Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 7

Speedup: 1.2×

• 20.4% 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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 100.0

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

   7. lift-+.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-57}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e-57)
   (* z y)
   (if (<= y 4.2e-35) x (if (<= y 2.9e+103) (* z y) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-57) {
		tmp = z * y;
	} else if (y <= 4.2e-35) {
		tmp = x;
	} else if (y <= 2.9e+103) {
		tmp = z * y;
	} 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 <= (-8d-57)) then
        tmp = z * y
    else if (y <= 4.2d-35) then
        tmp = x
    else if (y <= 2.9d+103) then
        tmp = z * y
    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 <= -8e-57) {
		tmp = z * y;
	} else if (y <= 4.2e-35) {
		tmp = x;
	} else if (y <= 2.9e+103) {
		tmp = z * y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e-57:
		tmp = z * y
	elif y <= 4.2e-35:
		tmp = x
	elif y <= 2.9e+103:
		tmp = z * y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e-57)
		tmp = Float64(z * y);
	elseif (y <= 4.2e-35)
		tmp = x;
	elseif (y <= 2.9e+103)
		tmp = Float64(z * y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e-57)
		tmp = z * y;
	elseif (y <= 4.2e-35)
		tmp = x;
	elseif (y <= 2.9e+103)
		tmp = z * y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e-57], N[(z * y), $MachinePrecision], If[LessEqual[y, 4.2e-35], x, If[LessEqual[y, 2.9e+103], N[(z * y), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999964e-57 or 4.2e-35 < y < 2.8999999999999998e103

   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. lower-*.f64 64.5

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

   5. Simplified 64.5%

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

   if -7.99999999999999964e-57 < y < 4.2e-35

   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. lower-fma.f64 79.2

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

   5. Simplified 79.2%

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

      1. distribute-lft1-in N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 79.2

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

   7. Applied egg-rr 79.2%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Simplified 79.2%

       \[\leadsto \color{blue}{1} \cdot x \]
   11. Step-by-step derivation

       1. *-lft-identity 79.2

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

   12. Applied egg-rr 79.2%

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

   if 2.8999999999999998e103 < y

   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. lower-fma.f64 60.1

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.1

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

   8. Simplified 60.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-57}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -160000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -160000000000.0) t_0 (if (<= y 1.0) (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 <= -160000000000.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		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 <= -160000000000.0)
		tmp = t_0;
	elseif (y <= 1.0)
		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, -160000000000.0], t$95$0, If[LessEqual[y, 1.0], N[(z * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e11 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. lower-*.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. lower-+.f64 99.7

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

   5. Simplified 99.7%

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

   if -1.6e11 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 98.7

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

   5. Simplified 98.7%

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

      1. lift-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.7

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

   7. Applied egg-rr 98.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160000000000:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-16) (fma z y x) (if (<= z 1.3e-139) (fma y x x) (fma z y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-16) {
		tmp = fma(z, y, x);
	} else if (z <= 1.3e-139) {
		tmp = fma(y, x, x);
	} else {
		tmp = fma(z, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-16)
		tmp = fma(z, y, x);
	elseif (z <= 1.3e-139)
		tmp = fma(y, x, x);
	else
		tmp = fma(z, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-16], N[(z * y + x), $MachinePrecision], If[LessEqual[z, 1.3e-139], N[(y * x + x), $MachinePrecision], N[(z * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e-16 or 1.2999999999999999e-139 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 91.6

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

   5. Simplified 91.6%

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

      1. lift-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 91.6

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

   7. Applied egg-rr 91.6%

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

   if -8.5000000000000001e-16 < z < 1.2999999999999999e-139

   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. lower-fma.f64 89.6

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

   5. Simplified 89.6%

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

Alternative 5: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.35e+30) (* z y) (if (<= z 2.55e+160) (fma y x x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.35e+30) {
		tmp = z * y;
	} else if (z <= 2.55e+160) {
		tmp = fma(y, x, x);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.35e+30)
		tmp = Float64(z * y);
	elseif (z <= 2.55e+160)
		tmp = fma(y, x, x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.35e+30], N[(z * y), $MachinePrecision], If[LessEqual[z, 2.55e+160], N[(y * x + x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e30 or 2.5500000000000001e160 < 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. lower-*.f64 78.5

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

   5. Simplified 78.5%

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

   if -1.3499999999999999e30 < z < 2.5500000000000001e160

   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. lower-fma.f64 80.4

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

   5. Simplified 80.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -160000000000.0) (* x y) (if (<= y 1000000000.0) x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -160000000000.0) {
		tmp = x * y;
	} else if (y <= 1000000000.0) {
		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 <= (-160000000000.0d0)) then
        tmp = x * y
    else if (y <= 1000000000.0d0) 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 <= -160000000000.0) {
		tmp = x * y;
	} else if (y <= 1000000000.0) {
		tmp = x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -160000000000.0:
		tmp = x * y
	elif y <= 1000000000.0:
		tmp = x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -160000000000.0)
		tmp = Float64(x * y);
	elseif (y <= 1000000000.0)
		tmp = x;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -160000000000.0)
		tmp = x * y;
	elseif (y <= 1000000000.0)
		tmp = x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -160000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 1000000000.0], x, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e11 or 1e9 < y

   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. lower-fma.f64 52.0

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

   5. Simplified 52.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 51.7

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

   8. Simplified 51.7%

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

   if -1.6e11 < y < 1e9

   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. lower-fma.f64 72.9

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

   5. Simplified 72.9%

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

      1. distribute-lft1-in N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 72.8

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

   7. Applied egg-rr 72.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Simplified 71.8%

       \[\leadsto \color{blue}{1} \cdot x \]
   11. Step-by-step derivation

       1. *-lft-identity 71.8

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

   12. Applied egg-rr 71.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.3% 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 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. lower-fma.f64 63.3

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

5. Simplified 63.3%

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

   1. distribute-lft1-in N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 63.3

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

7. Applied egg-rr 63.3%

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

8. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1} \cdot x \]
9. Step-by-step derivation

10. Simplified 40.3%

    \[\leadsto \color{blue}{1} \cdot x \]
11. Step-by-step derivation

    1. *-lft-identity 40.3

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

12. Applied egg-rr 40.3%

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

Reproduce

herbie shell --seed 2024208 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))