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

Percentage Accurate: 98.0% → 100.0%

Time: 5.7s

Alternatives: 7

Speedup: 1.3×

• 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: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 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 98.4%

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

   1. +-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. +-commutative 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+l+ 98.4%

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

   8. distribute-lft-neg-out 98.4%

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

   9. remove-double-neg 98.4%

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

   10. distribute-rgt-neg-out 98.4%

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

   11. distribute-neg-out 98.4%

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

   12. sub-neg 98.4%

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

   13. distribute-rgt-neg-out 98.4%

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

   14. sub-neg 98.4%

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

   15. distribute-rgt-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto z + y \cdot \left(x - z\right) \]
6. Add Preprocessing

Alternative 2: 60.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+29}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1750000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-293}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-275}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-87}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+242} \lor \neg \left(y \leq 7 \cdot 10^{+303}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -1.22e+125)
     t_0
     (if (<= y -9.6e+29)
       (* y x)
       (if (<= y -1750000000000.0)
         t_0
         (if (<= y -2.7e-17)
           (* y x)
           (if (<= y 2.2e-293)
             z
             (if (<= y 2.25e-275)
               (* y x)
               (if (<= y 2.1e-87)
                 z
                 (if (or (<= y 2.75e+242) (not (<= y 7e+303)))
                   (* y x)
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -1.22e+125) {
		tmp = t_0;
	} else if (y <= -9.6e+29) {
		tmp = y * x;
	} else if (y <= -1750000000000.0) {
		tmp = t_0;
	} else if (y <= -2.7e-17) {
		tmp = y * x;
	} else if (y <= 2.2e-293) {
		tmp = z;
	} else if (y <= 2.25e-275) {
		tmp = y * x;
	} else if (y <= 2.1e-87) {
		tmp = z;
	} else if ((y <= 2.75e+242) || !(y <= 7e+303)) {
		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 <= (-1.22d+125)) then
        tmp = t_0
    else if (y <= (-9.6d+29)) then
        tmp = y * x
    else if (y <= (-1750000000000.0d0)) then
        tmp = t_0
    else if (y <= (-2.7d-17)) then
        tmp = y * x
    else if (y <= 2.2d-293) then
        tmp = z
    else if (y <= 2.25d-275) then
        tmp = y * x
    else if (y <= 2.1d-87) then
        tmp = z
    else if ((y <= 2.75d+242) .or. (.not. (y <= 7d+303))) 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 <= -1.22e+125) {
		tmp = t_0;
	} else if (y <= -9.6e+29) {
		tmp = y * x;
	} else if (y <= -1750000000000.0) {
		tmp = t_0;
	} else if (y <= -2.7e-17) {
		tmp = y * x;
	} else if (y <= 2.2e-293) {
		tmp = z;
	} else if (y <= 2.25e-275) {
		tmp = y * x;
	} else if (y <= 2.1e-87) {
		tmp = z;
	} else if ((y <= 2.75e+242) || !(y <= 7e+303)) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -1.22e+125:
		tmp = t_0
	elif y <= -9.6e+29:
		tmp = y * x
	elif y <= -1750000000000.0:
		tmp = t_0
	elif y <= -2.7e-17:
		tmp = y * x
	elif y <= 2.2e-293:
		tmp = z
	elif y <= 2.25e-275:
		tmp = y * x
	elif y <= 2.1e-87:
		tmp = z
	elif (y <= 2.75e+242) or not (y <= 7e+303):
		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 <= -1.22e+125)
		tmp = t_0;
	elseif (y <= -9.6e+29)
		tmp = Float64(y * x);
	elseif (y <= -1750000000000.0)
		tmp = t_0;
	elseif (y <= -2.7e-17)
		tmp = Float64(y * x);
	elseif (y <= 2.2e-293)
		tmp = z;
	elseif (y <= 2.25e-275)
		tmp = Float64(y * x);
	elseif (y <= 2.1e-87)
		tmp = z;
	elseif ((y <= 2.75e+242) || !(y <= 7e+303))
		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 <= -1.22e+125)
		tmp = t_0;
	elseif (y <= -9.6e+29)
		tmp = y * x;
	elseif (y <= -1750000000000.0)
		tmp = t_0;
	elseif (y <= -2.7e-17)
		tmp = y * x;
	elseif (y <= 2.2e-293)
		tmp = z;
	elseif (y <= 2.25e-275)
		tmp = y * x;
	elseif (y <= 2.1e-87)
		tmp = z;
	elseif ((y <= 2.75e+242) || ~((y <= 7e+303)))
		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, -1.22e+125], t$95$0, If[LessEqual[y, -9.6e+29], N[(y * x), $MachinePrecision], If[LessEqual[y, -1750000000000.0], t$95$0, If[LessEqual[y, -2.7e-17], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.2e-293], z, If[LessEqual[y, 2.25e-275], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.1e-87], z, If[Or[LessEqual[y, 2.75e+242], N[Not[LessEqual[y, 7e+303]], $MachinePrecision]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22e125 or -9.6000000000000003e29 < y < -1.75e12 or 2.75000000000000011e242 < y < 7.00000000000000031e303

