7%

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

4. Final simplification 59.8%

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

Alternative 6: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0) (* y x) (if (<= y 1.8e-6) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.8e-6) {
		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 <= (-1.0d0)) then
        tmp = y * x
    else if (y <= 1.8d-6) 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 <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.8e-6) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= 1.8e-6:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y * x);
	elseif (y <= 1.8e-6)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = y * x;
	elseif (y <= 1.8e-6)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.8e-6], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 73.4%

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

      1. associate-+r+ 73.4%

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

      2. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in y around inf 93.3%

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

      1. associate-*r* 93.1%

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

   8. Simplified 93.1%

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

   9. Taylor expanded in z around 0 61.7%

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

   if -1 < y < 1.79999999999999992e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.0%

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

      1. clear-num 78.9%

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

      2. inv-pow 78.9%

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

   5. Applied egg-rr 78.9%

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

      1. unpow-1 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in y around 0 66.2%

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

   if 1.79999999999999992e-6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 54.7%

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

   4. Taylor expanded in z around inf 64.3%

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

   5. Taylor expanded in y around inf 53.7%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(x + z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (+ x z))))

C

double code(double x, double y, double z) {
	return x + (y * (x + z));
}

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 * (x + z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (x + z));
}

Python

def code(x, y, z):
	return x + (y * (x + z))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(x + z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (x + z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 36.1% 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 inf 90.0%

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

   1. clear-num 89.9%

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

   2. inv-pow 89.9%

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

5. Applied egg-rr 89.9%

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

   1. unpow-1 89.9%

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

7. Simplified 89.9%

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

8. Taylor expanded in y around 0 33.0%

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

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))