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

Percentage Accurate: 98.1% → 100.0%

Time: 4.0s

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: 98.1% 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: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+68}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -195:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-89}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+25} \lor \neg \left(y \leq 4.4 \cdot 10^{+241}\right) \land y \leq 2 \cdot 10^{+293}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -3.1e+176)
     t_0
     (if (<= y -9e+68)
       (* y x)
       (if (<= y -6.2e+16)
         t_0
         (if (<= y -195.0)
           (* y x)
           (if (<= y -2.25e-89)
             z
             (if (<= y -5.2e-122)
               (* y x)
               (if (<= y 6.5e-69)
                 z
                 (if (or (<= y 5.6e+25)
                         (and (not (<= y 4.4e+241)) (<= y 2e+293)))
                   (* y x)
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -3.1e+176) {
		tmp = t_0;
	} else if (y <= -9e+68) {
		tmp = y * x;
	} else if (y <= -6.2e+16) {
		tmp = t_0;
	} else if (y <= -195.0) {
		tmp = y * x;
	} else if (y <= -2.25e-89) {
		tmp = z;
	} else if (y <= -5.2e-122) {
		tmp = y * x;
	} else if (y <= 6.5e-69) {
		tmp = z;
	} else if ((y <= 5.6e+25) || (!(y <= 4.4e+241) && (y <= 2e+293))) {
		tmp = y * x;
	} 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 = z * -y
    if (y <= (-3.1d+176)) then
        tmp = t_0
    else if (y <= (-9d+68)) then
        tmp = y * x
    else if (y <= (-6.2d+16)) then
        tmp = t_0
    else if (y <= (-195.0d0)) then
        tmp = y * x
    else if (y <= (-2.25d-89)) then
        tmp = z
    else if (y <= (-5.2d-122)) then
        tmp = y * x
    else if (y <= 6.5d-69) then
        tmp = z
    else if ((y <= 5.6d+25) .or. (.not. (y <= 4.4d+241)) .and. (y <= 2d+293)) then
        tmp = y * x
    else
        tmp = t_0
    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 <= -3.1e+176) {
		tmp = t_0;
	} else if (y <= -9e+68) {
		tmp = y * x;
	} else if (y <= -6.2e+16) {
		tmp = t_0;
	} else if (y <= -195.0) {
		tmp = y * x;
	} else if (y <= -2.25e-89) {
		tmp = z;
	} else if (y <= -5.2e-122) {
		tmp = y * x;
	} else if (y <= 6.5e-69) {
		tmp = z;
	} else if ((y <= 5.6e+25) || (!(y <= 4.4e+241) && (y <= 2e+293))) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -3.1e+176:
		tmp = t_0
	elif y <= -9e+68:
		tmp = y * x
	elif y <= -6.2e+16:
		tmp = t_0
	elif y <= -195.0:
		tmp = y * x
	elif y <= -2.25e-89:
		tmp = z
	elif y <= -5.2e-122:
		tmp = y * x
	elif y <= 6.5e-69:
		tmp = z
	elif (y <= 5.6e+25) or (not (y <= 4.4e+241) and (y <= 2e+293)):
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -3.1e+176)
		tmp = t_0;
	elseif (y <= -9e+68)
		tmp = Float64(y * x);
	elseif (y <= -6.2e+16)
		tmp = t_0;
	elseif (y <= -195.0)
		tmp = Float64(y * x);
	elseif (y <= -2.25e-89)
		tmp = z;
	elseif (y <= -5.2e-122)
		tmp = Float64(y * x);
	elseif (y <= 6.5e-69)
		tmp = z;
	elseif ((y <= 5.6e+25) || (!(y <= 4.4e+241) && (y <= 2e+293)))
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	tmp = 0.0;
	if (y <= -3.1e+176)
		tmp = t_0;
	elseif (y <= -9e+68)
		tmp = y * x;
	elseif (y <= -6.2e+16)
		tmp = t_0;
	elseif (y <= -195.0)
		tmp = y * x;
	elseif (y <= -2.25e-89)
		tmp = z;
	elseif (y <= -5.2e-122)
		tmp = y * x;
	elseif (y <= 6.5e-69)
		tmp = z;
	elseif ((y <= 5.6e+25) || (~((y <= 4.4e+241)) && (y <= 2e+293)))
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -3.1e+176], t$95$0, If[LessEqual[y, -9e+68], N[(y * x), $MachinePrecision], If[LessEqual[y, -6.2e+16], t$95$0, If[LessEqual[y, -195.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -2.25e-89], z, If[LessEqual[y, -5.2e-122], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.5e-69], z, If[Or[LessEqual[y, 5.6e+25], And[N[Not[LessEqual[y, 4.4e+241]], $MachinePrecision], LessEqual[y, 2e+293]]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0999999999999999e176 or -9.0000000000000007e68 < y < -6.2e16 or 5.6000000000000003e25 < y < 4.4e241 or 1.9999999999999998e293 < y

