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

Percentage Accurate: 98.0% → 100.0%

Time: 2.8s

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 97.6%

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

   1. +-commutative 97.6%

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

   2. sub-neg 97.6%

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

   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: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (- 1.0 y)) (* y x))))
   (if (<= t_0 2e+299) 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 <= 2e+299) {
		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 <= 2d+299) 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 <= 2e+299) {
		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 <= 2e+299:
		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 <= 2e+299)
		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 <= 2e+299)
		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, 2e+299], 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))) < 2.0000000000000001e299

   1. Initial program 100.0%

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

   if 2.0000000000000001e299 < (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y)))

   1. Initial program 78.6%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) + y \cdot x \leq 2 \cdot 10^{+299}:\\ \;\;\;\;z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 3: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-17}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+114)
   (* y x)
   (if (<= y -5.5e+63)
     (* y (- z))
     (if (<= y -1.5e-6) (* y x) (if (<= y 7.6e-17) z (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+114) {
		tmp = y * x;
	} else if (y <= -5.5e+63) {
		tmp = y * -z;
	} else if (y <= -1.5e-6) {
		tmp = y * x;
	} else if (y <= 7.6e-17) {
		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 <= (-2d+114)) then
        tmp = y * x
    else if (y <= (-5.5d+63)) then
        tmp = y * -z
    else if (y <= (-1.5d-6)) then
        tmp = y * x
    else if (y <= 7.6d-17) 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 <= -2e+114) {
		tmp = y * x;
	} else if (y <= -5.5e+63) {
		tmp = y * -z;
	} else if (y <= -1.5e-6) {
		tmp = y * x;
	} else if (y <= 7.6e-17) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+114:
		tmp = y * x
	elif y <= -5.5e+63:
		tmp = y * -z
	elif y <= -1.5e-6:
		tmp = y * x
	elif y <= 7.6e-17:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+114)
		tmp = Float64(y * x);
	elseif (y <= -5.5e+63)
		tmp = Float64(y * Float64(-z));
	elseif (y <= -1.5e-6)
		tmp = Float64(y * x);
	elseif (y <= 7.6e-17)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+114)
		tmp = y * x;
	elseif (y <= -5.5e+63)
		tmp = y * -z;
	elseif (y <= -1.5e-6)
		tmp = y * x;
	elseif (y <= 7.6e-17)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+114], N[(y * x), $MachinePrecision], If[LessEqual[y, -5.5e+63], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, -1.5e-6], N[(y * x), $MachinePrecision], If[LessEqual[y, 7.6e-17], z, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e114 or -5.50000000000000004e63 < y < -1.5e-6 or 7.6000000000000002e-17 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in x around inf 67.6%

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

   if -2e114 < y < -5.50000000000000004e63

   1. Initial program 100.0%

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

   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%

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

   5. Taylor expanded in x around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. distribute-rgt-neg-out 80.2%

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

   7. Simplified 80.2%

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

   if -1.5e-6 < y < 7.6000000000000002e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-17}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-6} \lor \neg \left(y \leq 9.8 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e-6) (not (<= y 9.8e-17))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-6) || !(y <= 9.8e-17)) {
		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 <= (-1.5d-6)) .or. (.not. (y <= 9.8d-17))) 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 <= -1.5e-6) || !(y <= 9.8e-17)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e-6) or not (y <= 9.8e-17):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e-6) || !(y <= 9.8e-17))
		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 <= -1.5e-6) || ~((y <= 9.8e-17)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e-6], N[Not[LessEqual[y, 9.8e-17]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e-6 or 9.80000000000000024e-17 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

   4. Simplified 98.7%

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

   if -1.5e-6 < y < 9.80000000000000024e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-6} \lor \neg \left(y \leq 9.8 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-6} \lor \neg \left(y \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e-6) (not (<= y 9.5e-16))) (* y (- x z)) (- z (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-6) || !(y <= 9.5e-16)) {
		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 ((y <= (-1.8d-6)) .or. (.not. (y <= 9.5d-16))) 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 ((y <= -1.8e-6) || !(y <= 9.5e-16)) {
		tmp = y * (x - z);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e-6) or not (y <= 9.5e-16):
		tmp = y * (x - z)
	else:
		tmp = z - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e-6) || !(y <= 9.5e-16))
		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 ((y <= -1.8e-6) || ~((y <= 9.5e-16)))
		tmp = y * (x - z);
	else
		tmp = z - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e-6], N[Not[LessEqual[y, 9.5e-16]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999992e-6 or 9.5000000000000005e-16 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

   4. Simplified 98.7%

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

   if -1.79999999999999992e-6 < y < 9.5000000000000005e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.3%

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

      1. distribute-lft-out-- 75.3%

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

      2. *-rgt-identity 75.3%

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

   4. Simplified 75.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-6} \lor \neg \left(y \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \]

Alternative 6: 61.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-6}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e-6) (* y x) (if (<= y 6.6e-16) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e-6) {
		tmp = y * x;
	} else if (y <= 6.6e-16) {
		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 <= (-1.65d-6)) then
        tmp = y * x
    else if (y <= 6.6d-16) 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 <= -1.65e-6) {
		tmp = y * x;
	} else if (y <= 6.6e-16) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e-6:
		tmp = y * x
	elif y <= 6.6e-16:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e-6)
		tmp = Float64(y * x);
	elseif (y <= 6.6e-16)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e-6)
		tmp = y * x;
	elseif (y <= 6.6e-16)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e-6], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.6e-16], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65000000000000008e-6 or 6.59999999999999976e-16 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 64.0%

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

   if -1.65000000000000008e-6 < y < 6.59999999999999976e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-6}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7: 36.2% 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 97.6%

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

2. Taylor expanded in y around 0 40.6%

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

3. Final simplification 40.6%

   \[\leadsto z \]

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 2023238 
(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))))