Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 8

Speedup: 1.0×

• 20.8% 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: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+214}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-71}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-49}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+214)
   (* y z)
   (if (<= y -3.5e+167)
     (* y x)
     (if (<= y -4e-71)
       (* y z)
       (if (<= y 9.2e-104)
         x
         (if (<= y 6.4e-49) (* y z) (if (<= y 1.6e-14) x (* y z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+214) {
		tmp = y * z;
	} else if (y <= -3.5e+167) {
		tmp = y * x;
	} else if (y <= -4e-71) {
		tmp = y * z;
	} else if (y <= 9.2e-104) {
		tmp = x;
	} else if (y <= 6.4e-49) {
		tmp = y * z;
	} else if (y <= 1.6e-14) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.05d+214)) then
        tmp = y * z
    else if (y <= (-3.5d+167)) then
        tmp = y * x
    else if (y <= (-4d-71)) then
        tmp = y * z
    else if (y <= 9.2d-104) then
        tmp = x
    else if (y <= 6.4d-49) then
        tmp = y * z
    else if (y <= 1.6d-14) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+214) {
		tmp = y * z;
	} else if (y <= -3.5e+167) {
		tmp = y * x;
	} else if (y <= -4e-71) {
		tmp = y * z;
	} else if (y <= 9.2e-104) {
		tmp = x;
	} else if (y <= 6.4e-49) {
		tmp = y * z;
	} else if (y <= 1.6e-14) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+214:
		tmp = y * z
	elif y <= -3.5e+167:
		tmp = y * x
	elif y <= -4e-71:
		tmp = y * z
	elif y <= 9.2e-104:
		tmp = x
	elif y <= 6.4e-49:
		tmp = y * z
	elif y <= 1.6e-14:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+214)
		tmp = Float64(y * z);
	elseif (y <= -3.5e+167)
		tmp = Float64(y * x);
	elseif (y <= -4e-71)
		tmp = Float64(y * z);
	elseif (y <= 9.2e-104)
		tmp = x;
	elseif (y <= 6.4e-49)
		tmp = Float64(y * z);
	elseif (y <= 1.6e-14)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+214)
		tmp = y * z;
	elseif (y <= -3.5e+167)
		tmp = y * x;
	elseif (y <= -4e-71)
		tmp = y * z;
	elseif (y <= 9.2e-104)
		tmp = x;
	elseif (y <= 6.4e-49)
		tmp = y * z;
	elseif (y <= 1.6e-14)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+214], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.5e+167], N[(y * x), $MachinePrecision], If[LessEqual[y, -4e-71], N[(y * z), $MachinePrecision], If[LessEqual[y, 9.2e-104], x, If[LessEqual[y, 6.4e-49], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.6e-14], x, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e214 or -3.49999999999999987e167 < y < -3.9999999999999997e-71 or 9.1999999999999998e-104 < y < 6.40000000000000005e-49 or 1.6000000000000001e-14 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 95.7%

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

      1. mul-1-neg 95.7%

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

      2. unsub-neg 95.7%

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

      3. *-commutative 95.7%

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

      4. sub-neg 95.7%

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

      5. metadata-eval 95.7%

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

      6. +-commutative 95.7%

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

      7. mul-1-neg 95.7%

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

      8. unsub-neg 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in z around inf 65.3%

