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

Percentage Accurate: 97.6% → 100.0%

Time: 3.3s

Alternatives: 7

Speedup: 0.5×

• 20.9% 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: 97.6% 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 98.0%

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

   1. distribute-lft-out-- 98.0%

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

   2. *-rgt-identity 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. distribute-rgt-out 100.0%

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

   8. fma-def 100.0%

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

   9. +-commutative 100.0%

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

   10. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{if}\;t_0 \leq 10^{+303}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (- 1.0 y)) (* y x))))
   (if (<= t_0 1e+303) 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 <= 1e+303) {
		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 <= 1d+303) 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 <= 1e+303) {
		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 <= 1e+303:
		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 <= 1e+303)
		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 <= 1e+303)
		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, 1e+303], 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))) < 1e303

   1. Initial program 100.0%

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

   if 1e303 < (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y)))

   1. Initial program 81.5%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) + y \cdot x \leq 10^{+303}:\\ \;\;\;\;z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 3: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+220}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-40}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+209}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+235}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -2.25e+220)
     t_0
     (if (<= y -0.18)
       (* y x)
       (if (<= y 1.55e-40)
         z
         (if (<= y 2.65e+209) (* y x) (if (<= y 5e+235) t_0 (* y x))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -2.25e+220) {
		tmp = t_0;
	} else if (y <= -0.18) {
		tmp = y * x;
	} else if (y <= 1.55e-40) {
		tmp = z;
	} else if (y <= 2.65e+209) {
		tmp = y * x;
	} else if (y <= 5e+235) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * -y
    if (y <= (-2.25d+220)) then
        tmp = t_0
    else if (y <= (-0.18d0)) then
        tmp = y * x
    else if (y <= 1.55d-40) then
        tmp = z
    else if (y <= 2.65d+209) then
        tmp = y * x
    else if (y <= 5d+235) then
        tmp = t_0
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -2.25e+220) {
		tmp = t_0;
	} else if (y <= -0.18) {
		tmp = y * x;
	} else if (y <= 1.55e-40) {
		tmp = z;
	} else if (y <= 2.65e+209) {
		tmp = y * x;
	} else if (y <= 5e+235) {
		tmp = t_0;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -2.25e+220:
		tmp = t_0
	elif y <= -0.18:
		tmp = y * x
	elif y <= 1.55e-40:
		tmp = z
	elif y <= 2.65e+209:
		tmp = y * x
	elif y <= 5e+235:
		tmp = t_0
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -2.25e+220)
		tmp = t_0;
	elseif (y <= -0.18)
		tmp = Float64(y * x);
	elseif (y <= 1.55e-40)
		tmp = z;
	elseif (y <= 2.65e+209)
		tmp = Float64(y * x);
	elseif (y <= 5e+235)
		tmp = t_0;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	tmp = 0.0;
	if (y <= -2.25e+220)
		tmp = t_0;
	elseif (y <= -0.18)
		tmp = y * x;
	elseif (y <= 1.55e-40)
		tmp = z;
	elseif (y <= 2.65e+209)
		tmp = y * x;
	elseif (y <= 5e+235)
		tmp = t_0;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -2.25e+220], t$95$0, If[LessEqual[y, -0.18], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.55e-40], z, If[LessEqual[y, 2.65e+209], N[(y * x), $MachinePrecision], If[LessEqual[y, 5e+235], t$95$0, N[(y * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25000000000000005e220 or 2.64999999999999997e209 < y < 5.00000000000000027e235

   1. Initial program 96.7%

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

   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 71.5%

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

      1. associate-*r* 71.5%

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

      2. neg-mul-1 71.5%

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

   7. Simplified 71.5%

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

   if -2.25000000000000005e220 < y < -0.17999999999999999 or 1.55000000000000005e-40 < y < 2.64999999999999997e209 or 5.00000000000000027e235 < y

   1. Initial program 95.9%

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

   2. Taylor expanded in x around inf 66.4%

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

   if -0.17999999999999999 < y < 1.55000000000000005e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+220}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-40}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+209}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+235}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-28} \lor \neg \left(y \leq 4.5 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e-28) (not (<= y 4.5e-40))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e-28) || !(y <= 4.5e-40)) {
		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 <= (-1.1d-28)) .or. (.not. (y <= 4.5d-40))) 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 <= -1.1e-28) || !(y <= 4.5e-40)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e-28) or not (y <= 4.5e-40):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e-28) || !(y <= 4.5e-40))
		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 <= -1.1e-28) || ~((y <= 4.5e-40)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e-28], N[Not[LessEqual[y, 4.5e-40]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.09999999999999998e-28 or 4.5000000000000001e-40 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 92.8%

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

      1. +-commutative 92.8%

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

      2. mul-1-neg 92.8%

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

      3. unsub-neg 92.8%

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

   4. Simplified 92.8%

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

   if -1.09999999999999998e-28 < y < 4.5000000000000001e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-28} \lor \neg \left(y \leq 4.5 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.96 \lor \neg \left(y \leq 1.7 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.96) (not (<= y 1.7e-40))) (* y (- x z)) (- z (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.96) || !(y <= 1.7e-40)) {
		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 <= (-1.96d0)) .or. (.not. (y <= 1.7d-40))) 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 <= -1.96) || !(y <= 1.7e-40)) {
		tmp = y * (x - z);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.96) or not (y <= 1.7e-40):
		tmp = y * (x - z)
	else:
		tmp = z - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.96) || !(y <= 1.7e-40))
		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 <= -1.96) || ~((y <= 1.7e-40)))
		tmp = y * (x - z);
	else
		tmp = z - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.96], N[Not[LessEqual[y, 1.7e-40]], $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 < -1.96 or 1.69999999999999992e-40 < y

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. +-commutative 94.6%

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

      2. mul-1-neg 94.6%

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

      3. unsub-neg 94.6%

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

   4. Simplified 94.6%

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

   if -1.96 < y < 1.69999999999999992e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.2%

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

      1. distribute-lft-out-- 79.2%

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

      2. *-rgt-identity 79.2%

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

   4. Simplified 79.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.96 \lor \neg \left(y \leq 1.7 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \]

Alternative 6: 61.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.18:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-40}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.18) (* y x) (if (<= y 1.25e-40) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.18) {
		tmp = y * x;
	} else if (y <= 1.25e-40) {
		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 <= (-0.18d0)) then
        tmp = y * x
    else if (y <= 1.25d-40) 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 <= -0.18) {
		tmp = y * x;
	} else if (y <= 1.25e-40) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.18:
		tmp = y * x
	elif y <= 1.25e-40:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.18)
		tmp = Float64(y * x);
	elseif (y <= 1.25e-40)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.18)
		tmp = y * x;
	elseif (y <= 1.25e-40)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.18], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.25e-40], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.17999999999999999 or 1.24999999999999991e-40 < y

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 59.0%

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

   if -0.17999999999999999 < y < 1.24999999999999991e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.18:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-40}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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 98.0%

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

2. Taylor expanded in y around 0 41.6%

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

3. Final simplification 41.6%

   \[\leadsto z \]

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 2023268 
(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))))