   1. Initial program 96.2%

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

   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. mul-1-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-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 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-rgt-neg-out 71.3%

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

   7. Simplified 71.3%

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

   if -3.0999999999999999e176 < y < -9.0000000000000007e68 or -6.2e16 < y < -195 or -2.25e-89 < y < -5.1999999999999995e-122 or 6.49999999999999951e-69 < y < 5.6000000000000003e25 or 4.4e241 < y < 1.9999999999999998e293

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 72.2%

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

   if -195 < y < -2.25e-89 or -5.1999999999999995e-122 < y < 6.49999999999999951e-69

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+68}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -195:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-89}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+25} \lor \neg \left(y \leq 4.4 \cdot 10^{+241}\right) \land y \leq 2 \cdot 10^{+293}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-5} \lor \neg \left(y \leq -1.9 \cdot 10^{-67} \lor \neg \left(y \leq -9.2 \cdot 10^{-124}\right) \land y \leq 4.5 \cdot 10^{-46}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e-5)
         (not
          (or (<= y -1.9e-67) (and (not (<= y -9.2e-124)) (<= y 4.5e-46)))))
   (* y (- x z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-5) || !((y <= -1.9e-67) || (!(y <= -9.2e-124) && (y <= 4.5e-46)))) {
		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 <= (-2.5d-5)) .or. (.not. (y <= (-1.9d-67)) .or. (.not. (y <= (-9.2d-124))) .and. (y <= 4.5d-46))) 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 <= -2.5e-5) || !((y <= -1.9e-67) || (!(y <= -9.2e-124) && (y <= 4.5e-46)))) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e-5) or not ((y <= -1.9e-67) or (not (y <= -9.2e-124) and (y <= 4.5e-46))):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e-5) || !((y <= -1.9e-67) || (!(y <= -9.2e-124) && (y <= 4.5e-46))))
		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 <= -2.5e-5) || ~(((y <= -1.9e-67) || (~((y <= -9.2e-124)) && (y <= 4.5e-46)))))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e-5], N[Not[Or[LessEqual[y, -1.9e-67], And[N[Not[LessEqual[y, -9.2e-124]], $MachinePrecision], LessEqual[y, 4.5e-46]]]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000012e-5 or -1.89999999999999994e-67 < y < -9.20000000000000048e-124 or 4.50000000000000001e-46 < y

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. +-commutative 93.5%

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

      3. sub-neg 93.5%

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

   4. Simplified 93.5%

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

   if -2.50000000000000012e-5 < y < -1.89999999999999994e-67 or -9.20000000000000048e-124 < y < 4.50000000000000001e-46

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-5} \lor \neg \left(y \leq -1.9 \cdot 10^{-67} \lor \neg \left(y \leq -9.2 \cdot 10^{-124}\right) \land y \leq 4.5 \cdot 10^{-46}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -460:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-123} \lor \neg \left(y \leq 4.8 \cdot 10^{-48}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -460.0)
     t_0
     (if (<= y -8.5e-67)
       (* z (- 1.0 y))
       (if (or (<= y -7e-123) (not (<= y 4.8e-48))) t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -460.0) {
		tmp = t_0;
	} else if (y <= -8.5e-67) {
		tmp = z * (1.0 - y);
	} else if ((y <= -7e-123) || !(y <= 4.8e-48)) {
		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 * (x - z)
    if (y <= (-460.0d0)) then
        tmp = t_0
    else if (y <= (-8.5d-67)) then
        tmp = z * (1.0d0 - y)
    else if ((y <= (-7d-123)) .or. (.not. (y <= 4.8d-48))) 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 * (x - z);
	double tmp;
	if (y <= -460.0) {
		tmp = t_0;
	} else if (y <= -8.5e-67) {
		tmp = z * (1.0 - y);
	} else if ((y <= -7e-123) || !(y <= 4.8e-48)) {
		tmp = t_0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -460.0:
		tmp = t_0
	elif y <= -8.5e-67:
		tmp = z * (1.0 - y)
	elif (y <= -7e-123) or not (y <= 4.8e-48):
		tmp = t_0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	tmp = 0.0
	if (y <= -460.0)
		tmp = t_0;
	elseif (y <= -8.5e-67)
		tmp = Float64(z * Float64(1.0 - y));
	elseif ((y <= -7e-123) || !(y <= 4.8e-48))
		tmp = t_0;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	tmp = 0.0;
	if (y <= -460.0)
		tmp = t_0;
	elseif (y <= -8.5e-67)
		tmp = z * (1.0 - y);
	elseif ((y <= -7e-123) || ~((y <= 4.8e-48)))
		tmp = t_0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -460.0], t$95$0, If[LessEqual[y, -8.5e-67], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7e-123], N[Not[LessEqual[y, 4.8e-48]], $MachinePrecision]], t$95$0, z]]]]

