Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 8

Speedup: 1.0×

• 21.2% 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-def 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. Final simplification 100.0%

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

Alternative 2: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-28} \lor \neg \left(x \leq 2.5 \cdot 10^{-139}\right) \land \left(x \leq 1.8 \cdot 10^{-29} \lor \neg \left(x \leq 5.6 \cdot 10^{+40}\right)\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e-28)
         (and (not (<= x 2.5e-139)) (or (<= x 1.8e-29) (not (<= x 5.6e+40)))))
   (* x (+ y 1.0))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-28) || (!(x <= 2.5e-139) && ((x <= 1.8e-29) || !(x <= 5.6e+40)))) {
		tmp = x * (y + 1.0);
	} 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 ((x <= (-1.9d-28)) .or. (.not. (x <= 2.5d-139)) .and. (x <= 1.8d-29) .or. (.not. (x <= 5.6d+40))) then
        tmp = x * (y + 1.0d0)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-28) || (!(x <= 2.5e-139) && ((x <= 1.8e-29) || !(x <= 5.6e+40)))) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e-28) or (not (x <= 2.5e-139) and ((x <= 1.8e-29) or not (x <= 5.6e+40))):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e-28) || (!(x <= 2.5e-139) && ((x <= 1.8e-29) || !(x <= 5.6e+40))))
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e-28) || (~((x <= 2.5e-139)) && ((x <= 1.8e-29) || ~((x <= 5.6e+40)))))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e-28], And[N[Not[LessEqual[x, 2.5e-139]], $MachinePrecision], Or[LessEqual[x, 1.8e-29], N[Not[LessEqual[x, 5.6e+40]], $MachinePrecision]]]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000005e-28 or 2.50000000000000017e-139 < x < 1.79999999999999987e-29 or 5.6000000000000003e40 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -1.90000000000000005e-28 < x < 2.50000000000000017e-139 or 1.79999999999999987e-29 < x < 5.6000000000000003e40

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 93.6%

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

   3. Taylor expanded in x around 0 73.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-28} \lor \neg \left(x \leq 2.5 \cdot 10^{-139}\right) \land \left(x \leq 1.8 \cdot 10^{-29} \lor \neg \left(x \leq 5.6 \cdot 10^{+40}\right)\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+260}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+104)
   (* y x)
   (if (<= y -1.75e-6)
     (* y z)
     (if (<= y 4.4e-27) x (if (<= y 6e+260) (* y z) (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+104) {
		tmp = y * x;
	} else if (y <= -1.75e-6) {
		tmp = y * z;
	} else if (y <= 4.4e-27) {
		tmp = x;
	} else if (y <= 6e+260) {
		tmp = y * z;
	} 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 <= (-7d+104)) then
        tmp = y * x
    else if (y <= (-1.75d-6)) then
        tmp = y * z
    else if (y <= 4.4d-27) then
        tmp = x
    else if (y <= 6d+260) then
        tmp = y * z
    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 <= -7e+104) {
		tmp = y * x;
	} else if (y <= -1.75e-6) {
		tmp = y * z;
	} else if (y <= 4.4e-27) {
		tmp = x;
	} else if (y <= 6e+260) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+104:
		tmp = y * x
	elif y <= -1.75e-6:
		tmp = y * z
	elif y <= 4.4e-27:
		tmp = x
	elif y <= 6e+260:
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+104)
		tmp = Float64(y * x);
	elseif (y <= -1.75e-6)
		tmp = Float64(y * z);
	elseif (y <= 4.4e-27)
		tmp = x;
	elseif (y <= 6e+260)
		tmp = Float64(y * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+104)
		tmp = y * x;
	elseif (y <= -1.75e-6)
		tmp = y * z;
	elseif (y <= 4.4e-27)
		tmp = x;
	elseif (y <= 6e+260)
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+104], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.75e-6], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.4e-27], x, If[LessEqual[y, 6e+260], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000003e104 or 5.9999999999999996e260 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.6%

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

      1. +-commutative 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in y around inf 65.6%

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

   if -7.0000000000000003e104 < y < -1.74999999999999997e-6 or 4.39999999999999974e-27 < y < 5.9999999999999996e260

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 62.9%

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

   3. Taylor expanded in x around 0 59.9%

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

   if -1.74999999999999997e-6 < y < 4.39999999999999974e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+260}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-6} \lor \neg \left(y \leq 8.6 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.85e-6) (not (<= y 8.6e-30))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e-6) || !(y <= 8.6e-30)) {
		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 ((y <= (-1.85d-6)) .or. (.not. (y <= 8.6d-30))) 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 ((y <= -1.85e-6) || !(y <= 8.6e-30)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.85e-6) or not (y <= 8.6e-30):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.85e-6) || !(y <= 8.6e-30))
		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 ((y <= -1.85e-6) || ~((y <= 8.6e-30)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.85e-6], N[Not[LessEqual[y, 8.6e-30]], $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 y < -1.8500000000000001e-6 or 8.59999999999999932e-30 < 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-def 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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-rgt-in 93.4%

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

      5. associate-+r+ 93.4%

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

      6. *-commutative 93.4%

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

      7. *-commutative 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around inf 97.9%

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

   if -1.8500000000000001e-6 < y < 8.59999999999999932e-30

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.3%

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

      1. +-commutative 75.3%

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

   4. Simplified 75.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-6} \lor \neg \left(y \leq 8.6 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 5: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3100000000000 \lor \neg \left(y \leq 0.00185\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3100000000000.0) (not (<= y 0.00185)))
   (* y (+ x z))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3100000000000.0) || !(y <= 0.00185)) {
		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 <= (-3100000000000.0d0)) .or. (.not. (y <= 0.00185d0))) 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 <= -3100000000000.0) || !(y <= 0.00185)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3100000000000.0) or not (y <= 0.00185):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3100000000000.0) || !(y <= 0.00185))
		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 <= -3100000000000.0) || ~((y <= 0.00185)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3100000000000.0], N[Not[LessEqual[y, 0.00185]], $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 < -3.1e12 or 0.0018500000000000001 < 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-def 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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-rgt-in 92.9%

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

      5. associate-+r+ 92.9%

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

      6. *-commutative 92.9%

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

      7. *-commutative 92.9%

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

   5. Applied egg-rr 92.9%

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

   6. Taylor expanded in y around inf 99.9%

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

   if -3.1e12 < y < 0.0018500000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.7%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3100000000000 \lor \neg \left(y \leq 0.00185\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 59.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y * x);
	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 <= -1.0)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], x, N[(y * x), $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. Taylor expanded in x around inf 54.9%

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

      1. +-commutative 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in y around inf 54.8%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.7%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 8: 36.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 37.0%

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

3. Final simplification 37.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))