Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 8

Speedup: 1.0×

• 21.9% 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. Final simplification 100.0%

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

Alternative 2: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-22} \lor \neg \left(y \leq 1.32 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e-22) (not (<= y 1.32e-17))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-22) || !(y <= 1.32e-17)) {
		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 <= (-2.9d-22)) .or. (.not. (y <= 1.32d-17))) 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 <= -2.9e-22) || !(y <= 1.32e-17)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e-22) or not (y <= 1.32e-17):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e-22) || !(y <= 1.32e-17))
		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 <= -2.9e-22) || ~((y <= 1.32e-17)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e-22], N[Not[LessEqual[y, 1.32e-17]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e-22 or 1.3200000000000001e-17 < 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 96.9%

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

      5. associate-+r+ 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in y around inf 99.9%

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

      1. +-commutative 99.9%

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

   9. Simplified 99.9%

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

   if -2.9000000000000002e-22 < y < 1.3200000000000001e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.9%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-22} \lor \neg \left(y \leq 1.32 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-16} \lor \neg \left(y \leq 8.2 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e-16) (not (<= y 8.2e-19))) (* y (+ x z)) (+ x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-16) || !(y <= 8.2e-19)) {
		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 <= (-3.2d-16)) .or. (.not. (y <= 8.2d-19))) 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 <= -3.2e-16) || !(y <= 8.2e-19)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e-16) or not (y <= 8.2e-19):
		tmp = y * (x + z)
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e-16) || !(y <= 8.2e-19))
		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 <= -3.2e-16) || ~((y <= 8.2e-19)))
		tmp = y * (x + z);
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e-16], N[Not[LessEqual[y, 8.2e-19]], $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 < -3.20000000000000023e-16 or 8.1999999999999997e-19 < 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 96.9%

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

      5. associate-+r+ 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in y around inf 99.9%

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

      1. +-commutative 99.9%

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

   9. Simplified 99.9%

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

   if -3.20000000000000023e-16 < y < 8.1999999999999997e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 3.9%

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

   5. Simplified 72.9%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-16} \lor \neg \left(y \leq 8.2 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62000 \lor \neg \left(y \leq 6 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -62000.0) (not (<= y 6e-16))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -62000.0) || !(y <= 6e-16)) {
		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 <= (-62000.0d0)) .or. (.not. (y <= 6d-16))) 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 <= -62000.0) || !(y <= 6e-16)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -62000.0) or not (y <= 6e-16):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -62000.0) || !(y <= 6e-16))
		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 <= -62000.0) || ~((y <= 6e-16)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -62000.0], N[Not[LessEqual[y, 6e-16]], $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 < -62000 or 5.99999999999999987e-16 < 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 96.8%

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

      5. associate-+r+ 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in y around inf 99.9%

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

      1. +-commutative 99.9%

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

   9. Simplified 99.9%

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

   if -62000 < y < 5.99999999999999987e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000 \lor \neg \left(y \leq 6 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -62000.0) (not (<= y 1.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -62000.0) || !(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 <= (-62000.0d0)) .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 <= -62000.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -62000.0) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -62000.0) || !(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 <= -62000.0) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -62000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -62000 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 96.7%

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

      5. associate-+r+ 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around inf 99.9%

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

      1. +-commutative 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in z around 0 50.9%

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

       1. *-commutative 50.9%

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

   12. Simplified 50.9%

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

   if -62000 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-71) (* y z) (if (<= y 1.0) x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-71) {
		tmp = y * z;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 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 <= (-4.2d-71)) then
        tmp = y * z
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-71) {
		tmp = y * z;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e-71:
		tmp = y * z
	elif y <= 1.0:
		tmp = x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e-71)
		tmp = Float64(y * z);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e-71)
		tmp = y * z;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e-71], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.0], x, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000002e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 82.4%

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

      1. associate-+r+ 82.4%

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

      2. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x around 0 58.8%

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

   if -4.2000000000000002e-71 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.3%

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

   if 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 95.0%

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

      5. associate-+r+ 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in z around 0 56.2%

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

       1. *-commutative 56.2%

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

   12. Simplified 56.2%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
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: 35.5% 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. Taylor expanded in y around 0 37.7%

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

4. Final simplification 37.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024050 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))