Derivation

1. Split input into 3 regimes

2. if y < -460 or -8.49999999999999993e-67 < y < -6.9999999999999997e-123 or 4.8e-48 < y

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. +-commutative 93.9%

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

      3. sub-neg 93.9%

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

   4. Simplified 93.9%

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

   if -460 < y < -8.49999999999999993e-67

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.0%

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

   if -6.9999999999999997e-123 < y < 4.8e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -460:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-123} \lor \neg \left(y \leq 4.8 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -195:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-92}:\\ \;\;\;\;z\\ \mathbf{elif}\;\neg \left(y \leq -5.2 \cdot 10^{-122}\right) \land y \leq 2.8 \cdot 10^{-69}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -195.0)
   (* y x)
   (if (<= y -1.2e-92)
     z
     (if (and (not (<= y -5.2e-122)) (<= y 2.8e-69)) z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -195.0) {
		tmp = y * x;
	} else if (y <= -1.2e-92) {
		tmp = z;
	} else if (!(y <= -5.2e-122) && (y <= 2.8e-69)) {
		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 <= (-195.0d0)) then
        tmp = y * x
    else if (y <= (-1.2d-92)) then
        tmp = z
    else if ((.not. (y <= (-5.2d-122))) .and. (y <= 2.8d-69)) 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 <= -195.0) {
		tmp = y * x;
	} else if (y <= -1.2e-92) {
		tmp = z;
	} else if (!(y <= -5.2e-122) && (y <= 2.8e-69)) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -195.0:
		tmp = y * x
	elif y <= -1.2e-92:
		tmp = z
	elif not (y <= -5.2e-122) and (y <= 2.8e-69):
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -195.0)
		tmp = Float64(y * x);
	elseif (y <= -1.2e-92)
		tmp = z;
	elseif (!(y <= -5.2e-122) && (y <= 2.8e-69))
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -195.0)
		tmp = y * x;
	elseif (y <= -1.2e-92)
		tmp = z;
	elseif (~((y <= -5.2e-122)) && (y <= 2.8e-69))
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -195.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.2e-92], z, If[And[N[Not[LessEqual[y, -5.2e-122]], $MachinePrecision], LessEqual[y, 2.8e-69]], z, N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if y < -195 or -1.2000000000000001e-92 < y < -5.1999999999999995e-122 or 2.79999999999999979e-69 < y

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 50.6%

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

   if -195 < y < -1.2000000000000001e-92 or -5.1999999999999995e-122 < y < 2.79999999999999979e-69

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -195:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-92}:\\ \;\;\;\;z\\ \mathbf{elif}\;\neg \left(y \leq -5.2 \cdot 10^{-122}\right) \land y \leq 2.8 \cdot 10^{-69}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.82 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.82e-6))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.82e-6)) {
		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 <= 1.82d-6))) 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 <= 1.82e-6)) {
		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 <= 1.82e-6):
		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 <= 1.82e-6))
		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 <= 1.82e-6)))
		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, 1.82e-6]], $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 1.8199999999999999e-6 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. +-commutative 98.6%

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

      3. sub-neg 98.6%

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

   4. Simplified 98.6%

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

   if -1 < y < 1.8199999999999999e-6

   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 99.2%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.82 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

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 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. 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: 36.6% 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 38.2%

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

3. Final simplification 38.2%

   \[\leadsto z \]

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 2023221 
(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))))