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

Percentage Accurate: 97.9% → 100.0%

Time: 6.4s

Alternatives: 7

Speedup: 1.3×

• 21.4% 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: 97.9% 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, 0.1× 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 99.2%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. distribute-lft-out-- 99.2%

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

   2. *-rgt-identity 99.2%

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

   3. cancel-sign-sub-inv 99.2%

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

   4. +-commutative 99.2%

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

   5. associate-+r+ 99.2%

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

   6. +-commutative 99.2%

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

   7. distribute-rgt-out 100.0%

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

   8. fma-define 100.0%

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

   9. +-commutative 100.0%

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

   10. unsub-neg 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+193}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+155}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -6.6e+193)
     (* y x)
     (if (<= y -1.15e+113)
       t_0
       (if (<= y -4.3e-97)
         (* y x)
         (if (<= y 6.8e-12) z (if (<= y 1.22e+155) (* y x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -6.6e+193) {
		tmp = y * x;
	} else if (y <= -1.15e+113) {
		tmp = t_0;
	} else if (y <= -4.3e-97) {
		tmp = y * x;
	} else if (y <= 6.8e-12) {
		tmp = z;
	} else if (y <= 1.22e+155) {
		tmp = y * 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 * -z
    if (y <= (-6.6d+193)) then
        tmp = y * x
    else if (y <= (-1.15d+113)) then
        tmp = t_0
    else if (y <= (-4.3d-97)) then
        tmp = y * x
    else if (y <= 6.8d-12) then
        tmp = z
    else if (y <= 1.22d+155) then
        tmp = y * 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 * -z;
	double tmp;
	if (y <= -6.6e+193) {
		tmp = y * x;
	} else if (y <= -1.15e+113) {
		tmp = t_0;
	} else if (y <= -4.3e-97) {
		tmp = y * x;
	} else if (y <= 6.8e-12) {
		tmp = z;
	} else if (y <= 1.22e+155) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -6.6e+193:
		tmp = y * x
	elif y <= -1.15e+113:
		tmp = t_0
	elif y <= -4.3e-97:
		tmp = y * x
	elif y <= 6.8e-12:
		tmp = z
	elif y <= 1.22e+155:
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -6.6e+193)
		tmp = Float64(y * x);
	elseif (y <= -1.15e+113)
		tmp = t_0;
	elseif (y <= -4.3e-97)
		tmp = Float64(y * x);
	elseif (y <= 6.8e-12)
		tmp = z;
	elseif (y <= 1.22e+155)
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (y <= -6.6e+193)
		tmp = y * x;
	elseif (y <= -1.15e+113)
		tmp = t_0;
	elseif (y <= -4.3e-97)
		tmp = y * x;
	elseif (y <= 6.8e-12)
		tmp = z;
	elseif (y <= 1.22e+155)
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -6.6e+193], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.15e+113], t$95$0, If[LessEqual[y, -4.3e-97], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.8e-12], z, If[LessEqual[y, 1.22e+155], N[(y * x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6e193 or -1.14999999999999998e113 < y < -4.3e-97 or 6.8000000000000001e-12 < y < 1.21999999999999996e155

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 61.0%

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

      1. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   if -6.6e193 < y < -1.14999999999999998e113 or 1.21999999999999996e155 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. distribute-rgt-neg-in 73.8%

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

   8. Simplified 73.8%

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

   if -4.3e-97 < y < 6.8000000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.7%

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

   4. Taylor expanded in y around 0 73.3%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.3 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 4.3e-11))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 4.3e-11)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 4.3d-11))) then
        tmp = y * (x - z)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 4.3e-11)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 4.3e-11):
		tmp = y * (x - z)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 4.3e-11))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 4.3e-11)))
		tmp = y * (x - z);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 4.3e-11]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 4.30000000000000001e-11 < y

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. neg-mul-1 99.7%

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

      2. sub-neg 99.7%

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

   5. Simplified 99.7%

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

   if -1 < y < 4.30000000000000001e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.3 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-97} \lor \neg \left(y \leq 1.3 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e-97) (not (<= y 1.3e-11))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-97) || !(y <= 1.3e-11)) {
		tmp = y * (x - z);
	} else {
		tmp = 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 <= (-4.4d-97)) .or. (.not. (y <= 1.3d-11))) then
        tmp = y * (x - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-97) || !(y <= 1.3e-11)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e-97) or not (y <= 1.3e-11):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e-97) || !(y <= 1.3e-11))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.4e-97) || ~((y <= 1.3e-11)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e-97], N[Not[LessEqual[y, 1.3e-11]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e-97 or 1.3e-11 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 91.6%

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

      1. neg-mul-1 91.6%

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

      2. sub-neg 91.6%

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

   5. Simplified 91.6%

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

   if -4.3999999999999998e-97 < y < 1.3e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.7%

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

   4. Taylor expanded in y around 0 73.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-97} \lor \neg \left(y \leq 1.3 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-97} \lor \neg \left(y \leq 4.4 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e-97) (not (<= y 4.4e-12))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-97) || !(y <= 4.4e-12)) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-4.4d-97)) .or. (.not. (y <= 4.4d-12))) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-97) || !(y <= 4.4e-12)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e-97) or not (y <= 4.4e-12):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e-97) || !(y <= 4.4e-12))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.4e-97) || ~((y <= 4.4e-12)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e-97], N[Not[LessEqual[y, 4.4e-12]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e-97 or 4.39999999999999983e-12 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   if -4.3999999999999998e-97 < y < 4.39999999999999983e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.7%

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

   4. Taylor expanded in y around 0 73.3%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-97} \lor \neg \left(y \leq 4.4 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. +-commutative 99.2%

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

   2. distribute-lft-out-- 99.2%

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

   3. *-rgt-identity 99.2%

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

   4. cancel-sign-sub-inv 99.2%

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

   5. +-commutative 99.2%

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

   6. +-commutative 99.2%

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

   7. associate-+l+ 99.2%

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

   8. distribute-lft-neg-out 99.2%

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

   9. remove-double-neg 99.2%

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

   10. distribute-rgt-neg-out 99.2%

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

   11. distribute-neg-out 99.2%

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

   12. sub-neg 99.2%

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

   13. distribute-rgt-neg-out 99.2%

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

   14. sub-neg 99.2%

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

   15. distribute-rgt-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 35.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around inf 87.5%

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

4. Taylor expanded in y around 0 37.3%

   \[\leadsto \color{blue}{z} \]
5. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.3× 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 2024182 
(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))))