Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 8

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \left(z + x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z + x)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z + x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z + x)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x + z, x\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z)
	return fma(y, Float64(x + z), x)
end

Wolfram

code[x_, y_, z_] := N[(y * N[(x + z), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

   3. +-commutative 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-103}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+17} \lor \neg \left(y \leq 1.18 \cdot 10^{+39}\right) \land \left(y \leq 3.5 \cdot 10^{+123} \lor \neg \left(y \leq 2.25 \cdot 10^{+260}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (* y x)
   (if (<= y -2.2e-93)
     x
     (if (<= y -4.8e-103)
       (* y z)
       (if (<= y 1.5e-18)
         x
         (if (or (<= y 8.5e+17)
                 (and (not (<= y 1.18e+39))
                      (or (<= y 3.5e+123) (not (<= y 2.25e+260)))))
           (* y z)
           (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= -2.2e-93) {
		tmp = x;
	} else if (y <= -4.8e-103) {
		tmp = y * z;
	} else if (y <= 1.5e-18) {
		tmp = x;
	} else if ((y <= 8.5e+17) || (!(y <= 1.18e+39) && ((y <= 3.5e+123) || !(y <= 2.25e+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 <= (-1.0d0)) then
        tmp = y * x
    else if (y <= (-2.2d-93)) then
        tmp = x
    else if (y <= (-4.8d-103)) then
        tmp = y * z
    else if (y <= 1.5d-18) then
        tmp = x
    else if ((y <= 8.5d+17) .or. (.not. (y <= 1.18d+39)) .and. (y <= 3.5d+123) .or. (.not. (y <= 2.25d+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 <= -1.0) {
		tmp = y * x;
	} else if (y <= -2.2e-93) {
		tmp = x;
	} else if (y <= -4.8e-103) {
		tmp = y * z;
	} else if (y <= 1.5e-18) {
		tmp = x;
	} else if ((y <= 8.5e+17) || (!(y <= 1.18e+39) && ((y <= 3.5e+123) || !(y <= 2.25e+260)))) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= -2.2e-93:
		tmp = x
	elif y <= -4.8e-103:
		tmp = y * z
	elif y <= 1.5e-18:
		tmp = x
	elif (y <= 8.5e+17) or (not (y <= 1.18e+39) and ((y <= 3.5e+123) or not (y <= 2.25e+260))):
		tmp = y * z
	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 <= -2.2e-93)
		tmp = x;
	elseif (y <= -4.8e-103)
		tmp = Float64(y * z);
	elseif (y <= 1.5e-18)
		tmp = x;
	elseif ((y <= 8.5e+17) || (!(y <= 1.18e+39) && ((y <= 3.5e+123) || !(y <= 2.25e+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 <= -1.0)
		tmp = y * x;
	elseif (y <= -2.2e-93)
		tmp = x;
	elseif (y <= -4.8e-103)
		tmp = y * z;
	elseif (y <= 1.5e-18)
		tmp = x;
	elseif ((y <= 8.5e+17) || (~((y <= 1.18e+39)) && ((y <= 3.5e+123) || ~((y <= 2.25e+260)))))
		tmp = y * z;
	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, -2.2e-93], x, If[LessEqual[y, -4.8e-103], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.5e-18], x, If[Or[LessEqual[y, 8.5e+17], And[N[Not[LessEqual[y, 1.18e+39]], $MachinePrecision], Or[LessEqual[y, 3.5e+123], N[Not[LessEqual[y, 2.25e+260]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 8.5e17 < y < 1.17999999999999996e39 or 3.5e123 < y < 2.25000000000000011e260

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.5%

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

      1. +-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around inf 58.4%

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

   if -1 < y < -2.19999999999999996e-93 or -4.8000000000000004e-103 < y < 1.49999999999999991e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.6%

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

   if -2.19999999999999996e-93 < y < -4.8000000000000004e-103 or 1.49999999999999991e-18 < y < 8.5e17 or 1.17999999999999996e39 < y < 3.5e123 or 2.25000000000000011e260 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.4%