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

   if -1.05e214 < y < -3.49999999999999987e167

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.6%

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

   3. Taylor expanded in y around inf 83.6%

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

   if -3.9999999999999997e-71 < y < 9.1999999999999998e-104 or 6.40000000000000005e-49 < y < 1.6000000000000001e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+214}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-71}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-49}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-71} \lor \neg \left(y \leq 9.2 \cdot 10^{-104}\right) \land \left(y \leq 5.9 \cdot 10^{-49} \lor \neg \left(y \leq 2 \cdot 10^{-16}\right)\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-71)
         (and (not (<= y 9.2e-104)) (or (<= y 5.9e-49) (not (<= y 2e-16)))))
   (* y (+ x z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-71) || (!(y <= 9.2e-104) && ((y <= 5.9e-49) || !(y <= 2e-16)))) {
		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 <= (-6.5d-71)) .or. (.not. (y <= 9.2d-104)) .and. (y <= 5.9d-49) .or. (.not. (y <= 2d-16))) 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 <= -6.5e-71) || (!(y <= 9.2e-104) && ((y <= 5.9e-49) || !(y <= 2e-16)))) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-71) or (not (y <= 9.2e-104) and ((y <= 5.9e-49) or not (y <= 2e-16))):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-71) || (!(y <= 9.2e-104) && ((y <= 5.9e-49) || !(y <= 2e-16))))
		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 <= -6.5e-71) || (~((y <= 9.2e-104)) && ((y <= 5.9e-49) || ~((y <= 2e-16)))))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-71], And[N[Not[LessEqual[y, 9.2e-104]], $MachinePrecision], Or[LessEqual[y, 5.9e-49], N[Not[LessEqual[y, 2e-16]], $MachinePrecision]]]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000005e-71 or 9.1999999999999998e-104 < y < 5.90000000000000037e-49 or 2e-16 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.6%

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

   if -6.50000000000000005e-71 < y < 9.1999999999999998e-104 or 5.90000000000000037e-49 < y < 2e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-71} \lor \neg \left(y \leq 9.2 \cdot 10^{-104}\right) \land \left(y \leq 5.9 \cdot 10^{-49} \lor \neg \left(y \leq 2 \cdot 10^{-16}\right)\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-70} \lor \neg \left(y \leq 9.2 \cdot 10^{-104}\right) \land \left(y \leq 5.8 \cdot 10^{-49} \lor \neg \left(y \leq 2.1 \cdot 10^{-14}\right)\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.15e-70)
         (and (not (<= y 9.2e-104)) (or (<= y 5.8e-49) (not (<= y 2.1e-14)))))
   (* y (+ x z))
   (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e-70) || (!(y <= 9.2e-104) && ((y <= 5.8e-49) || !(y <= 2.1e-14)))) {
		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 <= (-2.15d-70)) .or. (.not. (y <= 9.2d-104)) .and. (y <= 5.8d-49) .or. (.not. (y <= 2.1d-14))) 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 <= -2.15e-70) || (!(y <= 9.2e-104) && ((y <= 5.8e-49) || !(y <= 2.1e-14)))) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.15e-70) or (not (y <= 9.2e-104) and ((y <= 5.8e-49) or not (y <= 2.1e-14))):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.15e-70) || (!(y <= 9.2e-104) && ((y <= 5.8e-49) || !(y <= 2.1e-14))))
		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 <= -2.15e-70) || (~((y <= 9.2e-104)) && ((y <= 5.8e-49) || ~((y <= 2.1e-14)))))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.15e-70], And[N[Not[LessEqual[y, 9.2e-104]], $MachinePrecision], Or[LessEqual[y, 5.8e-49], N[Not[LessEqual[y, 2.1e-14]], $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 < -2.15e-70 or 9.1999999999999998e-104 < y < 5.8e-49 or 2.0999999999999999e-14 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.6%

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

   if -2.15e-70 < y < 9.1999999999999998e-104 or 5.8e-49 < y < 2.0999999999999999e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-70} \lor \neg \left(y \leq 9.2 \cdot 10^{-104}\right) \land \left(y \leq 5.8 \cdot 10^{-49} \lor \neg \left(y \leq 2.1 \cdot 10^{-14}\right)\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.4 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.4e-7))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.4e-7)) {
		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 <= 2.4d-7))) 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 <= 2.4e-7)) {
		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 <= 2.4e-7):
		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 <= 2.4e-7))
		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 <= 2.4e-7)))
		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, 2.4e-7]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.39999999999999979e-7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.1%

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

   if -1 < y < 2.39999999999999979e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.4 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1020000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0) (* y x) (if (<= y 1020000000.0) x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1020000000.0) {
		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 <= 1020000000.0d0) 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 <= 1020000000.0) {
		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 <= 1020000000.0:
		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 <= 1020000000.0)
		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 <= 1020000000.0)
		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, 1020000000.0], x, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.02e9 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 45.9%

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

   3. Taylor expanded in y around inf 45.0%

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

   if -1 < y < 1.02e9

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1020000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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: 36.6% 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. Taylor expanded in y around 0 37.6%

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

3. Final simplification 37.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))