Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 8

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

   3. +-commutative 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+151}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+128}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+46}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+28}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+51} \lor \neg \left(y \leq 2.05 \cdot 10^{+151}\right) \land y \leq 1.1 \cdot 10^{+234}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+151)
   (* y z)
   (if (<= y -6.6e+128)
     (* y x)
     (if (<= y -3.3e+63)
       (* y z)
       (if (<= y -3.45e+46)
         (* y x)
         (if (<= y -1.9e-64)
           (* y z)
           (if (<= y 4.2e-23)
             x
             (if (<= y 6.4e+28)
               (* y z)
               (if (or (<= y 1.15e+51)
                       (and (not (<= y 2.05e+151)) (<= y 1.1e+234)))
                 (* y x)
                 (* y z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+151) {
		tmp = y * z;
	} else if (y <= -6.6e+128) {
		tmp = y * x;
	} else if (y <= -3.3e+63) {
		tmp = y * z;
	} else if (y <= -3.45e+46) {
		tmp = y * x;
	} else if (y <= -1.9e-64) {
		tmp = y * z;
	} else if (y <= 4.2e-23) {
		tmp = x;
	} else if (y <= 6.4e+28) {
		tmp = y * z;
	} else if ((y <= 1.15e+51) || (!(y <= 2.05e+151) && (y <= 1.1e+234))) {
		tmp = y * x;
	} 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 (y <= (-8d+151)) then
        tmp = y * z
    else if (y <= (-6.6d+128)) then
        tmp = y * x
    else if (y <= (-3.3d+63)) then
        tmp = y * z
    else if (y <= (-3.45d+46)) then
        tmp = y * x
    else if (y <= (-1.9d-64)) then
        tmp = y * z
    else if (y <= 4.2d-23) then
        tmp = x
    else if (y <= 6.4d+28) then
        tmp = y * z
    else if ((y <= 1.15d+51) .or. (.not. (y <= 2.05d+151)) .and. (y <= 1.1d+234)) then
        tmp = y * x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+151) {
		tmp = y * z;
	} else if (y <= -6.6e+128) {
		tmp = y * x;
	} else if (y <= -3.3e+63) {
		tmp = y * z;
	} else if (y <= -3.45e+46) {
		tmp = y * x;
	} else if (y <= -1.9e-64) {
		tmp = y * z;
	} else if (y <= 4.2e-23) {
		tmp = x;
	} else if (y <= 6.4e+28) {
		tmp = y * z;
	} else if ((y <= 1.15e+51) || (!(y <= 2.05e+151) && (y <= 1.1e+234))) {
		tmp = y * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+151:
		tmp = y * z
	elif y <= -6.6e+128:
		tmp = y * x
	elif y <= -3.3e+63:
		tmp = y * z
	elif y <= -3.45e+46:
		tmp = y * x
	elif y <= -1.9e-64:
		tmp = y * z
	elif y <= 4.2e-23:
		tmp = x
	elif y <= 6.4e+28:
		tmp = y * z
	elif (y <= 1.15e+51) or (not (y <= 2.05e+151) and (y <= 1.1e+234)):
		tmp = y * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+151)
		tmp = Float64(y * z);
	elseif (y <= -6.6e+128)
		tmp = Float64(y * x);
	elseif (y <= -3.3e+63)
		tmp = Float64(y * z);
	elseif (y <= -3.45e+46)
		tmp = Float64(y * x);
	elseif (y <= -1.9e-64)
		tmp = Float64(y * z);
	elseif (y <= 4.2e-23)
		tmp = x;
	elseif (y <= 6.4e+28)
		tmp = Float64(y * z);
	elseif ((y <= 1.15e+51) || (!(y <= 2.05e+151) && (y <= 1.1e+234)))
		tmp = Float64(y * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+151)
		tmp = y * z;
	elseif (y <= -6.6e+128)
		tmp = y * x;
	elseif (y <= -3.3e+63)
		tmp = y * z;
	elseif (y <= -3.45e+46)
		tmp = y * x;
	elseif (y <= -1.9e-64)
		tmp = y * z;
	elseif (y <= 4.2e-23)
		tmp = x;
	elseif (y <= 6.4e+28)
		tmp = y * z;
	elseif ((y <= 1.15e+51) || (~((y <= 2.05e+151)) && (y <= 1.1e+234)))
		tmp = y * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+151], N[(y * z), $MachinePrecision], If[LessEqual[y, -6.6e+128], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.3e+63], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.45e+46], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.9e-64], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.2e-23], x, If[LessEqual[y, 6.4e+28], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, 1.15e+51], And[N[Not[LessEqual[y, 2.05e+151]], $MachinePrecision], LessEqual[y, 1.1e+234]]], N[(y * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000014e151 or -6.6000000000000001e128 < y < -3.3000000000000002e63 or -3.45000000000000009e46 < y < -1.9000000000000001e-64 or 4.2000000000000002e-23 < y < 6.4000000000000001e28 or 1.15000000000000003e51 < y < 2.0499999999999999e151 or 1.10000000000000004e234 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.2%

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

      1. +-commutative 97.2%

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

      2. mul-1-neg 97.2%

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

      3. unsub-neg 97.2%

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

      4. sub-neg 97.2%

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

      5. metadata-eval 97.2%

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

      6. +-commutative 97.2%

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

      7. mul-1-neg 97.2%

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

      8. unsub-neg 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -8.00000000000000014e151 < y < -6.6000000000000001e128 or -3.3000000000000002e63 < y < -3.45000000000000009e46 or 6.4000000000000001e28 < y < 1.15000000000000003e51 or 2.0499999999999999e151 < y < 1.10000000000000004e234