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

   4. Taylor expanded in x around 0 76.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-103}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+17} \lor \neg \left(y \leq 1.18 \cdot 10^{+39}\right) \land \left(y \leq 3.5 \cdot 10^{+123} \lor \neg \left(y \leq 2.25 \cdot 10^{+260}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-31} \lor \neg \left(x \leq 7 \cdot 10^{-94} \lor \neg \left(x \leq 1.7 \cdot 10^{-73}\right) \land x \leq 1.4 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.6e-31)
         (not (or (<= x 7e-94) (and (not (<= x 1.7e-73)) (<= x 1.4e-21)))))
   (* x (+ y 1.0))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e-31) || !((x <= 7e-94) || (!(x <= 1.7e-73) && (x <= 1.4e-21)))) {
		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 <= (-7.6d-31)) .or. (.not. (x <= 7d-94) .or. (.not. (x <= 1.7d-73)) .and. (x <= 1.4d-21))) 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 <= -7.6e-31) || !((x <= 7e-94) || (!(x <= 1.7e-73) && (x <= 1.4e-21)))) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.6e-31) or not ((x <= 7e-94) or (not (x <= 1.7e-73) and (x <= 1.4e-21))):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.6e-31) || !((x <= 7e-94) || (!(x <= 1.7e-73) && (x <= 1.4e-21))))
		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 <= -7.6e-31) || ~(((x <= 7e-94) || (~((x <= 1.7e-73)) && (x <= 1.4e-21)))))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.6e-31], N[Not[Or[LessEqual[x, 7e-94], And[N[Not[LessEqual[x, 1.7e-73]], $MachinePrecision], LessEqual[x, 1.4e-21]]]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5999999999999999e-31 or 6.99999999999999996e-94 < x < 1.7000000000000001e-73 or 1.40000000000000002e-21 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.8%

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

      1. +-commutative 86.8%

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

   5. Simplified 86.8%

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

   if -7.5999999999999999e-31 < x < 6.99999999999999996e-94 or 1.7000000000000001e-73 < x < 1.40000000000000002e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.7%

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

   4. Taylor expanded in x around 0 75.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-31} \lor \neg \left(x \leq 7 \cdot 10^{-94} \lor \neg \left(x \leq 1.7 \cdot 10^{-73}\right) \land x \leq 1.4 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -620000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -620000000.0) (not (<= x 2.6e+94)))
   (* x (+ y 1.0))
   (* y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -620000000.0) || !(x <= 2.6e+94)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * (x + 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 <= (-620000000.0d0)) .or. (.not. (x <= 2.6d+94))) then
        tmp = x * (y + 1.0d0)
    else
        tmp = y * (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -620000000.0) || !(x <= 2.6e+94)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -620000000.0) or not (x <= 2.6e+94):
		tmp = x * (y + 1.0)
	else:
		tmp = y * (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -620000000.0) || !(x <= 2.6e+94))
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = Float64(y * Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -620000000.0) || ~((x <= 2.6e+94)))
		tmp = x * (y + 1.0);
	else
		tmp = y * (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -620000000.0], N[Not[LessEqual[x, 2.6e+94]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e8 or 2.5999999999999999e94 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.9%

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

      1. +-commutative 89.9%

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

   5. Simplified 89.9%

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

   if -6.2e8 < x < 2.5999999999999999e94

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x + z, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. associate-+r+ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 82.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -620000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32 \lor \neg \left(y \leq 0.045\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -32.0) (not (<= y 0.045))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32.0) || !(y <= 0.045)) {
		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 <= (-32.0d0)) .or. (.not. (y <= 0.045d0))) 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 <= -32.0) || !(y <= 0.045)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -32.0) or not (y <= 0.045):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -32.0) || !(y <= 0.045))
		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 <= -32.0) || ~((y <= 0.045)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -32.0], N[Not[LessEqual[y, 0.045]], $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 < -32 or 0.044999999999999998 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x + z, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 96.9%

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

      5. associate-+r+ 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in y around inf 99.1%

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

   if -32 < y < 0.044999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32 \lor \neg \left(y \leq 0.045\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1950000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1950000000.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1950000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1950000000.0d0))) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1950000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 1950000000.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1950000000.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1950000000.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1950000000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.95e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.3%

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

      1. +-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in y around inf 52.4%

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

   if -1 < y < 1.95e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 66.6%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1950000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(x + z\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(x + z)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 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. Add Preprocessing

3. Taylor expanded in y around 0 34.1%

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

4. Final simplification 34.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024044 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))