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

Percentage Accurate: 97.8% → 100.0%

Time: 3.6s

Alternatives: 8

Speedup: 1.3×

• 20.6% 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: 97.8% 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 98.8%

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

   1. +-commutative 98.8%

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

   2. sub-neg 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. *-lft-identity 98.8%

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

   5. associate-+l+ 98.8%

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

   6. +-commutative 98.8%

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

   7. *-commutative 98.8%

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

   8. neg-mul-1 98.8%

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

   9. associate-*r* 98.8%

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

   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: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-236}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -6.6e-50)
     t_0
     (if (<= y -4e-219)
       z
       (if (<= y -3.6e-236) (* y x) (if (<= y 6.6e-38) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -6.6e-50) {
		tmp = t_0;
	} else if (y <= -4e-219) {
		tmp = z;
	} else if (y <= -3.6e-236) {
		tmp = y * x;
	} else if (y <= 6.6e-38) {
		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 <= (-6.6d-50)) then
        tmp = t_0
    else if (y <= (-4d-219)) then
        tmp = z
    else if (y <= (-3.6d-236)) then
        tmp = y * x
    else if (y <= 6.6d-38) 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 <= -6.6e-50) {
		tmp = t_0;
	} else if (y <= -4e-219) {
		tmp = z;
	} else if (y <= -3.6e-236) {
		tmp = y * x;
	} else if (y <= 6.6e-38) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -6.6e-50:
		tmp = t_0
	elif y <= -4e-219:
		tmp = z
	elif y <= -3.6e-236:
		tmp = y * x
	elif y <= 6.6e-38:
		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 <= -6.6e-50)
		tmp = t_0;
	elseif (y <= -4e-219)
		tmp = z;
	elseif (y <= -3.6e-236)
		tmp = Float64(y * x);
	elseif (y <= 6.6e-38)
		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 <= -6.6e-50)
		tmp = t_0;
	elseif (y <= -4e-219)
		tmp = z;
	elseif (y <= -3.6e-236)
		tmp = y * x;
	elseif (y <= 6.6e-38)
		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, -6.6e-50], t$95$0, If[LessEqual[y, -4e-219], z, If[LessEqual[y, -3.6e-236], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.6e-38], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5999999999999997e-50 or 6.6000000000000005e-38 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 95.7%

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

      1. mul-1-neg 95.7%

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

      2. +-commutative 95.7%

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

      3. sub-neg 95.7%

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

   4. Simplified 95.7%

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

   if -6.5999999999999997e-50 < y < -4.0000000000000001e-219 or -3.60000000000000008e-236 < y < 6.6000000000000005e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.2%

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

   if -4.0000000000000001e-219 < y < -3.60000000000000008e-236

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-236}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 3: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+119}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= z -2.8e+155)
     z
     (if (<= z -2.15e+15)
       t_0
       (if (<= z 1.1e-14) (* y x) (if (<= z 4.7e+119) t_0 z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -2.8e+155) {
		tmp = z;
	} else if (z <= -2.15e+15) {
		tmp = t_0;
	} else if (z <= 1.1e-14) {
		tmp = y * x;
	} else if (z <= 4.7e+119) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * -z
    if (z <= (-2.8d+155)) then
        tmp = z
    else if (z <= (-2.15d+15)) then
        tmp = t_0
    else if (z <= 1.1d-14) then
        tmp = y * x
    else if (z <= 4.7d+119) then
        tmp = t_0
    else
        tmp = z
    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 <= -2.8e+155) {
		tmp = z;
	} else if (z <= -2.15e+15) {
		tmp = t_0;
	} else if (z <= 1.1e-14) {
		tmp = y * x;
	} else if (z <= 4.7e+119) {
		tmp = t_0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if z <= -2.8e+155:
		tmp = z
	elif z <= -2.15e+15:
		tmp = t_0
	elif z <= 1.1e-14:
		tmp = y * x
	elif z <= 4.7e+119:
		tmp = t_0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -2.8e+155)
		tmp = z;
	elseif (z <= -2.15e+15)
		tmp = t_0;
	elseif (z <= 1.1e-14)
		tmp = Float64(y * x);
	elseif (z <= 4.7e+119)
		tmp = t_0;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (z <= -2.8e+155)
		tmp = z;
	elseif (z <= -2.15e+15)
		tmp = t_0;
	elseif (z <= 1.1e-14)
		tmp = y * x;
	elseif (z <= 4.7e+119)
		tmp = t_0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.8e+155], z, If[LessEqual[z, -2.15e+15], t$95$0, If[LessEqual[z, 1.1e-14], N[(y * x), $MachinePrecision], If[LessEqual[z, 4.7e+119], t$95$0, z]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.80000000000000016e155 or 4.70000000000000008e119 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 61.2%

