Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 8

Speedup: 1.0×

• 20.6% 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: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-35}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e-35)
   (* y z)
   (if (<= z -1.1e-250) x (if (<= z 1.9e+15) (* y x) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-35) {
		tmp = y * z;
	} else if (z <= -1.1e-250) {
		tmp = x;
	} else if (z <= 1.9e+15) {
		tmp = y * 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 (z <= (-1.55d-35)) then
        tmp = y * z
    else if (z <= (-1.1d-250)) then
        tmp = x
    else if (z <= 1.9d+15) then
        tmp = y * 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 (z <= -1.55e-35) {
		tmp = y * z;
	} else if (z <= -1.1e-250) {
		tmp = x;
	} else if (z <= 1.9e+15) {
		tmp = y * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e-35:
		tmp = y * z
	elif z <= -1.1e-250:
		tmp = x
	elif z <= 1.9e+15:
		tmp = y * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e-35)
		tmp = Float64(y * z);
	elseif (z <= -1.1e-250)
		tmp = x;
	elseif (z <= 1.9e+15)
		tmp = Float64(y * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e-35)
		tmp = y * z;
	elseif (z <= -1.1e-250)
		tmp = x;
	elseif (z <= 1.9e+15)
		tmp = y * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e-35], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.1e-250], x, If[LessEqual[z, 1.9e+15], N[(y * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000006e-35 or 1.9e15 < z

   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. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 93.7%

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

      5. associate-+r+ 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in x around 0 73.5%

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

   if -1.55000000000000006e-35 < z < -1.1e-250

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 62.9%

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

   if -1.1e-250 < z < 1.9e15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 89.2%

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

      1. +-commutative 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 54.5%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-35}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 1 < y

   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. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 93.9%

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

      5. associate-+r+ 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in y around inf 99.2%

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

      1. +-commutative 99.2%

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

   9. Simplified 99.2%

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

   if -1 < y < 1

   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 99.2%

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

Alternative 4: 79.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.22 \cdot 10^{-35} \lor \neg \left(z \leq 9800000000000\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.22e-35) (not (<= z 9800000000000.0)))
   (* y (+ x z))
   (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.22e-35) || !(z <= 9800000000000.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	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) :: tmp
    if ((z <= (-2.22d-35)) .or. (.not. (z <= 9800000000000.0d0))) then
        tmp = y * (x + z)
    else
        tmp = x * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.22e-35) || !(z <= 9800000000000.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.22e-35) or not (z <= 9800000000000.0):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.22e-35) || !(z <= 9800000000000.0))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.22e-35) || ~((z <= 9800000000000.0)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.22e-35], N[Not[LessEqual[z, 9800000000000.0]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.21999999999999988e-35 or 9.8e12 < z

   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. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 93.7%

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

      5. associate-+r+ 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in y around inf 82.7%

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

      1. +-commutative 82.7%

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

   9. Simplified 82.7%

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

   if -2.21999999999999988e-35 < z < 9.8e12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.3%

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

      1. +-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.22 \cdot 10^{-35} \lor \neg \left(z \leq 9800000000000\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{-6} \lor \neg \left(z \leq 4 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.1e-6) (not (<= z 4e+15))) (* y z) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.1e-6) || !(z <= 4e+15)) {
		tmp = y * z;
	} else {
		tmp = x * (y + 1.0);
	}
	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) :: tmp
    if ((z <= (-7.1d-6)) .or. (.not. (z <= 4d+15))) then
        tmp = y * z
    else
        tmp = x * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.1e-6) || !(z <= 4e+15)) {
		tmp = y * z;
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.1e-6) or not (z <= 4e+15):
		tmp = y * z
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.1e-6) || !(z <= 4e+15))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.1e-6) || ~((z <= 4e+15)))
		tmp = y * z;
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.1e-6], N[Not[LessEqual[z, 4e+15]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0999999999999998e-6 or 4e15 < z

   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. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 93.4%

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

      5. associate-+r+ 93.4%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in x around 0 74.9%

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

   if -7.0999999999999998e-6 < z < 4e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{-6} \lor \neg \left(z \leq 4 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 235\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 235.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 235.0)) {
		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 <= 235.0d0))) 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 <= 235.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 235.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 235.0))
		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 <= 235.0)))
		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, 235.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 235 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.4%

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

      1. +-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in y around inf 55.6%

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

   if -1 < y < 235

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 63.9%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 235\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 36.6% 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 32.6%

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))