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

Percentage Accurate: 97.9% → 100.0%

Time: 3.9s

Alternatives: 8

Speedup: 1.3×

• 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: 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 97.7%

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

   1. +-commutative 97.7%

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

   2. sub-neg 97.7%

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

   3. distribute-rgt-in 97.6%

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

   4. *-lft-identity 97.6%

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

   5. associate-+l+ 97.6%

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

   6. +-commutative 97.6%

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

   7. *-commutative 97.6%

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

   8. neg-mul-1 97.6%

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

   9. associate-*r* 97.6%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. 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. Final simplification 100.0%

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

Alternative 2: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-57}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 850:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-35)
   (* y x)
   (if (<= y -3.25e-57)
     z
     (if (<= y -1.8e-70)
       (* y x)
       (if (<= y 1.2e-60) z (if (<= y 850.0) (* y x) (* z (- y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-35) {
		tmp = y * x;
	} else if (y <= -3.25e-57) {
		tmp = z;
	} else if (y <= -1.8e-70) {
		tmp = y * x;
	} else if (y <= 1.2e-60) {
		tmp = z;
	} else if (y <= 850.0) {
		tmp = y * x;
	} else {
		tmp = z * -y;
	}
	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 <= (-1.9d-35)) then
        tmp = y * x
    else if (y <= (-3.25d-57)) then
        tmp = z
    else if (y <= (-1.8d-70)) then
        tmp = y * x
    else if (y <= 1.2d-60) then
        tmp = z
    else if (y <= 850.0d0) then
        tmp = y * x
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-35) {
		tmp = y * x;
	} else if (y <= -3.25e-57) {
		tmp = z;
	} else if (y <= -1.8e-70) {
		tmp = y * x;
	} else if (y <= 1.2e-60) {
		tmp = z;
	} else if (y <= 850.0) {
		tmp = y * x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e-35:
		tmp = y * x
	elif y <= -3.25e-57:
		tmp = z
	elif y <= -1.8e-70:
		tmp = y * x
	elif y <= 1.2e-60:
		tmp = z
	elif y <= 850.0:
		tmp = y * x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e-35)
		tmp = Float64(y * x);
	elseif (y <= -3.25e-57)
		tmp = z;
	elseif (y <= -1.8e-70)
		tmp = Float64(y * x);
	elseif (y <= 1.2e-60)
		tmp = z;
	elseif (y <= 850.0)
		tmp = Float64(y * x);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e-35)
		tmp = y * x;
	elseif (y <= -3.25e-57)
		tmp = z;
	elseif (y <= -1.8e-70)
		tmp = y * x;
	elseif (y <= 1.2e-60)
		tmp = z;
	elseif (y <= 850.0)
		tmp = y * x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e-35], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.25e-57], z, If[LessEqual[y, -1.8e-70], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.2e-60], z, If[LessEqual[y, 850.0], N[(y * x), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e-35 or -3.24999999999999996e-57 < y < -1.8000000000000001e-70 or 1.20000000000000005e-60 < y < 850

   1. Initial program 92.8%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 61.0%

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

   if -1.9000000000000001e-35 < y < -3.24999999999999996e-57 or -1.8000000000000001e-70 < y < 1.20000000000000005e-60

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 75.3%

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

   if 850 < y

   1. Initial program 98.5%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. +-commutative 97.1%

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

      3. sub-neg 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-*r* 58.6%

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

      2. neg-mul-1 58.6%

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

   7. Simplified 58.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-57}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 850:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-57}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -8.6e-34)
     t_0
     (if (<= y -3.25e-57)
       z
       (if (<= y -2.25e-70) (* y x) (if (<= y 5.2e-55) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -8.6e-34) {
		tmp = t_0;
	} else if (y <= -3.25e-57) {
		tmp = z;
	} else if (y <= -2.25e-70) {
		tmp = y * x;
	} else if (y <= 5.2e-55) {
		tmp = 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 <= (-8.6d-34)) then
        tmp = t_0
    else if (y <= (-3.25d-57)) then
        tmp = z
    else if (y <= (-2.25d-70)) then
        tmp = y * x
    else if (y <= 5.2d-55) then
        tmp = 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 <= -8.6e-34) {
		tmp = t_0;
	} else if (y <= -3.25e-57) {
		tmp = z;
	} else if (y <= -2.25e-70) {
		tmp = y * x;
	} else if (y <= 5.2e-55) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -8.6e-34:
		tmp = t_0
	elif y <= -3.25e-57:
		tmp = z
	elif y <= -2.25e-70:
		tmp = y * x
	elif y <= 5.2e-55:
		tmp = 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 <= -8.6e-34)
		tmp = t_0;
	elseif (y <= -3.25e-57)
		tmp = z;
	elseif (y <= -2.25e-70)
		tmp = Float64(y * x);
	elseif (y <= 5.2e-55)
		tmp = 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 <= -8.6e-34)
		tmp = t_0;
	elseif (y <= -3.25e-57)
		tmp = z;
	elseif (y <= -2.25e-70)
		tmp = y * x;
	elseif (y <= 5.2e-55)
		tmp = 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, -8.6e-34], t$95$0, If[LessEqual[y, -3.25e-57], z, If[LessEqual[y, -2.25e-70], N[(y * x), $MachinePrecision], If[LessEqual[y, 5.2e-55], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5999999999999999e-34 or 5.1999999999999998e-55 < y

