Linear.Quaternion:$c/ from linear-1.19.1.3, C

Percentage Accurate: 63.2% → 99.0%

Time: 7.6s

Alternatives: 4

Speedup: 3.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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) + (y * y)) - (y * z)) - (y * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 63.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (y * y)) - (y * z)) - (y * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (fma y x (* y (- z))))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 58.8%

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

   1. sqr-neg 58.8%

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

   2. cancel-sign-sub 58.8%

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

   3. +-commutative 58.8%

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

   4. +-commutative 58.8%

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

   5. *-commutative 58.8%

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

   6. associate--l+ 58.8%

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

   7. associate-+r+ 76.2%

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

   8. sqr-neg 76.2%

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

   9. distribute-lft-neg-out 76.2%

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

   10. sub-neg 76.2%

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

   11. +-inverses 99.6%

       \[\leadsto \color{blue}{0} + \left(y \cdot x - y \cdot z\right) \]

   12. +-lft-identity 99.6%

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

   13. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

   1. sub-neg 100.0%

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

   2. distribute-lft-in 99.6%

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

5. Applied egg-rr 99.6%

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

   1. distribute-rgt-neg-out 99.6%

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

   2. distribute-lft-neg-in 99.6%

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

   3. add-sqr-sqrt 46.7%

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

   4. sqrt-unprod 65.1%

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

   5. sqr-neg 65.1%

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

   6. sqrt-unprod 28.0%

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

   7. add-sqr-sqrt 54.7%

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

   8. cancel-sign-sub-inv 54.7%

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

   9. add-cube-cbrt 54.7%

      \[\leadsto y \cdot x - \color{blue}{\left(\sqrt[3]{y \cdot \left(-z\right)} \cdot \sqrt[3]{y \cdot \left(-z\right)}\right) \cdot \sqrt[3]{y \cdot \left(-z\right)}} \]

   10. cancel-sign-sub-inv 54.7%

       \[\leadsto \color{blue}{y \cdot x + \left(-\sqrt[3]{y \cdot \left(-z\right)} \cdot \sqrt[3]{y \cdot \left(-z\right)}\right) \cdot \sqrt[3]{y \cdot \left(-z\right)}} \]

   11. fma-def 54.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-\sqrt[3]{y \cdot \left(-z\right)} \cdot \sqrt[3]{y \cdot \left(-z\right)}\right) \cdot \sqrt[3]{y \cdot \left(-z\right)}\right)} \]

7. Applied egg-rr 99.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-{\left(\sqrt[3]{y \cdot z}\right)}^{2}\right) \cdot \sqrt[3]{y \cdot z}\right)} \]
8. Step-by-step derivation

   1. distribute-lft-neg-out 99.1%

      \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{-{\left(\sqrt[3]{y \cdot z}\right)}^{2} \cdot \sqrt[3]{y \cdot z}}\right) \]

   2. unpow2 99.1%

      \[\leadsto \mathsf{fma}\left(y, x, -\color{blue}{\left(\sqrt[3]{y \cdot z} \cdot \sqrt[3]{y \cdot z}\right)} \cdot \sqrt[3]{y \cdot z}\right) \]

   3. add-cube-cbrt 100.0%

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

9. Applied egg-rr 100.0%

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

10. Final simplification 100.0%

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

Alternative 2: 77.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.2e-22) (* y x) (if (<= x 1.85e-75) (* y (- z)) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e-22) {
		tmp = y * x;
	} else if (x <= 1.85e-75) {
		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 (x <= (-2.2d-22)) then
        tmp = y * x
    else if (x <= 1.85d-75) 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 (x <= -2.2e-22) {
		tmp = y * x;
	} else if (x <= 1.85e-75) {
		tmp = y * -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.2e-22:
		tmp = y * x
	elif x <= 1.85e-75:
		tmp = y * -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.2e-22)
		tmp = Float64(y * x);
	elseif (x <= 1.85e-75)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.2e-22)
		tmp = y * x;
	elseif (x <= 1.85e-75)
		tmp = y * -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.2e-22], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.85e-75], N[(y * (-z)), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000001e-22 or 1.85000000000000012e-75 < x

   1. Initial program 67.3%

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

      1. sqr-neg 67.3%

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

      2. cancel-sign-sub 67.3%

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

      3. +-commutative 67.3%

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

      4. +-commutative 67.3%

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

      5. *-commutative 67.3%

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

      6. associate--l+ 67.3%

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

      7. associate-+r+ 76.4%

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

      8. sqr-neg 76.4%

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

      9. distribute-lft-neg-out 76.4%

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

      10. sub-neg 76.4%

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

      11. +-inverses 99.3%

          \[\leadsto \color{blue}{0} + \left(y \cdot x - y \cdot z\right) \]

      12. +-lft-identity 99.3%

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

      13. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.2%

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

   if -2.2000000000000001e-22 < x < 1.85000000000000012e-75

   1. Initial program 45.3%

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

      1. sqr-neg 45.3%

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

      2. cancel-sign-sub 45.3%

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

      3. +-commutative 45.3%

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

      4. +-commutative 45.3%

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

      5. *-commutative 45.3%

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

      6. associate--l+ 45.3%

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

      7. associate-+r+ 75.7%

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

      8. sqr-neg 75.7%

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

      9. distribute-lft-neg-out 75.7%

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

      10. sub-neg 75.7%

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

      11. +-inverses 100.0%

          \[\leadsto \color{blue}{0} + \left(y \cdot x - y \cdot z\right) \]

      12. +-lft-identity 100.0%

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

      13. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-out 87.3%

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

   6. Simplified 87.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 100.0% accurate, 3.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y * (x - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.8%

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

   1. sqr-neg 58.8%

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

   2. cancel-sign-sub 58.8%

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

   3. +-commutative 58.8%

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

   4. +-commutative 58.8%

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

   5. *-commutative 58.8%

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

   6. associate--l+ 58.8%

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

   7. associate-+r+ 76.2%

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

   8. sqr-neg 76.2%

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

   9. distribute-lft-neg-out 76.2%

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

   10. sub-neg 76.2%

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

   11. +-inverses 99.6%

       \[\leadsto \color{blue}{0} + \left(y \cdot x - y \cdot z\right) \]

   12. +-lft-identity 99.6%

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

   13. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 4: 53.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return y * 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 = y * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.8%

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

   1. sqr-neg 58.8%

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

   2. cancel-sign-sub 58.8%

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

   3. +-commutative 58.8%

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

   4. +-commutative 58.8%

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

   5. *-commutative 58.8%

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

   6. associate--l+ 58.8%

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

   7. associate-+r+ 76.2%

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

   8. sqr-neg 76.2%

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

   9. distribute-lft-neg-out 76.2%

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

   10. sub-neg 76.2%

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

   11. +-inverses 99.6%

       \[\leadsto \color{blue}{0} + \left(y \cdot x - y \cdot z\right) \]

   12. +-lft-identity 99.6%

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

   13. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 57.8%

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

5. Final simplification 57.8%

   \[\leadsto y \cdot x \]

Developer target: 100.0% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

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 - z) * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))