Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 8

Speedup: 1.0×

• 21.2% 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: 61.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+91} \lor \neg \left(y \leq 1.7 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.42e+20)
   (* y x)
   (if (<= y 5.7e-18)
     x
     (if (or (<= y 1.4e+91) (not (<= y 1.7e+204))) (* y z) (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.42e+20) {
		tmp = y * x;
	} else if (y <= 5.7e-18) {
		tmp = x;
	} else if ((y <= 1.4e+91) || !(y <= 1.7e+204)) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.42d+20)) then
        tmp = y * x
    else if (y <= 5.7d-18) then
        tmp = x
    else if ((y <= 1.4d+91) .or. (.not. (y <= 1.7d+204))) then
        tmp = y * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.42e+20) {
		tmp = y * x;
	} else if (y <= 5.7e-18) {
		tmp = x;
	} else if ((y <= 1.4e+91) || !(y <= 1.7e+204)) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.42e+20:
		tmp = y * x
	elif y <= 5.7e-18:
		tmp = x
	elif (y <= 1.4e+91) or not (y <= 1.7e+204):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.42e+20)
		tmp = Float64(y * x);
	elseif (y <= 5.7e-18)
		tmp = x;
	elseif ((y <= 1.4e+91) || !(y <= 1.7e+204))
		tmp = Float64(y * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.42e+20)
		tmp = y * x;
	elseif (y <= 5.7e-18)
		tmp = x;
	elseif ((y <= 1.4e+91) || ~((y <= 1.7e+204)))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.42e+20], N[(y * x), $MachinePrecision], If[LessEqual[y, 5.7e-18], x, If[Or[LessEqual[y, 1.4e+91], N[Not[LessEqual[y, 1.7e+204]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42e20 or 1.3999999999999999e91 < y < 1.70000000000000005e204

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in y around inf 63.2%

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

   if -1.42e20 < y < 5.69999999999999971e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.3%

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

   if 5.69999999999999971e-18 < y < 1.3999999999999999e91 or 1.70000000000000005e204 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 80.4%

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

   4. Taylor expanded in x around 0 79.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+91} \lor \neg \left(y \leq 1.7 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-15} \lor \neg \left(y \leq 6.4 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.2e-15) (not (<= y 6.4e-18))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.2e-15) || !(y <= 6.4e-18)) {
		tmp = y * (x + z);
	} 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 <= (-9.2d-15)) .or. (.not. (y <= 6.4d-18))) then
        tmp = y * (x + z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.2e-15) || !(y <= 6.4e-18)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.2e-15) or not (y <= 6.4e-18):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.2e-15) || !(y <= 6.4e-18))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.2e-15) || ~((y <= 6.4e-18)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.2e-15], N[Not[LessEqual[y, 6.4e-18]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.19999999999999961e-15 or 6.3999999999999998e-18 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

      4. sub-neg 97.5%

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

      5. metadata-eval 97.5%

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

      6. +-commutative 97.5%

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

      7. mul-1-neg 97.5%

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

      8. unsub-neg 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in y around inf 99.2%

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

      1. cancel-sign-sub-inv 99.2%

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

      2. metadata-eval 99.2%

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

      3. *-lft-identity 99.2%

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

      4. +-commutative 99.2%

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

   8. Simplified 99.2%

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

   if -9.19999999999999961e-15 < y < 6.3999999999999998e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-15} \lor \neg \left(y \leq 6.4 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-23} \lor \neg \left(x \leq 50000000000\right):\\ \;\;\;\;x + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e-23) (not (<= x 50000000000.0)))
   (+ x (* y x))
   (* y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-23) || !(x <= 50000000000.0)) {
		tmp = x + (y * x);
	} else {
		tmp = y * (x + 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 <= (-1.4d-23)) .or. (.not. (x <= 50000000000.0d0))) then
        tmp = x + (y * x)
    else
        tmp = y * (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-23) || !(x <= 50000000000.0)) {
		tmp = x + (y * x);
	} else {
		tmp = y * (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e-23) or not (x <= 50000000000.0):
		tmp = x + (y * x)
	else:
		tmp = y * (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e-23) || !(x <= 50000000000.0))
		tmp = Float64(x + Float64(y * x));
	else
		tmp = Float64(y * Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e-23) || ~((x <= 50000000000.0)))
		tmp = x + (y * x);
	else
		tmp = y * (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e-23], N[Not[LessEqual[x, 50000000000.0]], $MachinePrecision]], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999e-23 or 5e10 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.6%

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

      1. *-commutative 89.6%

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

   5. Simplified 89.6%

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

   if -1.3999999999999999e-23 < x < 5e10

   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 y around inf 79.7%

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

      1. cancel-sign-sub-inv 79.7%

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

      2. metadata-eval 79.7%

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

      3. *-lft-identity 79.7%

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

      4. +-commutative 79.7%

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

   8. Simplified 79.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-23} \lor \neg \left(x \leq 50000000000\right):\\ \;\;\;\;x + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+22} \lor \neg \left(y \leq 6.5 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.05e+22) (not (<= y 6.5e-18))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.05e+22) || !(y <= 6.5e-18)) {
		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 <= (-3.05d+22)) .or. (.not. (y <= 6.5d-18))) 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 <= -3.05e+22) || !(y <= 6.5e-18)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.05e+22) or not (y <= 6.5e-18):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.05e+22) || !(y <= 6.5e-18))
		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 <= -3.05e+22) || ~((y <= 6.5e-18)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.05e+22], N[Not[LessEqual[y, 6.5e-18]], $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 < -3.0499999999999999e22 or 6.50000000000000008e-18 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 97.4%

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

      1. +-commutative 97.4%

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

      2. mul-1-neg 97.4%

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

      3. unsub-neg 97.4%

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

      4. sub-neg 97.4%

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

      5. metadata-eval 97.4%

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

      6. +-commutative 97.4%

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

      7. mul-1-neg 97.4%

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

      8. unsub-neg 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. *-lft-identity 100.0%

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

      4. +-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -3.0499999999999999e22 < y < 6.50000000000000008e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.5%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+22} \lor \neg \left(y \leq 6.5 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+20} \lor \neg \left(y \leq 42000000000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.42e+20) (not (<= y 42000000000000.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42e+20) || !(y <= 42000000000000.0)) {
		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 <= (-1.42d+20)) .or. (.not. (y <= 42000000000000.0d0))) 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 <= -1.42e+20) || !(y <= 42000000000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.42e+20) or not (y <= 42000000000000.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.42e+20) || !(y <= 42000000000000.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.42e+20) || ~((y <= 42000000000000.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.42e+20], N[Not[LessEqual[y, 42000000000000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.42e20 or 4.2e13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in y around inf 54.8%

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

   if -1.42e20 < y < 4.2e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+20} \lor \neg \left(y \leq 42000000000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 37.2% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 38.4%

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

4. Final simplification 38.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))