Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 8

Speedup: 1.0×

• 21.5% 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: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-43} \lor \neg \left(x \leq 1.8 \cdot 10^{-143} \lor \neg \left(x \leq 7.4 \cdot 10^{-17}\right) \land x \leq 2.9 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.22e-43)
         (not (or (<= x 1.8e-143) (and (not (<= x 7.4e-17)) (<= x 2.9e+54)))))
   (* x (+ y 1.0))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.22e-43) || !((x <= 1.8e-143) || (!(x <= 7.4e-17) && (x <= 2.9e+54)))) {
		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 <= (-1.22d-43)) .or. (.not. (x <= 1.8d-143) .or. (.not. (x <= 7.4d-17)) .and. (x <= 2.9d+54))) 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 <= -1.22e-43) || !((x <= 1.8e-143) || (!(x <= 7.4e-17) && (x <= 2.9e+54)))) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.22e-43) or not ((x <= 1.8e-143) or (not (x <= 7.4e-17) and (x <= 2.9e+54))):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.22e-43) || !((x <= 1.8e-143) || (!(x <= 7.4e-17) && (x <= 2.9e+54))))
		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 <= -1.22e-43) || ~(((x <= 1.8e-143) || (~((x <= 7.4e-17)) && (x <= 2.9e+54)))))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.22e-43], N[Not[Or[LessEqual[x, 1.8e-143], And[N[Not[LessEqual[x, 7.4e-17]], $MachinePrecision], LessEqual[x, 2.9e+54]]]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2199999999999999e-43 or 1.7999999999999999e-143 < x < 7.3999999999999995e-17 or 2.8999999999999999e54 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.0%

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

      1. +-commutative 82.0%

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

   4. Simplified 82.0%

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

   if -1.2199999999999999e-43 < x < 1.7999999999999999e-143 or 7.3999999999999995e-17 < x < 2.8999999999999999e54

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-43} \lor \neg \left(x \leq 1.8 \cdot 10^{-143} \lor \neg \left(x \leq 7.4 \cdot 10^{-17}\right) \land x \leq 2.9 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+191}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-12}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e+191)
   (* y x)
   (if (<= y -1.9e-12)
     (* y z)
     (if (<= y 2.8e-58) x (if (<= y 7.5e+278) (* y z) (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+191) {
		tmp = y * x;
	} else if (y <= -1.9e-12) {
		tmp = y * z;
	} else if (y <= 2.8e-58) {
		tmp = x;
	} else if (y <= 7.5e+278) {
		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 <= (-4.8d+191)) then
        tmp = y * x
    else if (y <= (-1.9d-12)) then
        tmp = y * z
    else if (y <= 2.8d-58) then
        tmp = x
    else if (y <= 7.5d+278) 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 <= -4.8e+191) {
		tmp = y * x;
	} else if (y <= -1.9e-12) {
		tmp = y * z;
	} else if (y <= 2.8e-58) {
		tmp = x;
	} else if (y <= 7.5e+278) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e+191:
		tmp = y * x
	elif y <= -1.9e-12:
		tmp = y * z
	elif y <= 2.8e-58:
		tmp = x
	elif y <= 7.5e+278:
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e+191)
		tmp = Float64(y * x);
	elseif (y <= -1.9e-12)
		tmp = Float64(y * z);
	elseif (y <= 2.8e-58)
		tmp = x;
	elseif (y <= 7.5e+278)
		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 <= -4.8e+191)
		tmp = y * x;
	elseif (y <= -1.9e-12)
		tmp = y * z;
	elseif (y <= 2.8e-58)
		tmp = x;
	elseif (y <= 7.5e+278)
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e+191], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.9e-12], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.8e-58], x, If[LessEqual[y, 7.5e+278], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999972e191 or 7.49999999999999949e278 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   7. Simplified 72.9%

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

   if -4.79999999999999972e191 < y < -1.89999999999999998e-12 or 2.8000000000000001e-58 < y < 7.49999999999999949e278

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 66.8%

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

   if -1.89999999999999998e-12 < y < 2.8000000000000001e-58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+191}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-12}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00135 \lor \neg \left(y \leq 1.55 \cdot 10^{-56}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00135) (not (<= y 1.55e-56))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00135) || !(y <= 1.55e-56)) {
		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 <= (-0.00135d0)) .or. (.not. (y <= 1.55d-56))) 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 <= -0.00135) || !(y <= 1.55e-56)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00135) or not (y <= 1.55e-56):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00135) || !(y <= 1.55e-56))
		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 <= -0.00135) || ~((y <= 1.55e-56)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00135], N[Not[LessEqual[y, 1.55e-56]], $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 < -0.0013500000000000001 or 1.54999999999999994e-56 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 94.7%

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

      1. +-commutative 94.7%

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

   4. Simplified 94.7%

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

   if -0.0013500000000000001 < y < 1.54999999999999994e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.7%

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

      1. +-commutative 74.7%

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

   4. Simplified 74.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00135 \lor \neg \left(y \leq 1.55 \cdot 10^{-56}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 5: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 8.2 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -11500.0) (not (<= y 8.2e-6))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -11500.0) || !(y <= 8.2e-6)) {
		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 <= (-11500.0d0)) .or. (.not. (y <= 8.2d-6))) 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 <= -11500.0) || !(y <= 8.2e-6)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -11500.0) or not (y <= 8.2e-6):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -11500.0) || !(y <= 8.2e-6))
		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 <= -11500.0) || ~((y <= 8.2e-6)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -11500.0], N[Not[LessEqual[y, 8.2e-6]], $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 < -11500 or 8.1999999999999994e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.6%

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

      1. +-commutative 98.6%

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

   4. Simplified 98.6%

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

   if -11500 < y < 8.1999999999999994e-6

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Step-by-step derivation

      1. distribute-lft-in 100.0%

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

      2. flip-+ 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. *-commutative 80.1%

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

   3. Applied egg-rr 80.1%

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

      1. difference-of-squares 80.2%

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

      2. +-commutative 80.2%

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

      3. *-commutative 80.2%

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

      4. distribute-lft-in 80.2%

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

      5. associate-/l* 94.6%

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

      6. *-inverses 100.0%

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

      7. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{1}{x + z}}} \]

      8. +-commutative 99.8%

         \[\leadsto x + \frac{y}{\frac{1}{\color{blue}{z + x}}} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{1}{z + x}}} \]

   6. Taylor expanded in z around inf 98.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 8.2 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00195 \lor \neg \left(y \leq 8.2 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00195) (not (<= y 8.2e-6))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00195) || !(y <= 8.2e-6)) {
		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 <= (-0.00195d0)) .or. (.not. (y <= 8.2d-6))) 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 <= -0.00195) || !(y <= 8.2e-6)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00195) or not (y <= 8.2e-6):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00195) || !(y <= 8.2e-6))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00195) || ~((y <= 8.2e-6)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00195], N[Not[LessEqual[y, 8.2e-6]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.0019499999999999999 or 8.1999999999999994e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.6%

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

      1. +-commutative 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in z around 0 41.7%

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

      1. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   if -0.0019499999999999999 < y < 8.1999999999999994e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.6%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00195 \lor \neg \left(y \leq 8.2 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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: 37.0% 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 37.1%

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

3. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))