Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 8

Speedup: 1.0×

• 20.3% 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: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -0.0048:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-85} \lor \neg \left(y \leq 1.65 \cdot 10^{-51}\right) \land y \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -0.0048)
     t_0
     (if (<= y -3.8e-44)
       x
       (if (<= y -1.12e-63)
         (* y z)
         (if (or (<= y 9e-85) (and (not (<= y 1.65e-51)) (<= y 5.8e-9)))
           x
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -0.0048) {
		tmp = t_0;
	} else if (y <= -3.8e-44) {
		tmp = x;
	} else if (y <= -1.12e-63) {
		tmp = y * z;
	} else if ((y <= 9e-85) || (!(y <= 1.65e-51) && (y <= 5.8e-9))) {
		tmp = x;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * (x + z)
    if (y <= (-0.0048d0)) then
        tmp = t_0
    else if (y <= (-3.8d-44)) then
        tmp = x
    else if (y <= (-1.12d-63)) then
        tmp = y * z
    else if ((y <= 9d-85) .or. (.not. (y <= 1.65d-51)) .and. (y <= 5.8d-9)) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -0.0048) {
		tmp = t_0;
	} else if (y <= -3.8e-44) {
		tmp = x;
	} else if (y <= -1.12e-63) {
		tmp = y * z;
	} else if ((y <= 9e-85) || (!(y <= 1.65e-51) && (y <= 5.8e-9))) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -0.0048:
		tmp = t_0
	elif y <= -3.8e-44:
		tmp = x
	elif y <= -1.12e-63:
		tmp = y * z
	elif (y <= 9e-85) or (not (y <= 1.65e-51) and (y <= 5.8e-9)):
		tmp = 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 <= -0.0048)
		tmp = t_0;
	elseif (y <= -3.8e-44)
		tmp = x;
	elseif (y <= -1.12e-63)
		tmp = Float64(y * z);
	elseif ((y <= 9e-85) || (!(y <= 1.65e-51) && (y <= 5.8e-9)))
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x + z);
	tmp = 0.0;
	if (y <= -0.0048)
		tmp = t_0;
	elseif (y <= -3.8e-44)
		tmp = x;
	elseif (y <= -1.12e-63)
		tmp = y * z;
	elseif ((y <= 9e-85) || (~((y <= 1.65e-51)) && (y <= 5.8e-9)))
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0048], t$95$0, If[LessEqual[y, -3.8e-44], x, If[LessEqual[y, -1.12e-63], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, 9e-85], And[N[Not[LessEqual[y, 1.65e-51]], $MachinePrecision], LessEqual[y, 5.8e-9]]], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00479999999999999958 or 9.00000000000000008e-85 < y < 1.64999999999999986e-51 or 5.79999999999999982e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

      4. sub-neg 98.5%

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

      5. metadata-eval 98.5%

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

      6. +-commutative 98.5%

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

      7. mul-1-neg 98.5%

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

      8. unsub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around inf 95.4%

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

      1. cancel-sign-sub-inv 95.4%

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

      2. metadata-eval 95.4%

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

      3. *-lft-identity 95.4%

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

      4. +-commutative 95.4%

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

   8. Simplified 95.4%

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

   if -0.00479999999999999958 < y < -3.8000000000000001e-44 or -1.12000000000000002e-63 < y < 9.00000000000000008e-85 or 1.64999999999999986e-51 < y < 5.79999999999999982e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.4%

