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

Percentage Accurate: 97.8% → 100.0%

Time: 4.7s

Alternatives: 8

Speedup: 1.3×

• 20.5% 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 97.2%

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

   1. distribute-lft-out-- 97.2%

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

   2. *-rgt-identity 97.2%

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

   3. cancel-sign-sub-inv 97.2%

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

   4. +-commutative 97.2%

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

   5. associate-+r+ 97.2%

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

   6. +-commutative 97.2%

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

   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: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-32}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-110}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-61}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6500000000 \lor \neg \left(y \leq 2.6 \cdot 10^{+35}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.4e-17)
   (* y x)
   (if (<= y -6.4e-32)
     z
     (if (<= y -1.15e-110)
       (* y x)
       (if (<= y 1.65e-61)
         z
         (if (or (<= y 6500000000.0) (not (<= y 2.6e+35)))
           (* y x)
           (* y (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.4e-17) {
		tmp = y * x;
	} else if (y <= -6.4e-32) {
		tmp = z;
	} else if (y <= -1.15e-110) {
		tmp = y * x;
	} else if (y <= 1.65e-61) {
		tmp = z;
	} else if ((y <= 6500000000.0) || !(y <= 2.6e+35)) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-8.4d-17)) then
        tmp = y * x
    else if (y <= (-6.4d-32)) then
        tmp = z
    else if (y <= (-1.15d-110)) then
        tmp = y * x
    else if (y <= 1.65d-61) then
        tmp = z
    else if ((y <= 6500000000.0d0) .or. (.not. (y <= 2.6d+35))) then
        tmp = y * x
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.4e-17) {
		tmp = y * x;
	} else if (y <= -6.4e-32) {
		tmp = z;
	} else if (y <= -1.15e-110) {
		tmp = y * x;
	} else if (y <= 1.65e-61) {
		tmp = z;
	} else if ((y <= 6500000000.0) || !(y <= 2.6e+35)) {
		tmp = y * x;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.4e-17:
		tmp = y * x
	elif y <= -6.4e-32:
		tmp = z
	elif y <= -1.15e-110:
		tmp = y * x
	elif y <= 1.65e-61:
		tmp = z
	elif (y <= 6500000000.0) or not (y <= 2.6e+35):
		tmp = y * x
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.4e-17)
		tmp = Float64(y * x);
	elseif (y <= -6.4e-32)
		tmp = z;
	elseif (y <= -1.15e-110)
		tmp = Float64(y * x);
	elseif (y <= 1.65e-61)
		tmp = z;
	elseif ((y <= 6500000000.0) || !(y <= 2.6e+35))
		tmp = Float64(y * x);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.4e-17)
		tmp = y * x;
	elseif (y <= -6.4e-32)
		tmp = z;
	elseif (y <= -1.15e-110)
		tmp = y * x;
	elseif (y <= 1.65e-61)
		tmp = z;
	elseif ((y <= 6500000000.0) || ~((y <= 2.6e+35)))
		tmp = y * x;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.4e-17], N[(y * x), $MachinePrecision], If[LessEqual[y, -6.4e-32], z, If[LessEqual[y, -1.15e-110], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.65e-61], z, If[Or[LessEqual[y, 6500000000.0], N[Not[LessEqual[y, 2.6e+35]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.39999999999999968e-17 or -6.4000000000000004e-32 < y < -1.1500000000000001e-110 or 1.64999999999999998e-61 < y < 6.5e9 or 2.60000000000000007e35 < y

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf 63.7%

      \[\leadsto \color{blue}{x \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if -8.39999999999999968e-17 < y < -6.4000000000000004e-32 or -1.1500000000000001e-110 < y < 1.64999999999999998e-61

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.7%

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

   if 6.5e9 < y < 2.60000000000000007e35

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. distribute-lft-neg-out 89.6%