   1. Initial program 93.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.6%

      \[\leadsto \color{blue}{y \cdot \left(x + -1 \cdot z\right)} \]
   4. 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%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-out 76.9%

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

   8. Simplified 76.9%

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

   if -1.22e125 < y < -9.6000000000000003e29 or -1.75e12 < y < -2.7000000000000001e-17 or 2.2e-293 < y < 2.24999999999999989e-275 or 2.10000000000000007e-87 < y < 2.75000000000000011e242 or 7.00000000000000031e303 < y

   1. Initial program 99.1%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.5%

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

      1. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   if -2.7000000000000001e-17 < y < 2.2e-293 or 2.24999999999999989e-275 < y < 2.10000000000000007e-87

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+125}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+29}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1750000000000:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-293}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-275}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-87}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+242} \lor \neg \left(y \leq 7 \cdot 10^{+303}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-17} \lor \neg \left(y \leq 2.2 \cdot 10^{-293}\right) \land \left(y \leq 2.25 \cdot 10^{-275} \lor \neg \left(y \leq 4.7 \cdot 10^{-88}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e-17)
         (and (not (<= y 2.2e-293))
              (or (<= y 2.25e-275) (not (<= y 4.7e-88)))))
   (* y (- x z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e-17) || (!(y <= 2.2e-293) && ((y <= 2.25e-275) || !(y <= 4.7e-88)))) {
		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 <= (-4.3d-17)) .or. (.not. (y <= 2.2d-293)) .and. (y <= 2.25d-275) .or. (.not. (y <= 4.7d-88))) 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 <= -4.3e-17) || (!(y <= 2.2e-293) && ((y <= 2.25e-275) || !(y <= 4.7e-88)))) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e-17) or (not (y <= 2.2e-293) and ((y <= 2.25e-275) or not (y <= 4.7e-88))):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e-17) || (!(y <= 2.2e-293) && ((y <= 2.25e-275) || !(y <= 4.7e-88))))
		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 <= -4.3e-17) || (~((y <= 2.2e-293)) && ((y <= 2.25e-275) || ~((y <= 4.7e-88)))))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e-17], And[N[Not[LessEqual[y, 2.2e-293]], $MachinePrecision], Or[LessEqual[y, 2.25e-275], N[Not[LessEqual[y, 4.7e-88]], $MachinePrecision]]]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -4.30000000000000023e-17 or 2.2e-293 < y < 2.24999999999999989e-275 or 4.7e-88 < y

   1. Initial program 97.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 94.3%

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

      1. mul-1-neg 94.3%

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

      2. sub-neg 94.3%

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

   5. Simplified 94.3%

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

   if -4.30000000000000023e-17 < y < 2.2e-293 or 2.24999999999999989e-275 < y < 4.7e-88

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-17} \lor \neg \left(y \leq 2.2 \cdot 10^{-293}\right) \land \left(y \leq 2.25 \cdot 10^{-275} \lor \neg \left(y \leq 4.7 \cdot 10^{-88}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-293}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-275} \lor \neg \left(y \leq 2.65 \cdot 10^{-87}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -8.2e-17)
     t_0
     (if (<= y 2.2e-293)
       (* z (- 1.0 y))
       (if (or (<= y 2.25e-275) (not (<= y 2.65e-87))) t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -8.2e-17) {
		tmp = t_0;
	} else if (y <= 2.2e-293) {
		tmp = z * (1.0 - y);
	} else if ((y <= 2.25e-275) || !(y <= 2.65e-87)) {
		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 <= (-8.2d-17)) then
        tmp = t_0
    else if (y <= 2.2d-293) then
        tmp = z * (1.0d0 - y)
    else if ((y <= 2.25d-275) .or. (.not. (y <= 2.65d-87))) 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 <= -8.2e-17) {
		tmp = t_0;
	} else if (y <= 2.2e-293) {
		tmp = z * (1.0 - y);
	} else if ((y <= 2.25e-275) || !(y <= 2.65e-87)) {
		tmp = t_0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -8.2e-17:
		tmp = t_0
	elif y <= 2.2e-293:
		tmp = z * (1.0 - y)
	elif (y <= 2.25e-275) or not (y <= 2.65e-87):
		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 <= -8.2e-17)
		tmp = t_0;
	elseif (y <= 2.2e-293)
		tmp = Float64(z * Float64(1.0 - y));
	elseif ((y <= 2.25e-275) || !(y <= 2.65e-87))
		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 <= -8.2e-17)
		tmp = t_0;
	elseif (y <= 2.2e-293)
		tmp = z * (1.0 - y);
	elseif ((y <= 2.25e-275) || ~((y <= 2.65e-87)))
		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, -8.2e-17], t$95$0, If[LessEqual[y, 2.2e-293], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.25e-275], N[Not[LessEqual[y, 2.65e-87]], $MachinePrecision]], t$95$0, z]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2000000000000001e-17 or 2.2e-293 < y < 2.24999999999999989e-275 or 2.64999999999999993e-87 < y

