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

Percentage Accurate: 97.9% → 100.0%

Time: 5.0s

Alternatives: 7

Speedup: 1.3×

• 20.7% 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: 97.9% 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 97.7%

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

   1. +-commutative 97.7%

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

   2. +-lft-identity 97.7%

      \[\leadsto \color{blue}{\left(0 + z \cdot \left(1 - y\right)\right)} + x \cdot y \]

   3. cancel-sign-sub 97.7%

      \[\leadsto \color{blue}{\left(0 - \left(-z\right) \cdot \left(1 - y\right)\right)} + x \cdot y \]

   4. cancel-sign-sub 97.7%

      \[\leadsto \color{blue}{\left(0 + z \cdot \left(1 - y\right)\right)} + x \cdot y \]

   5. +-lft-identity 97.7%

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

   6. distribute-lft-out-- 97.6%

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

   7. *-rgt-identity 97.6%

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

   8. associate-+l- 97.6%

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

   9. 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: 61.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+84} \lor \neg \left(y \leq 2.4 \cdot 10^{+128}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -3.2e+58)
     t_0
     (if (<= y -4.5e+50)
       (* y x)
       (if (<= y -1.0)
         t_0
         (if (<= y -2.2e-96)
           z
           (if (<= y -3.5e-102)
             (* y x)
             (if (<= y 9.5e-20)
               z
               (if (or (<= y 6.8e+84) (not (<= y 2.4e+128)))
                 (* y x)
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -3.2e+58) {
		tmp = t_0;
	} else if (y <= -4.5e+50) {
		tmp = y * x;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -2.2e-96) {
		tmp = z;
	} else if (y <= -3.5e-102) {
		tmp = y * x;
	} else if (y <= 9.5e-20) {
		tmp = z;
	} else if ((y <= 6.8e+84) || !(y <= 2.4e+128)) {
		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 <= (-3.2d+58)) then
        tmp = t_0
    else if (y <= (-4.5d+50)) then
        tmp = y * x
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-2.2d-96)) then
        tmp = z
    else if (y <= (-3.5d-102)) then
        tmp = y * x
    else if (y <= 9.5d-20) then
        tmp = z
    else if ((y <= 6.8d+84) .or. (.not. (y <= 2.4d+128))) 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 <= -3.2e+58) {
		tmp = t_0;
	} else if (y <= -4.5e+50) {
		tmp = y * x;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -2.2e-96) {
		tmp = z;
	} else if (y <= -3.5e-102) {
		tmp = y * x;
	} else if (y <= 9.5e-20) {
		tmp = z;
	} else if ((y <= 6.8e+84) || !(y <= 2.4e+128)) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -3.2e+58:
		tmp = t_0
	elif y <= -4.5e+50:
		tmp = y * x
	elif y <= -1.0:
		tmp = t_0
	elif y <= -2.2e-96:
		tmp = z
	elif y <= -3.5e-102:
		tmp = y * x
	elif y <= 9.5e-20:
		tmp = z
	elif (y <= 6.8e+84) or not (y <= 2.4e+128):
		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 <= -3.2e+58)
		tmp = t_0;
	elseif (y <= -4.5e+50)
		tmp = Float64(y * x);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -2.2e-96)
		tmp = z;
	elseif (y <= -3.5e-102)
		tmp = Float64(y * x);
	elseif (y <= 9.5e-20)
		tmp = z;
	elseif ((y <= 6.8e+84) || !(y <= 2.4e+128))
		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 <= -3.2e+58)
		tmp = t_0;
	elseif (y <= -4.5e+50)
		tmp = y * x;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -2.2e-96)
		tmp = z;
	elseif (y <= -3.5e-102)
		tmp = y * x;
	elseif (y <= 9.5e-20)
		tmp = z;
	elseif ((y <= 6.8e+84) || ~((y <= 2.4e+128)))
		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, -3.2e+58], t$95$0, If[LessEqual[y, -4.5e+50], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -2.2e-96], z, If[LessEqual[y, -3.5e-102], N[(y * x), $MachinePrecision], If[LessEqual[y, 9.5e-20], z, If[Or[LessEqual[y, 6.8e+84], N[Not[LessEqual[y, 2.4e+128]], $MachinePrecision]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000015e58 or -4.50000000000000014e50 < y < -1 or 6.7999999999999996e84 < y < 2.4000000000000002e128

