Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 8

Speedup: 1.0×

• 21.1% 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 59.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+176}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -135000000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -0.0066:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+15} \lor \neg \left(y \leq 3.3 \cdot 10^{+116}\right) \land y \leq 1.72 \cdot 10^{+168}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.22e+176)
   (* y z)
   (if (<= y -135000000000.0)
     (* y x)
     (if (<= y -0.0066)
       (* y z)
       (if (<= y 1.16e-125)
         x
         (if (or (<= y 7e+15) (and (not (<= y 3.3e+116)) (<= y 1.72e+168)))
           (* y z)
           (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.22e+176) {
		tmp = y * z;
	} else if (y <= -135000000000.0) {
		tmp = y * x;
	} else if (y <= -0.0066) {
		tmp = y * z;
	} else if (y <= 1.16e-125) {
		tmp = x;
	} else if ((y <= 7e+15) || (!(y <= 3.3e+116) && (y <= 1.72e+168))) {
		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 <= (-1.22d+176)) then
        tmp = y * z
    else if (y <= (-135000000000.0d0)) then
        tmp = y * x
    else if (y <= (-0.0066d0)) then
        tmp = y * z
    else if (y <= 1.16d-125) then
        tmp = x
    else if ((y <= 7d+15) .or. (.not. (y <= 3.3d+116)) .and. (y <= 1.72d+168)) 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 <= -1.22e+176) {
		tmp = y * z;
	} else if (y <= -135000000000.0) {
		tmp = y * x;
	} else if (y <= -0.0066) {
		tmp = y * z;
	} else if (y <= 1.16e-125) {
		tmp = x;
	} else if ((y <= 7e+15) || (!(y <= 3.3e+116) && (y <= 1.72e+168))) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.22e+176:
		tmp = y * z
	elif y <= -135000000000.0:
		tmp = y * x
	elif y <= -0.0066:
		tmp = y * z
	elif y <= 1.16e-125:
		tmp = x
	elif (y <= 7e+15) or (not (y <= 3.3e+116) and (y <= 1.72e+168)):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.22e+176)
		tmp = Float64(y * z);
	elseif (y <= -135000000000.0)
		tmp = Float64(y * x);
	elseif (y <= -0.0066)
		tmp = Float64(y * z);
	elseif (y <= 1.16e-125)
		tmp = x;
	elseif ((y <= 7e+15) || (!(y <= 3.3e+116) && (y <= 1.72e+168)))
		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 <= -1.22e+176)
		tmp = y * z;
	elseif (y <= -135000000000.0)
		tmp = y * x;
	elseif (y <= -0.0066)
		tmp = y * z;
	elseif (y <= 1.16e-125)
		tmp = x;
	elseif ((y <= 7e+15) || (~((y <= 3.3e+116)) && (y <= 1.72e+168)))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.22e+176], N[(y * z), $MachinePrecision], If[LessEqual[y, -135000000000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -0.0066], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.16e-125], x, If[Or[LessEqual[y, 7e+15], And[N[Not[LessEqual[y, 3.3e+116]], $MachinePrecision], LessEqual[y, 1.72e+168]]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2199999999999999e176 or -1.35e11 < y < -0.0066 or 1.15999999999999995e-125 < y < 7e15 or 3.2999999999999998e116 < y < 1.7200000000000001e168

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.6%

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

   if -1.2199999999999999e176 < y < -1.35e11 or 7e15 < y < 3.2999999999999998e116 or 1.7200000000000001e168 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 67.9%

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

      1. *-commutative 67.9%

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

   8. Simplified 67.9%

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

   if -0.0066 < y < 1.15999999999999995e-125

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+176}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -135000000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -0.0066:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+15} \lor \neg \left(y \leq 3.3 \cdot 10^{+116}\right) \land y \leq 1.72 \cdot 10^{+168}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-18} \lor \neg \left(x \leq -2.45 \cdot 10^{-57} \lor \neg \left(x \leq -5.5 \cdot 10^{-134}\right) \land x \leq 2.4 \cdot 10^{-82}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e-18)
         (not
          (or (<= x -2.45e-57) (and (not (<= x -5.5e-134)) (<= x 2.4e-82)))))
   (* x (+ y 1.0))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-18) || !((x <= -2.45e-57) || (!(x <= -5.5e-134) && (x <= 2.4e-82)))) {
		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 <= (-2d-18)) .or. (.not. (x <= (-2.45d-57)) .or. (.not. (x <= (-5.5d-134))) .and. (x <= 2.4d-82))) 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 <= -2e-18) || !((x <= -2.45e-57) || (!(x <= -5.5e-134) && (x <= 2.4e-82)))) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e-18) or not ((x <= -2.45e-57) or (not (x <= -5.5e-134) and (x <= 2.4e-82))):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e-18) || !((x <= -2.45e-57) || (!(x <= -5.5e-134) && (x <= 2.4e-82))))
		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 <= -2e-18) || ~(((x <= -2.45e-57) || (~((x <= -5.5e-134)) && (x <= 2.4e-82)))))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e-18], N[Not[Or[LessEqual[x, -2.45e-57], And[N[Not[LessEqual[x, -5.5e-134]], $MachinePrecision], LessEqual[x, 2.4e-82]]]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-18 or -2.44999999999999994e-57 < x < -5.5000000000000002e-134 or 2.40000000000000008e-82 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.6%

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

      1. +-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -2.0000000000000001e-18 < x < -2.44999999999999994e-57 or -5.5000000000000002e-134 < x < 2.40000000000000008e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-18} \lor \neg \left(x \leq -2.45 \cdot 10^{-57} \lor \neg \left(x \leq -5.5 \cdot 10^{-134}\right) \land x \leq 2.4 \cdot 10^{-82}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.022 \lor \neg \left(y \leq 7.4 \cdot 10^{-126}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.022) (not (<= y 7.4e-126))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.022) || !(y <= 7.4e-126)) {
		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 <= (-0.022d0)) .or. (.not. (y <= 7.4d-126))) 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 <= -0.022) || !(y <= 7.4e-126)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.022) or not (y <= 7.4e-126):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.022) || !(y <= 7.4e-126))
		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 <= -0.022) || ~((y <= 7.4e-126)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.022], N[Not[LessEqual[y, 7.4e-126]], $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 < -0.021999999999999999 or 7.3999999999999998e-126 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 93.8%

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

      1. +-commutative 93.8%

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

   5. Simplified 93.8%

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

   if -0.021999999999999999 < y < 7.3999999999999998e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.022 \lor \neg \left(y \leq 7.4 \cdot 10^{-126}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2300 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2300.0) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2300.0) || !(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 <= (-2300.0d0)) .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 <= -2300.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2300.0) 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 <= -2300.0) || !(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 <= -2300.0) || ~((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, -2300.0], 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 < -2300 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.6%

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

      1. +-commutative 99.6%

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

   5. Simplified 99.6%

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

   if -2300 < y < 1

   1. Initial program 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. flip-+ 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

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

      5. *-commutative 77.2%

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

   4. Applied egg-rr 77.2%

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

      1. difference-of-squares 77.3%

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

      2. +-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. distribute-lft-in 77.3%

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

      5. associate-/l* 92.2%

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

      6. *-inverses 100.0%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around inf 97.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2300 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 54.4%

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

      1. *-commutative 54.4%

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

   8. Simplified 54.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 37.2% 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 32.4%

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

4. Final simplification 32.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024041 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))