Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

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

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

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: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+15} \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+15) (not (<= y 0.195))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+15) || !(y <= 0.195)) {
		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 <= (-3d+15)) .or. (.not. (y <= 0.195d0))) 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 <= -3e+15) || !(y <= 0.195)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+15) or not (y <= 0.195):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+15) || !(y <= 0.195))
		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 <= -3e+15) || ~((y <= 0.195)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+15], N[Not[LessEqual[y, 0.195]], $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 < -3e15 or 0.19500000000000001 < 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. Taylor expanded in z around inf 99.5%

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

   if -3e15 < y < 0.19500000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.1%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+15} \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-69} \lor \neg \left(y \leq 4.5 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-69) (not (<= y 4.5e-11))) (* y (+ x z)) (+ x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-69) || !(y <= 4.5e-11)) {
		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 <= (-4d-69)) .or. (.not. (y <= 4.5d-11))) 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 <= -4e-69) || !(y <= 4.5e-11)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-69) or not (y <= 4.5e-11):
		tmp = y * (x + z)
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-69) || !(y <= 4.5e-11))
		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 <= -4e-69) || ~((y <= 4.5e-11)))
		tmp = y * (x + z);
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-69], N[Not[LessEqual[y, 4.5e-11]], $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 < -3.9999999999999999e-69 or 4.5e-11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

   4. Taylor expanded in z around inf 95.0%

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

   if -3.9999999999999999e-69 < y < 4.5e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-69} \lor \neg \left(y \leq 4.5 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-70} \lor \neg \left(y \leq 1.05 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e-70) (not (<= y 1.05e-10))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e-70) || !(y <= 1.05e-10)) {
		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 <= (-7d-70)) .or. (.not. (y <= 1.05d-10))) 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 <= -7e-70) || !(y <= 1.05e-10)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e-70) or not (y <= 1.05e-10):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e-70) || !(y <= 1.05e-10))
		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 <= -7e-70) || ~((y <= 1.05e-10)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e-70], N[Not[LessEqual[y, 1.05e-10]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999949e-70 or 1.05e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

   4. Taylor expanded in z around inf 95.0%

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

   if -6.99999999999999949e-70 < y < 1.05e-10

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. distribute-rgt-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 70.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-70} \lor \neg \left(y \leq 1.05 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-72} \lor \neg \left(y \leq 1.6 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e-72) (not (<= y 1.6e-11))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e-72) || !(y <= 1.6e-11)) {
		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 <= (-7d-72)) .or. (.not. (y <= 1.6d-11))) 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 <= -7e-72) || !(y <= 1.6e-11)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e-72) or not (y <= 1.6e-11):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e-72) || !(y <= 1.6e-11))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e-72) || ~((y <= 1.6e-11)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e-72], N[Not[LessEqual[y, 1.6e-11]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000001e-72 or 1.59999999999999997e-11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

   4. Taylor expanded in z around inf 95.0%

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

   5. Taylor expanded in x around 0 61.2%

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

   if -7.00000000000000001e-72 < y < 1.59999999999999997e-11

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. distribute-rgt-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 70.3%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-72} \lor \neg \left(y \leq 1.6 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1800000 \lor \neg \left(y \leq 2.25 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1800000.0) (not (<= y 2.25e-8))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1800000.0) || !(y <= 2.25e-8)) {
		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 <= (-1800000.0d0)) .or. (.not. (y <= 2.25d-8))) 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 <= -1800000.0) || !(y <= 2.25e-8)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1800000.0) or not (y <= 2.25e-8):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1800000.0) || !(y <= 2.25e-8))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1800000.0) || ~((y <= 2.25e-8)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1800000.0], N[Not[LessEqual[y, 2.25e-8]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e6 or 2.24999999999999996e-8 < 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. Taylor expanded in z around inf 99.0%

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

   5. Taylor expanded in x around inf 44.5%

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

      1. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   if -1.8e6 < y < 2.24999999999999996e-8

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. distribute-rgt-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 65.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1800000 \lor \neg \left(y \leq 2.25 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 37.5% 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. Step-by-step derivation

   1. distribute-rgt-in 96.5%

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

   2. fma-define 97.3%

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

   3. *-commutative 97.3%

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

4. Applied egg-rr 97.3%

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

5. Taylor expanded in y around 0 34.7%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))