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

Percentage Accurate: 98.0% → 100.0%

Time: 2.6s

Alternatives: 7

Speedup: 0.5×

• 20.4% 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: 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, 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 97.7%

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

   4. *-lft-identity 97.7%

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

   5. associate-+l+ 97.7%

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

   6. +-commutative 97.7%

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

   7. *-commutative 97.7%

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

   8. neg-mul-1 97.7%

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

   9. associate-*r* 97.7%

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

   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: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (- 1.0 y)) (* y x))))
   (if (<= t_0 5e+302) t_0 (* y (- x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (1.0 - y)) + (y * x);
	double tmp;
	if (t_0 <= 5e+302) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (z * (1.0d0 - y)) + (y * x)
    if (t_0 <= 5d+302) then
        tmp = t_0
    else
        tmp = y * (x - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (1.0 - y)) + (y * x);
	double tmp;
	if (t_0 <= 5e+302) {
		tmp = t_0;
	} else {
		tmp = y * (x - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (1.0 - y)) + (y * x)
	tmp = 0
	if t_0 <= 5e+302:
		tmp = t_0
	else:
		tmp = y * (x - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(1.0 - y)) + Float64(y * x))
	tmp = 0.0
	if (t_0 <= 5e+302)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (1.0 - y)) + (y * x);
	tmp = 0.0;
	if (t_0 <= 5e+302)
		tmp = t_0;
	else
		tmp = y * (x - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+302], t$95$0, N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y))) < 5e302

   1. Initial program 100.0%

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

   if 5e302 < (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y)))

   1. Initial program 81.8%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) + y \cdot x \leq 5 \cdot 10^{+302}:\\ \;\;\;\;z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 3: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-256}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-244}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-183}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-138}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -7.6e-77)
     t_0
     (if (<= y 9.4e-256)
       z
       (if (<= y 1.06e-244)
         (* y x)
         (if (<= y 7e-183)
           z
           (if (<= y 5.1e-138) (* y x) (if (<= y 3.6e-48) z t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -7.6e-77) {
		tmp = t_0;
	} else if (y <= 9.4e-256) {
		tmp = z;
	} else if (y <= 1.06e-244) {
		tmp = y * x;
	} else if (y <= 7e-183) {
		tmp = z;
	} else if (y <= 5.1e-138) {
		tmp = y * x;
	} else if (y <= 3.6e-48) {
		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 <= (-7.6d-77)) then
        tmp = t_0
    else if (y <= 9.4d-256) then
        tmp = z
    else if (y <= 1.06d-244) then
        tmp = y * x
    else if (y <= 7d-183) then
        tmp = z
    else if (y <= 5.1d-138) then
        tmp = y * x
    else if (y <= 3.6d-48) 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 <= -7.6e-77) {
		tmp = t_0;
	} else if (y <= 9.4e-256) {
		tmp = z;
	} else if (y <= 1.06e-244) {
		tmp = y * x;
	} else if (y <= 7e-183) {
		tmp = z;
	} else if (y <= 5.1e-138) {
		tmp = y * x;
	} else if (y <= 3.6e-48) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -7.6e-77:
		tmp = t_0
	elif y <= 9.4e-256:
		tmp = z
	elif y <= 1.06e-244:
		tmp = y * x
	elif y <= 7e-183:
		tmp = z
	elif y <= 5.1e-138:
		tmp = y * x
	elif y <= 3.6e-48:
		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 <= -7.6e-77)
		tmp = t_0;
	elseif (y <= 9.4e-256)
		tmp = z;
	elseif (y <= 1.06e-244)
		tmp = Float64(y * x);
	elseif (y <= 7e-183)
		tmp = z;
	elseif (y <= 5.1e-138)
		tmp = Float64(y * x);
	elseif (y <= 3.6e-48)
		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 <= -7.6e-77)
		tmp = t_0;
	elseif (y <= 9.4e-256)
		tmp = z;
	elseif (y <= 1.06e-244)
		tmp = y * x;
	elseif (y <= 7e-183)
		tmp = z;
	elseif (y <= 5.1e-138)
		tmp = y * x;
	elseif (y <= 3.6e-48)
		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, -7.6e-77], t$95$0, If[LessEqual[y, 9.4e-256], z, If[LessEqual[y, 1.06e-244], N[(y * x), $MachinePrecision], If[LessEqual[y, 7e-183], z, If[LessEqual[y, 5.1e-138], N[(y * x), $MachinePrecision], If[LessEqual[y, 3.6e-48], z, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999998e-77 or 3.6000000000000002e-48 < y