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.9%

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

      1. +-commutative 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in y around inf 92.9%

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

   if -1.9000000000000001e-64 < y < 4.2000000000000002e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+151}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+128}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+46}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+28}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+51} \lor \neg \left(y \leq 2.05 \cdot 10^{+151}\right) \land y \leq 1.1 \cdot 10^{+234}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-84} \lor \neg \left(x \leq 6.5 \cdot 10^{-149}\right) \land \left(x \leq 7.6 \cdot 10^{-68} \lor \neg \left(x \leq 1.18 \cdot 10^{+24}\right)\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e-84)
         (and (not (<= x 6.5e-149)) (or (<= x 7.6e-68) (not (<= x 1.18e+24)))))
   (* x (+ y 1.0))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e-84) || (!(x <= 6.5e-149) && ((x <= 7.6e-68) || !(x <= 1.18e+24)))) {
		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 <= (-6.2d-84)) .or. (.not. (x <= 6.5d-149)) .and. (x <= 7.6d-68) .or. (.not. (x <= 1.18d+24))) 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 <= -6.2e-84) || (!(x <= 6.5e-149) && ((x <= 7.6e-68) || !(x <= 1.18e+24)))) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e-84) or (not (x <= 6.5e-149) and ((x <= 7.6e-68) or not (x <= 1.18e+24))):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e-84) || (!(x <= 6.5e-149) && ((x <= 7.6e-68) || !(x <= 1.18e+24))))
		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 <= -6.2e-84) || (~((x <= 6.5e-149)) && ((x <= 7.6e-68) || ~((x <= 1.18e+24)))))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e-84], And[N[Not[LessEqual[x, 6.5e-149]], $MachinePrecision], Or[LessEqual[x, 7.6e-68], N[Not[LessEqual[x, 1.18e+24]], $MachinePrecision]]]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.20000000000000003e-84 or 6.50000000000000019e-149 < x < 7.60000000000000075e-68 or 1.17999999999999997e24 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.8%

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

      1. +-commutative 86.8%

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

   4. Simplified 86.8%

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

   if -6.20000000000000003e-84 < x < 6.50000000000000019e-149 or 7.60000000000000075e-68 < x < 1.17999999999999997e24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. +-commutative 99.9%

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

      7. mul-1-neg 99.9%

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

      8. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-84} \lor \neg \left(x \leq 6.5 \cdot 10^{-149}\right) \land \left(x \leq 7.6 \cdot 10^{-68} \lor \neg \left(x \leq 1.18 \cdot 10^{+24}\right)\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-64} \lor \neg \left(y \leq 7.5 \cdot 10^{-83}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.35e-64) (not (<= y 7.5e-83))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e-64) || !(y <= 7.5e-83)) {
		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 <= (-2.35d-64)) .or. (.not. (y <= 7.5d-83))) 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 <= -2.35e-64) || !(y <= 7.5e-83)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.35e-64) or not (y <= 7.5e-83):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.35e-64) || !(y <= 7.5e-83))
		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 <= -2.35e-64) || ~((y <= 7.5e-83)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.35e-64], N[Not[LessEqual[y, 7.5e-83]], $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 < -2.3499999999999999e-64 or 7.4999999999999997e-83 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

      4. sub-neg 97.3%

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

      5. metadata-eval 97.3%

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

      6. +-commutative 97.3%

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

      7. mul-1-neg 97.3%

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

      8. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in y around inf 88.1%

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

      1. cancel-sign-sub-inv 88.1%

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

      2. metadata-eval 88.1%

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

      3. *-lft-identity 88.1%

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

      4. +-commutative 88.1%

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

   7. Simplified 88.1%

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

   if -2.3499999999999999e-64 < y < 7.4999999999999997e-83

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.8%

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

      1. +-commutative 80.8%

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

   4. Simplified 80.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-64} \lor \neg \left(y \leq 7.5 \cdot 10^{-83}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 5: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+29} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e+29) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e+29) || !(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 <= (-2.2d+29)) .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 <= -2.2e+29) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e+29) 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 <= -2.2e+29) || !(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 <= -2.2e+29) || ~((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, -2.2e+29], 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 < -2.2000000000000001e29 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 96.3%

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

      1. +-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. unsub-neg 96.3%

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

      4. sub-neg 96.3%

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

      5. metadata-eval 96.3%

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

      6. +-commutative 96.3%

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

      7. mul-1-neg 96.3%

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

      8. unsub-neg 96.3%

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

   4. Simplified 96.3%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. cancel-sign-sub-inv 98.6%

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

      2. metadata-eval 98.6%

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

      3. *-lft-identity 98.6%

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

      4. +-commutative 98.6%

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

   7. Simplified 98.6%

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

   if -2.2000000000000001e29 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+29} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 60.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= 1.0:
		tmp = x
	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 <= 1.0)
		tmp = x;
	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 <= 1.0)
		tmp = x;
	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, 1.0], x, N[(y * x), $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. Taylor expanded in x around inf 49.6%

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

      1. +-commutative 49.6%

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

   4. Simplified 49.6%

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

   5. Taylor expanded in y around inf 48.2%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.7%

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

4. Final simplification 60.4%

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

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 8: 36.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 40.7%

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

3. Final simplification 40.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))