   1. Initial program 95.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. +-commutative 94.1%

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

      3. sub-neg 94.1%

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

   4. Simplified 94.1%

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

   if -8.5999999999999999e-34 < y < -3.24999999999999996e-57 or -2.25000000000000011e-70 < y < 5.1999999999999998e-55

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 74.9%

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

   if -3.24999999999999996e-57 < y < -2.25000000000000011e-70

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 92.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-57}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 4: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-56}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-59}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e-35)
   (* y x)
   (if (<= y -1.52e-56)
     z
     (if (<= y -4.6e-70) (* y x) (if (<= y 2.1e-59) z (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e-35) {
		tmp = y * x;
	} else if (y <= -1.52e-56) {
		tmp = z;
	} else if (y <= -4.6e-70) {
		tmp = y * x;
	} else if (y <= 2.1e-59) {
		tmp = 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 <= (-8.2d-35)) then
        tmp = y * x
    else if (y <= (-1.52d-56)) then
        tmp = z
    else if (y <= (-4.6d-70)) then
        tmp = y * x
    else if (y <= 2.1d-59) then
        tmp = 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 <= -8.2e-35) {
		tmp = y * x;
	} else if (y <= -1.52e-56) {
		tmp = z;
	} else if (y <= -4.6e-70) {
		tmp = y * x;
	} else if (y <= 2.1e-59) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.2e-35:
		tmp = y * x
	elif y <= -1.52e-56:
		tmp = z
	elif y <= -4.6e-70:
		tmp = y * x
	elif y <= 2.1e-59:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e-35)
		tmp = Float64(y * x);
	elseif (y <= -1.52e-56)
		tmp = z;
	elseif (y <= -4.6e-70)
		tmp = Float64(y * x);
	elseif (y <= 2.1e-59)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.2e-35)
		tmp = y * x;
	elseif (y <= -1.52e-56)
		tmp = z;
	elseif (y <= -4.6e-70)
		tmp = y * x;
	elseif (y <= 2.1e-59)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e-35], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.52e-56], z, If[LessEqual[y, -4.6e-70], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.1e-59], z, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.20000000000000052e-35 or -1.5199999999999999e-56 < y < -4.60000000000000001e-70 or 2.09999999999999997e-59 < y

   1. Initial program 95.5%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 52.3%

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

   if -8.20000000000000052e-35 < y < -1.5199999999999999e-56 or -4.60000000000000001e-70 < y < 2.09999999999999997e-59

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 75.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-56}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-59}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-10} \lor \neg \left(z \leq 75\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-10) (not (<= z 75.0))) (* z (- 1.0 y)) (* y (- x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-10) || !(z <= 75.0)) {
		tmp = z * (1.0 - y);
	} 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 ((z <= (-1.7d-10)) .or. (.not. (z <= 75.0d0))) then
        tmp = z * (1.0d0 - y)
    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 ((z <= -1.7e-10) || !(z <= 75.0)) {
		tmp = z * (1.0 - y);
	} else {
		tmp = y * (x - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-10) or not (z <= 75.0):
		tmp = z * (1.0 - y)
	else:
		tmp = y * (x - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-10) || !(z <= 75.0))
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = Float64(y * Float64(x - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-10) || ~((z <= 75.0)))
		tmp = z * (1.0 - y);
	else
		tmp = y * (x - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-10], N[Not[LessEqual[z, 75.0]], $MachinePrecision]], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000007e-10 or 75 < z

   1. Initial program 95.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around 0 90.4%

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

   if -1.70000000000000007e-10 < z < 75

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. +-commutative 76.2%

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

      3. sub-neg 76.2%

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

   4. Simplified 76.2%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-10} \lor \neg \left(z \leq 75\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 6: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 7.5 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 7.5e-10))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 7.5e-10)) {
		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 <= 7.5d-10))) 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 <= 7.5e-10)) {
		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 <= 7.5e-10):
		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 <= 7.5e-10))
		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 <= 7.5e-10)))
		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, 7.5e-10]], $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 7.49999999999999995e-10 < y

   1. Initial program 94.7%

      \[x \cdot y + z \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. +-commutative 97.8%

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

      3. sub-neg 97.8%

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

   4. Simplified 97.8%

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

   if -1 < y < 7.49999999999999995e-10

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-*r* 100.0%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. 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. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 99.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 7.5 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 7: 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 97.7%

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

   1. +-commutative 97.7%

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

   2. sub-neg 97.7%

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

   3. distribute-rgt-in 97.6%

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

   4. *-lft-identity 97.6%

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

   5. associate-+l+ 97.6%

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

   6. +-commutative 97.6%

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

   7. *-commutative 97.6%

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

   8. neg-mul-1 97.6%

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

   9. associate-*r* 97.6%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. 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. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 8: 36.4% 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 97.7%

   \[x \cdot y + z \cdot \left(1 - y\right) \]

2. Taylor expanded in y around 0 39.5%

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

3. Final simplification 39.5%

   \[\leadsto z \]

Developer target: 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 2023171 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

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