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

   4. Simplified 94.9%

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

   if -7.5999999999999998e-77 < y < 9.39999999999999964e-256 or 1.05999999999999999e-244 < y < 6.99999999999999983e-183 or 5.1000000000000002e-138 < y < 3.6000000000000002e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.2%

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

   if 9.39999999999999964e-256 < y < 1.05999999999999999e-244 or 6.99999999999999983e-183 < y < 5.1000000000000002e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-256}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-244}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-183}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-138}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 4: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-62}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+96}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-62)
   z
   (if (<= z 1.8e+96) (* y x) (if (<= z 2.7e+213) (* z (- y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-62) {
		tmp = z;
	} else if (z <= 1.8e+96) {
		tmp = y * x;
	} else if (z <= 2.7e+213) {
		tmp = z * -y;
	} 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 (z <= (-8.5d-62)) then
        tmp = z
    else if (z <= 1.8d+96) then
        tmp = y * x
    else if (z <= 2.7d+213) then
        tmp = z * -y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-62) {
		tmp = z;
	} else if (z <= 1.8e+96) {
		tmp = y * x;
	} else if (z <= 2.7e+213) {
		tmp = z * -y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e-62:
		tmp = z
	elif z <= 1.8e+96:
		tmp = y * x
	elif z <= 2.7e+213:
		tmp = z * -y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-62)
		tmp = z;
	elseif (z <= 1.8e+96)
		tmp = Float64(y * x);
	elseif (z <= 2.7e+213)
		tmp = Float64(z * Float64(-y));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.5e-62)
		tmp = z;
	elseif (z <= 1.8e+96)
		tmp = y * x;
	elseif (z <= 2.7e+213)
		tmp = z * -y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-62], z, If[LessEqual[z, 1.8e+96], N[(y * x), $MachinePrecision], If[LessEqual[z, 2.7e+213], N[(z * (-y)), $MachinePrecision], z]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999995e-62 or 2.7000000000000001e213 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 57.0%

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

   if -8.4999999999999995e-62 < z < 1.80000000000000007e96

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 66.3%

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

   if 1.80000000000000007e96 < z < 2.7000000000000001e213

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 95.2%

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

      1. distribute-lft-out-- 95.2%

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

      2. *-rgt-identity 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in y around inf 80.4%

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

      1. associate-*r* 80.4%

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

      2. neg-mul-1 80.4%

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

      3. *-commutative 80.4%

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

   7. Simplified 80.4%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-62}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+96}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1150000000000 \lor \neg \left(x \leq 6 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1150000000000.0) (not (<= x 6e-13)))
   (* y (- x z))
   (- z (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1150000000000.0) || !(x <= 6e-13)) {
		tmp = y * (x - z);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1150000000000.0d0)) .or. (.not. (x <= 6d-13))) then
        tmp = y * (x - z)
    else
        tmp = z - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1150000000000.0) || !(x <= 6e-13)) {
		tmp = y * (x - z);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1150000000000.0) or not (x <= 6e-13):
		tmp = y * (x - z)
	else:
		tmp = z - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1150000000000.0) || !(x <= 6e-13))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = Float64(z - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1150000000000.0) || ~((x <= 6e-13)))
		tmp = y * (x - z);
	else
		tmp = z - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1150000000000.0], N[Not[LessEqual[x, 6e-13]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e12 or 5.99999999999999968e-13 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 83.2%

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

      1. +-commutative 83.2%

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

      2. mul-1-neg 83.2%

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

      3. unsub-neg 83.2%

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

   4. Simplified 83.2%

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

   if -1.15e12 < x < 5.99999999999999968e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.3%

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

      1. distribute-lft-out-- 86.3%

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

      2. *-rgt-identity 86.3%

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

   4. Simplified 86.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1150000000000 \lor \neg \left(x \leq 6 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \]

Alternative 6: 56.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.5e+16) (* y x) (if (<= x 1.15e-12) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e+16) {
		tmp = y * x;
	} else if (x <= 1.15e-12) {
		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 (x <= (-4.5d+16)) then
        tmp = y * x
    else if (x <= 1.15d-12) 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 (x <= -4.5e+16) {
		tmp = y * x;
	} else if (x <= 1.15e-12) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.5e+16:
		tmp = y * x
	elif x <= 1.15e-12:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.5e+16)
		tmp = Float64(y * x);
	elseif (x <= 1.15e-12)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.5e+16)
		tmp = y * x;
	elseif (x <= 1.15e-12)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.5e+16], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.15e-12], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e16 or 1.14999999999999995e-12 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 72.6%

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

   if -4.5e16 < x < 1.14999999999999995e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7: 36.5% 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 36.6%

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

3. Final simplification 36.6%

   \[\leadsto z \]

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 2023257 
(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))))