Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 7

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, 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 2: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+42}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2020000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e+135)
   (* y z)
   (if (<= y -7e+42)
     (* x y)
     (if (<= y -5.8e-85)
       (* y z)
       (if (<= y 1.5e-58) x (if (<= y 2020000.0) (* y z) (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e+135) {
		tmp = y * z;
	} else if (y <= -7e+42) {
		tmp = x * y;
	} else if (y <= -5.8e-85) {
		tmp = y * z;
	} else if (y <= 1.5e-58) {
		tmp = x;
	} else if (y <= 2020000.0) {
		tmp = y * z;
	} else {
		tmp = x * y;
	}
	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 <= (-9.5d+135)) then
        tmp = y * z
    else if (y <= (-7d+42)) then
        tmp = x * y
    else if (y <= (-5.8d-85)) then
        tmp = y * z
    else if (y <= 1.5d-58) then
        tmp = x
    else if (y <= 2020000.0d0) then
        tmp = y * z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e+135) {
		tmp = y * z;
	} else if (y <= -7e+42) {
		tmp = x * y;
	} else if (y <= -5.8e-85) {
		tmp = y * z;
	} else if (y <= 1.5e-58) {
		tmp = x;
	} else if (y <= 2020000.0) {
		tmp = y * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e+135:
		tmp = y * z
	elif y <= -7e+42:
		tmp = x * y
	elif y <= -5.8e-85:
		tmp = y * z
	elif y <= 1.5e-58:
		tmp = x
	elif y <= 2020000.0:
		tmp = y * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e+135)
		tmp = Float64(y * z);
	elseif (y <= -7e+42)
		tmp = Float64(x * y);
	elseif (y <= -5.8e-85)
		tmp = Float64(y * z);
	elseif (y <= 1.5e-58)
		tmp = x;
	elseif (y <= 2020000.0)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e+135)
		tmp = y * z;
	elseif (y <= -7e+42)
		tmp = x * y;
	elseif (y <= -5.8e-85)
		tmp = y * z;
	elseif (y <= 1.5e-58)
		tmp = x;
	elseif (y <= 2020000.0)
		tmp = y * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e+135], N[(y * z), $MachinePrecision], If[LessEqual[y, -7e+42], N[(x * y), $MachinePrecision], If[LessEqual[y, -5.8e-85], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.5e-58], x, If[LessEqual[y, 2020000.0], N[(y * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000036e135 or -7.00000000000000047e42 < y < -5.8000000000000004e-85 or 1.50000000000000004e-58 < y < 2.02e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 74.0

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

   5. Simplified 74.0%

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

   if -9.50000000000000036e135 < y < -7.00000000000000047e42 or 2.02e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 67.7%

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

   if -5.8000000000000004e-85 < y < 1.50000000000000004e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 76.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+42}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2020000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -76000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -76000.0) t_0 (if (<= y 8.6e-10) (fma z y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -76000.0) {
		tmp = t_0;
	} else if (y <= 8.6e-10) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -76000.0)
		tmp = t_0;
	elseif (y <= 8.6e-10)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -76000.0], t$95$0, If[LessEqual[y, 8.6e-10], N[(z * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -76000 or 8.60000000000000029e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.6

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

   5. Simplified 98.6%

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

   if -76000 < y < 8.60000000000000029e-10

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. associate-+l+ N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. accelerator-lowering-fma.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 99.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -76000:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e+149) (fma y x x) (if (<= x 5.5e+36) (fma z y x) (fma y x x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+149) {
		tmp = fma(y, x, x);
	} else if (x <= 5.5e+36) {
		tmp = fma(z, y, x);
	} else {
		tmp = fma(y, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e+149)
		tmp = fma(y, x, x);
	elseif (x <= 5.5e+36)
		tmp = fma(z, y, x);
	else
		tmp = fma(y, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e+149], N[(y * x + x), $MachinePrecision], If[LessEqual[x, 5.5e+36], N[(z * y + x), $MachinePrecision], N[(y * x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e149 or 5.5000000000000002e36 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. accelerator-lowering-fma.f64 93.6

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

   5. Simplified 93.6%

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

   if -1.9e149 < x < 5.5000000000000002e36

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. associate-+l+ N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. accelerator-lowering-fma.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 90.5%

      \[\leadsto \mathsf{fma}\left(z, y, \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e+156) (* y z) (if (<= z 1.6e+123) (fma y x x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+156) {
		tmp = y * z;
	} else if (z <= 1.6e+123) {
		tmp = fma(y, x, x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e+156)
		tmp = Float64(y * z);
	elseif (z <= 1.6e+123)
		tmp = fma(y, x, x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e+156], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.6e+123], N[(y * x + x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000024e156 or 1.60000000000000002e123 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 77.8

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

   5. Simplified 77.8%

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

   if -3.80000000000000024e156 < z < 1.60000000000000002e123

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. accelerator-lowering-fma.f64 78.1

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

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 61.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = x * y;
	}
	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 = x * y
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = x * y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = x * y
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.0], x, N[(x * y), $MachinePrecision]]]

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

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.5

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

   5. Simplified 98.5%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 57.7%

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

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.7%

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

4. Final simplification 62.4%

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

Alternative 7: 36.9% accurate, 12.0× 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

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 36.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))