   1. Initial program 97.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 94.3%

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

      1. mul-1-neg 94.3%

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

      2. sub-neg 94.3%

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

   5. Simplified 94.3%

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

   if -8.2000000000000001e-17 < y < 2.2e-293

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.1%

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

   if 2.24999999999999989e-275 < y < 2.64999999999999993e-87

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-293}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-275} \lor \neg \left(y \leq 2.65 \cdot 10^{-87}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-17} \lor \neg \left(y \leq 2.2 \cdot 10^{-293}\right) \land \left(y \leq 2.25 \cdot 10^{-275} \lor \neg \left(y \leq 1.2 \cdot 10^{-86}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-17)
         (and (not (<= y 2.2e-293))
              (or (<= y 2.25e-275) (not (<= y 1.2e-86)))))
   (* y x)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-17) || (!(y <= 2.2e-293) && ((y <= 2.25e-275) || !(y <= 1.2e-86)))) {
		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 <= (-3.4d-17)) .or. (.not. (y <= 2.2d-293)) .and. (y <= 2.25d-275) .or. (.not. (y <= 1.2d-86))) 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 <= -3.4e-17) || (!(y <= 2.2e-293) && ((y <= 2.25e-275) || !(y <= 1.2e-86)))) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-17) or (not (y <= 2.2e-293) and ((y <= 2.25e-275) or not (y <= 1.2e-86))):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-17) || (!(y <= 2.2e-293) && ((y <= 2.25e-275) || !(y <= 1.2e-86))))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-17) || (~((y <= 2.2e-293)) && ((y <= 2.25e-275) || ~((y <= 1.2e-86)))))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-17], And[N[Not[LessEqual[y, 2.2e-293]], $MachinePrecision], Or[LessEqual[y, 2.25e-275], N[Not[LessEqual[y, 1.2e-86]], $MachinePrecision]]]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -3.3999999999999998e-17 or 2.2e-293 < y < 2.24999999999999989e-275 or 1.20000000000000007e-86 < y

   1. Initial program 97.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -3.3999999999999998e-17 < y < 2.2e-293 or 2.24999999999999989e-275 < y < 1.20000000000000007e-86

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-17} \lor \neg \left(y \leq 2.2 \cdot 10^{-293}\right) \land \left(y \leq 2.25 \cdot 10^{-275} \lor \neg \left(y \leq 1.2 \cdot 10^{-86}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -840000000000 \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -840000000000.0) (not (<= y 0.00078)))
   (* y (- x z))
   (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -840000000000.0) || !(y <= 0.00078)) {
		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 <= (-840000000000.0d0)) .or. (.not. (y <= 0.00078d0))) 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 <= -840000000000.0) || !(y <= 0.00078)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -840000000000.0) or not (y <= 0.00078):
		tmp = y * (x - z)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -840000000000.0) || !(y <= 0.00078))
		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 <= -840000000000.0) || ~((y <= 0.00078)))
		tmp = y * (x - z);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -840000000000.0], N[Not[LessEqual[y, 0.00078]], $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 < -8.4e11 or 7.79999999999999986e-4 < y

   1. Initial program 96.8%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. sub-neg 98.1%

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

   5. Simplified 98.1%

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

   if -8.4e11 < y < 7.79999999999999986e-4

   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. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. remove-double-neg 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-rgt-neg-out 100.0%

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

      14. sub-neg 100.0%

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

      15. distribute-rgt-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. *-rgt-identity 96.4%

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

      4. *-commutative 96.4%

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

      5. associate-/l* 86.8%

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

      6. distribute-lft-out-- 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in z around 0 98.6%

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

      1. associate-*r* 98.6%

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

      2. neg-mul-1 98.6%

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

   10. Simplified 98.6%

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

       1. cancel-sign-sub 98.6%

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

       2. *-commutative 98.6%

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

       3. +-commutative 98.6%

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

   12. Applied egg-rr 98.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -840000000000 \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% 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 98.4%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 36.2%

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

4. Final simplification 36.2%

   \[\leadsto z \]
5. Add Preprocessing

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 2024115 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (- z (* (- z x) y))

  (+ (* x y) (* z (- 1.0 y))))