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

Percentage Accurate: 97.8% → 100.0%

Time: 2.6s

Alternatives: 7

Speedup: 0.5×

• 20.3% 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 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 97.6%

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

   4. *-lft-identity 97.6%

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

   5. associate-+l+ 97.6%

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

   6. +-commutative 97.6%

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

   7. *-commutative 97.6%

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

   8. neg-mul-1 97.6%

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

   9. associate-*r* 97.6%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (- 1.0 y)) (* y x))))
   (if (<= t_0 5e+291) 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+291) {
		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+291) 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+291) {
		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+291:
		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+291)
		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+291)
		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+291], 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))) < 5.0000000000000001e291

   1. Initial program 100.0%

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

   if 5.0000000000000001e291 < (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y)))

   1. Initial program 82.9%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) + y \cdot x \leq 5 \cdot 10^{+291}:\\ \;\;\;\;z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 3: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-210}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -1.6e-73)
     t_0
     (if (<= y -6e-210)
       z
       (if (<= y -2.5e-220) (* y x) (if (<= y 8e-16) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -1.6e-73) {
		tmp = t_0;
	} else if (y <= -6e-210) {
		tmp = z;
	} else if (y <= -2.5e-220) {
		tmp = y * x;
	} else if (y <= 8e-16) {
		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 <= (-1.6d-73)) then
        tmp = t_0
    else if (y <= (-6d-210)) then
        tmp = z
    else if (y <= (-2.5d-220)) then
        tmp = y * x
    else if (y <= 8d-16) 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 <= -1.6e-73) {
		tmp = t_0;
	} else if (y <= -6e-210) {
		tmp = z;
	} else if (y <= -2.5e-220) {
		tmp = y * x;
	} else if (y <= 8e-16) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -1.6e-73:
		tmp = t_0
	elif y <= -6e-210:
		tmp = z
	elif y <= -2.5e-220:
		tmp = y * x
	elif y <= 8e-16:
		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 <= -1.6e-73)
		tmp = t_0;
	elseif (y <= -6e-210)
		tmp = z;
	elseif (y <= -2.5e-220)
		tmp = Float64(y * x);
	elseif (y <= 8e-16)
		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 <= -1.6e-73)
		tmp = t_0;
	elseif (y <= -6e-210)
		tmp = z;
	elseif (y <= -2.5e-220)
		tmp = y * x;
	elseif (y <= 8e-16)
		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, -1.6e-73], t$95$0, If[LessEqual[y, -6e-210], z, If[LessEqual[y, -2.5e-220], N[(y * x), $MachinePrecision], If[LessEqual[y, 8e-16], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999993e-73 or 7.9999999999999998e-16 < y

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf 96.0%

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

      1. +-commutative 96.0%

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

      2. mul-1-neg 96.0%

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

      3. unsub-neg 96.0%

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

   4. Simplified 96.0%

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

   if -1.59999999999999993e-73 < y < -6.0000000000000003e-210 or -2.5000000000000001e-220 < y < 7.9999999999999998e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.1%

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

   if -6.0000000000000003e-210 < y < -2.5000000000000001e-220

   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 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-210}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 4: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 380000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))) (t_1 (* z (- 1.0 y))))
   (if (<= y -6.5e-69)
     t_0
     (if (<= y -5.7e-210)
       t_1
       (if (<= y -2.5e-220) (* y x) (if (<= y 380000000.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double t_1 = z * (1.0 - y);
	double tmp;
	if (y <= -6.5e-69) {
		tmp = t_0;
	} else if (y <= -5.7e-210) {
		tmp = t_1;
	} else if (y <= -2.5e-220) {
		tmp = y * x;
	} else if (y <= 380000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y * (x - z)
    t_1 = z * (1.0d0 - y)
    if (y <= (-6.5d-69)) then
        tmp = t_0
    else if (y <= (-5.7d-210)) then
        tmp = t_1
    else if (y <= (-2.5d-220)) then
        tmp = y * x
    else if (y <= 380000000.0d0) then
        tmp = t_1
    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 t_1 = z * (1.0 - y);
	double tmp;
	if (y <= -6.5e-69) {
		tmp = t_0;
	} else if (y <= -5.7e-210) {
		tmp = t_1;
	} else if (y <= -2.5e-220) {
		tmp = y * x;
	} else if (y <= 380000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	t_1 = z * (1.0 - y)
	tmp = 0
	if y <= -6.5e-69:
		tmp = t_0
	elif y <= -5.7e-210:
		tmp = t_1
	elif y <= -2.5e-220:
		tmp = y * x
	elif y <= 380000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (y <= -6.5e-69)
		tmp = t_0;
	elseif (y <= -5.7e-210)
		tmp = t_1;
	elseif (y <= -2.5e-220)
		tmp = Float64(y * x);
	elseif (y <= 380000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (y <= -6.5e-69)
		tmp = t_0;
	elseif (y <= -5.7e-210)
		tmp = t_1;
	elseif (y <= -2.5e-220)
		tmp = y * x;
	elseif (y <= 380000000.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-69], t$95$0, If[LessEqual[y, -5.7e-210], t$95$1, If[LessEqual[y, -2.5e-220], N[(y * x), $MachinePrecision], If[LessEqual[y, 380000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.49999999999999951e-69 or 3.8e8 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

