Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Percentage Accurate: 98.0% → 100.0%

Time: 6.5s

Alternatives: 5

Speedup: 1.7×

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

Specification

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. distribute-rgt-out-- N/A

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

   2. unsub-neg N/A

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

   3. *-lft-identity N/A

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

   4. mul-1-neg N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. *-commutative N/A

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

   8. mul-1-neg N/A

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

   9. distribute-rgt-neg-in N/A

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

   10. mul-1-neg N/A

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

   11. distribute-lft-in N/A

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

   12. +-commutative N/A

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

   13. remove-double-neg N/A

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

   14. mul-1-neg N/A

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

   15. mul-1-neg N/A

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

   16. distribute-neg-in N/A

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

   17. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

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

Alternative 2: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-25}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -2.3e-29) t_0 (if (<= y 1.8e-25) (- z (* y z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -2.3e-29) {
		tmp = t_0;
	} else if (y <= 1.8e-25) {
		tmp = z - (y * z);
	} 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 <= (-2.3d-29)) then
        tmp = t_0
    else if (y <= 1.8d-25) then
        tmp = z - (y * z)
    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 <= -2.3e-29) {
		tmp = t_0;
	} else if (y <= 1.8e-25) {
		tmp = z - (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -2.3e-29:
		tmp = t_0
	elif y <= 1.8e-25:
		tmp = z - (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	tmp = 0.0
	if (y <= -2.3e-29)
		tmp = t_0;
	elseif (y <= 1.8e-25)
		tmp = Float64(z - Float64(y * z));
	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 <= -2.3e-29)
		tmp = t_0;
	elseif (y <= 1.8e-25)
		tmp = z - (y * z);
	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, -2.3e-29], t$95$0, If[LessEqual[y, 1.8e-25], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.29999999999999991e-29 or 1.8e-25 < y

   1. Initial program 96.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -2.29999999999999991e-29 < y < 1.8e-25

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{1 \cdot z - y \cdot z} \]

      2. *-lft-identity N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-25}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+66}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-41}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= z -2.2e+66) t_0 (if (<= z 6e-41) (* x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -2.2e+66) {
		tmp = t_0;
	} else if (z <= 6e-41) {
		tmp = x * y;
	} 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 * -z
    if (z <= (-2.2d+66)) then
        tmp = t_0
    else if (z <= 6d-41) then
        tmp = x * y
    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 * -z;
	double tmp;
	if (z <= -2.2e+66) {
		tmp = t_0;
	} else if (z <= 6e-41) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if z <= -2.2e+66:
		tmp = t_0
	elif z <= 6e-41:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -2.2e+66)
		tmp = t_0;
	elseif (z <= 6e-41)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (z <= -2.2e+66)
		tmp = t_0;
	elseif (z <= 6e-41)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.2e+66], t$95$0, If[LessEqual[z, 6e-41], N[(x * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999998e66 or 5.99999999999999978e-41 < z

   1. Initial program 96.2%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 44.8%

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

   if -2.1999999999999998e66 < z < 5.99999999999999978e-41

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-41}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.6% accurate, 1.9× 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 98.0%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. +-commutative N/A

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

   2. remove-double-neg N/A

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

   3. mul-1-neg N/A

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

   4. mul-1-neg N/A

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

   5. distribute-neg-in N/A

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

   6. lower-*.f64 N/A

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

   7. +-commutative N/A

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

   8. distribute-neg-in N/A

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

   9. mul-1-neg N/A

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

   10. remove-double-neg N/A

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

   11. unsub-neg N/A

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

   12. lower--.f64 62.3

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

5. Applied rewrites 62.3%

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

Alternative 5: 40.8% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 39.3

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

5. Applied rewrites 39.3%

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

6. Final simplification 39.3%

   \[\leadsto x \cdot y \]
7. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024221 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- z (* (- z x) y)))

  (+ (* x y) (* z (- 1.0 y))))