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

   if -2.80000000000000016e155 < z < -2.15e15 or 1.1e-14 < z < 4.70000000000000008e119

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. +-commutative 69.3%

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

      3. sub-neg 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-rgt-neg-out 52.7%

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

   7. Simplified 52.7%

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

   if -2.15e15 < z < 1.1e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-236}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-65}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e-50)
   (* y x)
   (if (<= y -4e-219)
     z
     (if (<= y -3.6e-236) (* y x) (if (<= y 6e-65) z (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e-50) {
		tmp = y * x;
	} else if (y <= -4e-219) {
		tmp = z;
	} else if (y <= -3.6e-236) {
		tmp = y * x;
	} else if (y <= 6e-65) {
		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 <= (-9d-50)) then
        tmp = y * x
    else if (y <= (-4d-219)) then
        tmp = z
    else if (y <= (-3.6d-236)) then
        tmp = y * x
    else if (y <= 6d-65) 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 <= -9e-50) {
		tmp = y * x;
	} else if (y <= -4e-219) {
		tmp = z;
	} else if (y <= -3.6e-236) {
		tmp = y * x;
	} else if (y <= 6e-65) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e-50:
		tmp = y * x
	elif y <= -4e-219:
		tmp = z
	elif y <= -3.6e-236:
		tmp = y * x
	elif y <= 6e-65:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e-50)
		tmp = Float64(y * x);
	elseif (y <= -4e-219)
		tmp = z;
	elseif (y <= -3.6e-236)
		tmp = Float64(y * x);
	elseif (y <= 6e-65)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e-50)
		tmp = y * x;
	elseif (y <= -4e-219)
		tmp = z;
	elseif (y <= -3.6e-236)
		tmp = y * x;
	elseif (y <= 6e-65)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e-50], N[(y * x), $MachinePrecision], If[LessEqual[y, -4e-219], z, If[LessEqual[y, -3.6e-236], N[(y * x), $MachinePrecision], If[LessEqual[y, 6e-65], z, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999924e-50 or -4.0000000000000001e-219 < y < -3.60000000000000008e-236 or 5.99999999999999996e-65 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf 54.4%

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

   if -8.99999999999999924e-50 < y < -4.0000000000000001e-219 or -3.60000000000000008e-236 < y < 5.99999999999999996e-65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-236}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-65}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-20} \lor \neg \left(z \leq 3.4 \cdot 10^{+91}\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.65e-20) (not (<= z 3.4e+91))) (* z (- 1.0 y)) (* y (- x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e-20) || !(z <= 3.4e+91)) {
		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 <= (-1.65d-20)) .or. (.not. (z <= 3.4d+91))) 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 <= -1.65e-20) || !(z <= 3.4e+91)) {
		tmp = z * (1.0 - y);
	} else {
		tmp = y * (x - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.65e-20) or not (z <= 3.4e+91):
		tmp = z * (1.0 - y)
	else:
		tmp = y * (x - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.65e-20) || !(z <= 3.4e+91))
		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 <= -1.65e-20) || ~((z <= 3.4e+91)))
		tmp = z * (1.0 - y);
	else
		tmp = y * (x - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.65e-20], N[Not[LessEqual[z, 3.4e+91]], $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 < -1.65e-20 or 3.4000000000000001e91 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 92.5%

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

   if -1.65e-20 < z < 3.4000000000000001e91

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. +-commutative 78.3%

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

      3. sub-neg 78.3%

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

   4. Simplified 78.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-20} \lor \neg \left(z \leq 3.4 \cdot 10^{+91}\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 6: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 1 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. +-commutative 99.0%

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

      3. sub-neg 99.0%

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

   4. Simplified 99.0%

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

   if -1 < y < 1

   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 99.1%

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

4. Final simplification 99.1%

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

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 98.8%

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

   1. +-commutative 98.8%

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

   2. sub-neg 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. *-lft-identity 98.8%

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

   5. associate-+l+ 98.8%

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

   6. +-commutative 98.8%

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

   7. *-commutative 98.8%

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

   8. neg-mul-1 98.8%

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

   9. associate-*r* 98.8%

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

   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: 37.5% 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 98.8%

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

2. Taylor expanded in y around 0 35.5%

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

3. Final simplification 35.5%

   \[\leadsto z \]

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 2023214 
(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))))