   if -6.49999999999999951e-69 < y < -5.69999999999999971e-210 or -2.5000000000000001e-220 < y < 3.8e8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.3%

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

   if -5.69999999999999971e-210 < y < -2.5000000000000001e-220

   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 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 380000000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 5: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 380000000:\\ \;\;\;\;z - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -1.85e-70)
     t_0
     (if (<= y -5.7e-210)
       (* z (- 1.0 y))
       (if (<= y -2.5e-220)
         (* y x)
         (if (<= y 380000000.0) (- z (* y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -1.85e-70) {
		tmp = t_0;
	} else if (y <= -5.7e-210) {
		tmp = z * (1.0 - y);
	} else if (y <= -2.5e-220) {
		tmp = y * x;
	} else if (y <= 380000000.0) {
		tmp = z - (y * 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 <= (-1.85d-70)) then
        tmp = t_0
    else if (y <= (-5.7d-210)) then
        tmp = z * (1.0d0 - y)
    else if (y <= (-2.5d-220)) then
        tmp = y * x
    else if (y <= 380000000.0d0) then
        tmp = z - (y * 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 <= -1.85e-70) {
		tmp = t_0;
	} else if (y <= -5.7e-210) {
		tmp = z * (1.0 - y);
	} else if (y <= -2.5e-220) {
		tmp = y * x;
	} else if (y <= 380000000.0) {
		tmp = z - (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -1.85e-70:
		tmp = t_0
	elif y <= -5.7e-210:
		tmp = z * (1.0 - y)
	elif y <= -2.5e-220:
		tmp = y * x
	elif y <= 380000000.0:
		tmp = z - (y * 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 <= -1.85e-70)
		tmp = t_0;
	elseif (y <= -5.7e-210)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= -2.5e-220)
		tmp = Float64(y * x);
	elseif (y <= 380000000.0)
		tmp = Float64(z - Float64(y * 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 <= -1.85e-70)
		tmp = t_0;
	elseif (y <= -5.7e-210)
		tmp = z * (1.0 - y);
	elseif (y <= -2.5e-220)
		tmp = y * x;
	elseif (y <= 380000000.0)
		tmp = z - (y * 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, -1.85e-70], t$95$0, If[LessEqual[y, -5.7e-210], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-220], N[(y * x), $MachinePrecision], If[LessEqual[y, 380000000.0], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85e-70 or 3.8e8 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

   if -1.85e-70 < y < -5.69999999999999971e-210

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 71.3%

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

   if -5.69999999999999971e-210 < y < -2.5000000000000001e-220

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -2.5000000000000001e-220 < y < 3.8e8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.8%

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

      1. distribute-lft-out-- 80.8%

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

      2. *-rgt-identity 80.8%

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

   4. Simplified 80.8%

      \[\leadsto \color{blue}{z - z \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 380000000:\\ \;\;\;\;z - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 6: 54.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-76}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e+45) z (if (<= z 2e-76) (* y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+45) {
		tmp = z;
	} else if (z <= 2e-76) {
		tmp = y * x;
	} 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 <= (-1.5d+45)) then
        tmp = z
    else if (z <= 2d-76) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+45) {
		tmp = z;
	} else if (z <= 2e-76) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e+45:
		tmp = z
	elif z <= 2e-76:
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e+45)
		tmp = z;
	elseif (z <= 2e-76)
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e+45)
		tmp = z;
	elseif (z <= 2e-76)
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e+45], z, If[LessEqual[z, 2e-76], N[(y * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000005e45 or 1.99999999999999985e-76 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 53.7%

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

   if -1.50000000000000005e45 < z < 1.99999999999999985e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-76}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 36.8% 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 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 2023230 
(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))))