Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 7

Speedup: 1.0×

• 20.7% 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: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+89}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+56} \lor \neg \left(y \leq 7.6 \cdot 10^{+162} \lor \neg \left(y \leq 2.4 \cdot 10^{+256}\right) \land y \leq 2.1 \cdot 10^{+296}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.25e+89)
   (* y x)
   (if (<= y -1.85e-37)
     (* y z)
     (if (<= y 6.2e-17)
       x
       (if (or (<= y 1.32e+56)
               (not
                (or (<= y 7.6e+162)
                    (and (not (<= y 2.4e+256)) (<= y 2.1e+296)))))
         (* y z)
         (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.25e+89) {
		tmp = y * x;
	} else if (y <= -1.85e-37) {
		tmp = y * z;
	} else if (y <= 6.2e-17) {
		tmp = x;
	} else if ((y <= 1.32e+56) || !((y <= 7.6e+162) || (!(y <= 2.4e+256) && (y <= 2.1e+296)))) {
		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 <= (-2.25d+89)) then
        tmp = y * x
    else if (y <= (-1.85d-37)) then
        tmp = y * z
    else if (y <= 6.2d-17) then
        tmp = x
    else if ((y <= 1.32d+56) .or. (.not. (y <= 7.6d+162) .or. (.not. (y <= 2.4d+256)) .and. (y <= 2.1d+296))) 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 <= -2.25e+89) {
		tmp = y * x;
	} else if (y <= -1.85e-37) {
		tmp = y * z;
	} else if (y <= 6.2e-17) {
		tmp = x;
	} else if ((y <= 1.32e+56) || !((y <= 7.6e+162) || (!(y <= 2.4e+256) && (y <= 2.1e+296)))) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.25e+89:
		tmp = y * x
	elif y <= -1.85e-37:
		tmp = y * z
	elif y <= 6.2e-17:
		tmp = x
	elif (y <= 1.32e+56) or not ((y <= 7.6e+162) or (not (y <= 2.4e+256) and (y <= 2.1e+296))):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.25e+89)
		tmp = Float64(y * x);
	elseif (y <= -1.85e-37)
		tmp = Float64(y * z);
	elseif (y <= 6.2e-17)
		tmp = x;
	elseif ((y <= 1.32e+56) || !((y <= 7.6e+162) || (!(y <= 2.4e+256) && (y <= 2.1e+296))))
		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 <= -2.25e+89)
		tmp = y * x;
	elseif (y <= -1.85e-37)
		tmp = y * z;
	elseif (y <= 6.2e-17)
		tmp = x;
	elseif ((y <= 1.32e+56) || ~(((y <= 7.6e+162) || (~((y <= 2.4e+256)) && (y <= 2.1e+296)))))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.25e+89], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.85e-37], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.2e-17], x, If[Or[LessEqual[y, 1.32e+56], N[Not[Or[LessEqual[y, 7.6e+162], And[N[Not[LessEqual[y, 2.4e+256]], $MachinePrecision], LessEqual[y, 2.1e+296]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e89 or 1.32e56 < y < 7.60000000000000049e162 or 2.40000000000000014e256 < y < 2.10000000000000005e296

   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. Taylor expanded in x around -inf 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. unsub-neg 97.1%

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

      4. sub-neg 97.1%

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

      5. metadata-eval 97.1%

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

      6. +-commutative 97.1%

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

      7. mul-1-neg 97.1%

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

      8. unsub-neg 97.1%

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

   6. Simplified 97.1%

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

   7. Taylor expanded in y around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-lft-out-- 97.1%

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

      3. distribute-rgt-neg-in 97.1%

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

      4. distribute-lft-neg-out 97.1%

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

      5. cancel-sign-sub 97.1%

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

      6. distribute-lft-in 100.0%

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

      7. +-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in x around inf 70.4%

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

       1. *-commutative 70.4%

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

   12. Simplified 70.4%

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

   if -2.25e89 < y < -1.85e-37 or 6.1999999999999997e-17 < y < 1.32e56 or 7.60000000000000049e162 < y < 2.40000000000000014e256 or 2.10000000000000005e296 < 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. Taylor expanded in x around -inf 98.6%

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

      1. +-commutative 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

      4. sub-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. +-commutative 98.6%