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

      3. *-commutative 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-32}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-110}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-61}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6500000000 \lor \neg \left(y \leq 2.6 \cdot 10^{+35}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-17} \lor \neg \left(y \leq -5.1 \cdot 10^{-40}\right) \land \left(y \leq -8.5 \cdot 10^{-111} \lor \neg \left(y \leq 3.9 \cdot 10^{-61}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.4e-17)
         (and (not (<= y -5.1e-40))
              (or (<= y -8.5e-111) (not (<= y 3.9e-61)))))
   (* y (- x z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.4e-17) || (!(y <= -5.1e-40) && ((y <= -8.5e-111) || !(y <= 3.9e-61)))) {
		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 <= (-7.4d-17)) .or. (.not. (y <= (-5.1d-40))) .and. (y <= (-8.5d-111)) .or. (.not. (y <= 3.9d-61))) 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 <= -7.4e-17) || (!(y <= -5.1e-40) && ((y <= -8.5e-111) || !(y <= 3.9e-61)))) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.4e-17) or (not (y <= -5.1e-40) and ((y <= -8.5e-111) or not (y <= 3.9e-61))):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.4e-17) || (!(y <= -5.1e-40) && ((y <= -8.5e-111) || !(y <= 3.9e-61))))
		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 <= -7.4e-17) || (~((y <= -5.1e-40)) && ((y <= -8.5e-111) || ~((y <= 3.9e-61)))))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.4e-17], And[N[Not[LessEqual[y, -5.1e-40]], $MachinePrecision], Or[LessEqual[y, -8.5e-111], N[Not[LessEqual[y, 3.9e-61]], $MachinePrecision]]]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999995e-17 or -5.10000000000000037e-40 < y < -8.5000000000000003e-111 or 3.90000000000000033e-61 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. sub-neg 92.4%

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

   4. Simplified 92.4%

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

   if -7.3999999999999995e-17 < y < -5.10000000000000037e-40 or -8.5000000000000003e-111 < y < 3.90000000000000033e-61

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-17} \lor \neg \left(y \leq -5.1 \cdot 10^{-40}\right) \land \left(y \leq -8.5 \cdot 10^{-111} \lor \neg \left(y \leq 3.9 \cdot 10^{-61}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -0.31:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-107} \lor \neg \left(y \leq 3.8 \cdot 10^{-63}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -0.31)
     t_0
     (if (<= y -8.2e-32)
       (* z (- 1.0 y))
       (if (or (<= y -1.28e-107) (not (<= y 3.8e-63))) t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -0.31) {
		tmp = t_0;
	} else if (y <= -8.2e-32) {
		tmp = z * (1.0 - y);
	} else if ((y <= -1.28e-107) || !(y <= 3.8e-63)) {
		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 <= (-0.31d0)) then
        tmp = t_0
    else if (y <= (-8.2d-32)) then
        tmp = z * (1.0d0 - y)
    else if ((y <= (-1.28d-107)) .or. (.not. (y <= 3.8d-63))) 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 <= -0.31) {
		tmp = t_0;
	} else if (y <= -8.2e-32) {
		tmp = z * (1.0 - y);
	} else if ((y <= -1.28e-107) || !(y <= 3.8e-63)) {
		tmp = t_0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -0.31:
		tmp = t_0
	elif y <= -8.2e-32:
		tmp = z * (1.0 - y)
	elif (y <= -1.28e-107) or not (y <= 3.8e-63):
		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 <= -0.31)
		tmp = t_0;
	elseif (y <= -8.2e-32)
		tmp = Float64(z * Float64(1.0 - y));
	elseif ((y <= -1.28e-107) || !(y <= 3.8e-63))
		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 <= -0.31)
		tmp = t_0;
	elseif (y <= -8.2e-32)
		tmp = z * (1.0 - y);
	elseif ((y <= -1.28e-107) || ~((y <= 3.8e-63)))
		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, -0.31], t$95$0, If[LessEqual[y, -8.2e-32], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.28e-107], N[Not[LessEqual[y, 3.8e-63]], $MachinePrecision]], t$95$0, z]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.309999999999999998 or -8.1999999999999995e-32 < y < -1.28e-107 or 3.80000000000000017e-63 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. mul-1-neg 93.4%