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

   if -3.8000000000000001e-44 < y < -1.12000000000000002e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. +-commutative 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 81.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0048:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-85} \lor \neg \left(y \leq 1.65 \cdot 10^{-51}\right) \land y \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0048:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.65 \cdot 10^{+213} \lor \neg \left(y \leq 2.7 \cdot 10^{+252}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0048)
   (* y z)
   (if (<= y -1e-42)
     x
     (if (<= y -1e-63)
       (* y z)
       (if (<= y 1.0)
         x
         (if (or (<= y 4.65e+213) (not (<= y 2.7e+252))) (* y x) (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0048) {
		tmp = y * z;
	} else if (y <= -1e-42) {
		tmp = x;
	} else if (y <= -1e-63) {
		tmp = y * z;
	} else if (y <= 1.0) {
		tmp = x;
	} else if ((y <= 4.65e+213) || !(y <= 2.7e+252)) {
		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 <= (-0.0048d0)) then
        tmp = y * z
    else if (y <= (-1d-42)) then
        tmp = x
    else if (y <= (-1d-63)) then
        tmp = y * z
    else if (y <= 1.0d0) then
        tmp = x
    else if ((y <= 4.65d+213) .or. (.not. (y <= 2.7d+252))) 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 <= -0.0048) {
		tmp = y * z;
	} else if (y <= -1e-42) {
		tmp = x;
	} else if (y <= -1e-63) {
		tmp = y * z;
	} else if (y <= 1.0) {
		tmp = x;
	} else if ((y <= 4.65e+213) || !(y <= 2.7e+252)) {
		tmp = y * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0048:
		tmp = y * z
	elif y <= -1e-42:
		tmp = x
	elif y <= -1e-63:
		tmp = y * z
	elif y <= 1.0:
		tmp = x
	elif (y <= 4.65e+213) or not (y <= 2.7e+252):
		tmp = y * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0048)
		tmp = Float64(y * z);
	elseif (y <= -1e-42)
		tmp = x;
	elseif (y <= -1e-63)
		tmp = Float64(y * z);
	elseif (y <= 1.0)
		tmp = x;
	elseif ((y <= 4.65e+213) || !(y <= 2.7e+252))
		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 <= -0.0048)
		tmp = y * z;
	elseif (y <= -1e-42)
		tmp = x;
	elseif (y <= -1e-63)
		tmp = y * z;
	elseif (y <= 1.0)
		tmp = x;
	elseif ((y <= 4.65e+213) || ~((y <= 2.7e+252)))
		tmp = y * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0048], N[(y * z), $MachinePrecision], If[LessEqual[y, -1e-42], x, If[LessEqual[y, -1e-63], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.0], x, If[Or[LessEqual[y, 4.65e+213], N[Not[LessEqual[y, 2.7e+252]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00479999999999999958 or -1.00000000000000004e-42 < y < -1.00000000000000007e-63 or 4.6500000000000002e213 < y < 2.7000000000000001e252

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

      4. sub-neg 98.5%

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

      5. metadata-eval 98.5%

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

      6. +-commutative 98.5%

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

      7. mul-1-neg 98.5%

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

      8. unsub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in z around inf 65.1%

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

   if -0.00479999999999999958 < y < -1.00000000000000004e-42 or -1.00000000000000007e-63 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.0%

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

   if 1 < y < 4.6500000000000002e213 or 2.7000000000000001e252 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in y around inf 63.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0048:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.65 \cdot 10^{+213} \lor \neg \left(y \leq 2.7 \cdot 10^{+252}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-13} \lor \neg \left(z \leq 4.5 \cdot 10^{+88}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e-13) (not (<= z 4.5e+88))) (* y (+ x z)) (+ x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-13) || !(z <= 4.5e+88)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (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 ((z <= (-2.8d-13)) .or. (.not. (z <= 4.5d+88))) then
        tmp = y * (x + z)
    else
        tmp = x + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-13) || !(z <= 4.5e+88)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e-13) or not (z <= 4.5e+88):
		tmp = y * (x + z)
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e-13) || !(z <= 4.5e+88))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.8e-13) || ~((z <= 4.5e+88)))
		tmp = y * (x + z);
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e-13], N[Not[LessEqual[z, 4.5e+88]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000002e-13 or 4.5e88 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 98.3%

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

      1. +-commutative 98.3%

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

      2. mul-1-neg 98.3%

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

      3. unsub-neg 98.3%

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

      4. sub-neg 98.3%

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

      5. metadata-eval 98.3%

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

      6. +-commutative 98.3%

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

      7. mul-1-neg 98.3%

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

      8. unsub-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 80.7%

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

      1. cancel-sign-sub-inv 80.7%

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

      2. metadata-eval 80.7%

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

      3. *-lft-identity 80.7%

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

      4. +-commutative 80.7%

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

   8. Simplified 80.7%

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

   if -2.8000000000000002e-13 < z < 4.5e88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 87.1%

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

      1. *-commutative 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-13} \lor \neg \left(z \leq 4.5 \cdot 10^{+88}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0045\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.0045))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.0045)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 0.0045d0))) 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 <= -1.0) || !(y <= 0.0045)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.0045):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.0045))
		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 <= -1.0) || ~((y <= 0.0045)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.0045]], $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 < -1 or 0.00449999999999999966 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 98.3%

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

      1. +-commutative 98.3%

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

      2. mul-1-neg 98.3%

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

      3. unsub-neg 98.3%

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

      4. sub-neg 98.3%

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

      5. metadata-eval 98.3%

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

      6. +-commutative 98.3%

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

      7. mul-1-neg 98.3%

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

      8. unsub-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 97.9%

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

      1. cancel-sign-sub-inv 97.9%

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

      2. metadata-eval 97.9%

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

      3. *-lft-identity 97.9%

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

      4. +-commutative 97.9%

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

   8. Simplified 97.9%

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

   if -1 < y < 0.00449999999999999966

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0045\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
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 z around 0 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around inf 51.0%

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

   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 66.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 37.4% 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 36.9%

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

4. Final simplification 36.9%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))