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

      7. mul-1-neg 98.6%

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

      8. unsub-neg 98.6%

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

   6. Simplified 98.6%

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

   7. Taylor expanded in z around inf 73.0%

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

   if -1.85e-37 < y < 6.1999999999999997e-17

   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. Taylor expanded in y around 0 76.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+89}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+56} \lor \neg \left(y \leq 7.6 \cdot 10^{+162} \lor \neg \left(y \leq 2.4 \cdot 10^{+256}\right) \land y \leq 2.1 \cdot 10^{+296}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-29} \lor \neg \left(y \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.6e-29) (not (<= y 4.5e-17))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.6e-29) || !(y <= 4.5e-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 <= (-8.6d-29)) .or. (.not. (y <= 4.5d-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 <= -8.6e-29) || !(y <= 4.5e-17)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.6e-29) or not (y <= 4.5e-17):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.6e-29) || !(y <= 4.5e-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 <= -8.6e-29) || ~((y <= 4.5e-17)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.6e-29], N[Not[LessEqual[y, 4.5e-17]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.5999999999999996e-29 or 4.49999999999999978e-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-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. Taylor expanded in x around -inf 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

      6. +-commutative 97.8%

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

      7. mul-1-neg 97.8%

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

      8. unsub-neg 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in y around inf 97.1%

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

      1. neg-mul-1 97.1%

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

      2. distribute-lft-out-- 94.9%

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

      3. distribute-rgt-neg-in 94.9%

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

      4. distribute-lft-neg-out 94.9%

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

      5. cancel-sign-sub 94.9%

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

      6. distribute-lft-in 97.1%

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

      7. +-commutative 97.1%

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

   9. Simplified 97.1%

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

   if -8.5999999999999996e-29 < y < 4.49999999999999978e-17

   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. Taylor expanded in y around 0 76.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-29} \lor \neg \left(y \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -350 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -350.0) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -350.0) || !(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 <= (-350.0d0)) .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 <= -350.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -350.0) 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 <= -350.0) || !(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 <= -350.0) || ~((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, -350.0], 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 < -350 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-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. Taylor expanded in x around -inf 97.6%

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

      1. +-commutative 97.6%

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

      2. mul-1-neg 97.6%

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

      3. unsub-neg 97.6%

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

      4. sub-neg 97.6%

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

      5. metadata-eval 97.6%

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

      6. +-commutative 97.6%

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

      7. mul-1-neg 97.6%

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

      8. unsub-neg 97.6%

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

   6. Simplified 97.6%

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

   7. Taylor expanded in y around inf 99.5%

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

      1. neg-mul-1 99.5%

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

      2. distribute-lft-out-- 97.1%

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

      3. distribute-rgt-neg-in 97.1%

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

      4. distribute-lft-neg-out 97.1%

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

      5. cancel-sign-sub 97.1%

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

      6. distribute-lft-in 99.5%

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

      7. +-commutative 99.5%

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

   9. Simplified 99.5%

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

   if -350 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -350 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -350 \lor \neg \left(y \leq 3.2 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -350.0) (not (<= y 3.2e+32))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -350.0) || !(y <= 3.2e+32)) {
		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 <= (-350.0d0)) .or. (.not. (y <= 3.2d+32))) 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 <= -350.0) || !(y <= 3.2e+32)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -350.0) or not (y <= 3.2e+32):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -350.0) || !(y <= 3.2e+32))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -350.0) || ~((y <= 3.2e+32)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -350.0], N[Not[LessEqual[y, 3.2e+32]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -350 or 3.1999999999999999e32 < 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. Taylor expanded in x around -inf 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

      4. sub-neg 97.5%

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

      5. metadata-eval 97.5%

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

      6. +-commutative 97.5%

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

      7. mul-1-neg 97.5%

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

      8. unsub-neg 97.5%

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

   6. Simplified 97.5%

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

   7. Taylor expanded in y around inf 99.5%

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

      1. neg-mul-1 99.5%

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

      2. distribute-lft-out-- 97.0%

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

      3. distribute-rgt-neg-in 97.0%

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

      4. distribute-lft-neg-out 97.0%

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

      5. cancel-sign-sub 97.0%

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

      6. distribute-lft-in 99.5%

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

      7. +-commutative 99.5%

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

   9. Simplified 99.5%

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

   10. Taylor expanded in x around inf 57.4%

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

       1. *-commutative 57.4%

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

   12. Simplified 57.4%

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

   if -350 < y < 3.1999999999999999e32

   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. Taylor expanded in y around 0 69.2%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -350 \lor \neg \left(y \leq 3.2 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 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 7: 36.4% 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. 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. Taylor expanded in y around 0 38.1%

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

5. Final simplification 38.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))