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

      2. sub-neg 93.4%

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

   4. Simplified 93.4%

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

   if -0.309999999999999998 < y < -8.1999999999999995e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.9%

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

   if -1.28e-107 < y < 3.80000000000000017e-63

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.31:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-107} \lor \neg \left(y \leq 3.8 \cdot 10^{-63}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-17} \lor \neg \left(y \leq -5.2 \cdot 10^{-39}\right) \land \left(y \leq -2.7 \cdot 10^{-109} \lor \neg \left(y \leq 1.05 \cdot 10^{-62}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.8e-17)
         (and (not (<= y -5.2e-39))
              (or (<= y -2.7e-109) (not (<= y 1.05e-62)))))
   (* y x)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e-17) || (!(y <= -5.2e-39) && ((y <= -2.7e-109) || !(y <= 1.05e-62)))) {
		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 ((y <= (-7.8d-17)) .or. (.not. (y <= (-5.2d-39))) .and. (y <= (-2.7d-109)) .or. (.not. (y <= 1.05d-62))) 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 ((y <= -7.8e-17) || (!(y <= -5.2e-39) && ((y <= -2.7e-109) || !(y <= 1.05e-62)))) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.8e-17) or (not (y <= -5.2e-39) and ((y <= -2.7e-109) or not (y <= 1.05e-62))):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.8e-17) || (!(y <= -5.2e-39) && ((y <= -2.7e-109) || !(y <= 1.05e-62))))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.8e-17) || (~((y <= -5.2e-39)) && ((y <= -2.7e-109) || ~((y <= 1.05e-62)))))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.8e-17], And[N[Not[LessEqual[y, -5.2e-39]], $MachinePrecision], Or[LessEqual[y, -2.7e-109], N[Not[LessEqual[y, 1.05e-62]], $MachinePrecision]]]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -7.79999999999999979e-17 or -5.2e-39 < y < -2.7e-109 or 1.05e-62 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 61.8%

      \[\leadsto \color{blue}{x \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 61.8%

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

   4. Simplified 61.8%

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

   if -7.79999999999999979e-17 < y < -5.2e-39 or -2.7e-109 < y < 1.05e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-17} \lor \neg \left(y \leq -5.2 \cdot 10^{-39}\right) \land \left(y \leq -2.7 \cdot 10^{-109} \lor \neg \left(y \leq 1.05 \cdot 10^{-62}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e+15) (not (<= y 1.0))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+15) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7d+15)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x - z)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+15) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e+15) or not (y <= 1.0):
		tmp = y * (x - z)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e+15) || !(y <= 1.0))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e+15) || ~((y <= 1.0)))
		tmp = y * (x - z);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e+15], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e15 or 1 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. sub-neg 99.6%

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

   4. Simplified 99.6%

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

   if -7e15 < y < 1

   1. Initial program 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      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. Step-by-step derivation

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 98.4%

      \[\leadsto \color{blue}{x \cdot y} + z \]
   7. Step-by-step derivation

      1. *-commutative 98.4%

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

   8. Simplified 98.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z + y \cdot \left(x - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* y (- x z))))

C

double code(double x, double y, double z) {
	return z + (y * (x - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + (y * (x - z))
end function

Java

public static double code(double x, double y, double z) {
	return z + (y * (x - z));
}

Python

def code(x, y, z):
	return z + (y * (x - z))

Julia

function code(x, y, z)
	return Float64(z + Float64(y * Float64(x - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + (y * (x - z));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.2%

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

   1. distribute-lft-out-- 97.2%

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

   2. *-rgt-identity 97.2%

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

   3. cancel-sign-sub-inv 97.2%

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

   4. +-commutative 97.2%

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

   5. associate-+r+ 97.2%

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

   6. +-commutative 97.2%

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

   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. Step-by-step derivation

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 8: 37.2% 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 97.2%

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

2. Taylor expanded in y around 0 33.3%

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

3. Final simplification 33.3%

   \[\leadsto z \]

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 2023318 
(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))))