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. sub-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-out 67.8%

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

   8. Simplified 67.8%

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

   if -3.20000000000000015e58 < y < -4.50000000000000014e50 or -2.19999999999999979e-96 < y < -3.49999999999999986e-102 or 9.5e-20 < y < 6.7999999999999996e84 or 2.4000000000000002e128 < y

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -1 < y < -2.19999999999999979e-96 or -3.49999999999999986e-102 < y < 9.5e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+84} \lor \neg \left(y \leq 2.4 \cdot 10^{+128}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-103}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -9.5e-43)
     t_0
     (if (<= y -2.8e-96)
       z
       (if (<= y -2.2e-103) (* y x) (if (<= y 7.8e-19) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -9.5e-43) {
		tmp = t_0;
	} else if (y <= -2.8e-96) {
		tmp = z;
	} else if (y <= -2.2e-103) {
		tmp = y * x;
	} else if (y <= 7.8e-19) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x - z)
    if (y <= (-9.5d-43)) then
        tmp = t_0
    else if (y <= (-2.8d-96)) then
        tmp = z
    else if (y <= (-2.2d-103)) then
        tmp = y * x
    else if (y <= 7.8d-19) then
        tmp = z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -9.5e-43) {
		tmp = t_0;
	} else if (y <= -2.8e-96) {
		tmp = z;
	} else if (y <= -2.2e-103) {
		tmp = y * x;
	} else if (y <= 7.8e-19) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -9.5e-43:
		tmp = t_0
	elif y <= -2.8e-96:
		tmp = z
	elif y <= -2.2e-103:
		tmp = y * x
	elif y <= 7.8e-19:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	tmp = 0.0
	if (y <= -9.5e-43)
		tmp = t_0;
	elseif (y <= -2.8e-96)
		tmp = z;
	elseif (y <= -2.2e-103)
		tmp = Float64(y * x);
	elseif (y <= 7.8e-19)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	tmp = 0.0;
	if (y <= -9.5e-43)
		tmp = t_0;
	elseif (y <= -2.8e-96)
		tmp = z;
	elseif (y <= -2.2e-103)
		tmp = y * x;
	elseif (y <= 7.8e-19)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e-43], t$95$0, If[LessEqual[y, -2.8e-96], z, If[LessEqual[y, -2.2e-103], N[(y * x), $MachinePrecision], If[LessEqual[y, 7.8e-19], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000044e-43 or 7.7999999999999999e-19 < y

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 97.4%

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

      1. mul-1-neg 97.4%

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

      2. sub-neg 97.4%

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

   5. Simplified 97.4%

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

   if -9.50000000000000044e-43 < y < -2.80000000000000015e-96 or -2.1999999999999999e-103 < y < 7.7999999999999999e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.7%

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

   if -2.80000000000000015e-96 < y < -2.1999999999999999e-103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-103}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -4.3e+33)
     t_0
     (if (<= y -2.2e-96)
       (* z (- 1.0 y))
       (if (<= y -3.5e-102) (* y x) (if (<= y 1.5e-19) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -4.3e+33) {
		tmp = t_0;
	} else if (y <= -2.2e-96) {
		tmp = z * (1.0 - y);
	} else if (y <= -3.5e-102) {
		tmp = y * x;
	} else if (y <= 1.5e-19) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x - z)
    if (y <= (-4.3d+33)) then
        tmp = t_0
    else if (y <= (-2.2d-96)) then
        tmp = z * (1.0d0 - y)
    else if (y <= (-3.5d-102)) then
        tmp = y * x
    else if (y <= 1.5d-19) then
        tmp = z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -4.3e+33) {
		tmp = t_0;
	} else if (y <= -2.2e-96) {
		tmp = z * (1.0 - y);
	} else if (y <= -3.5e-102) {
		tmp = y * x;
	} else if (y <= 1.5e-19) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -4.3e+33:
		tmp = t_0
	elif y <= -2.2e-96:
		tmp = z * (1.0 - y)
	elif y <= -3.5e-102:
		tmp = y * x
	elif y <= 1.5e-19:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	tmp = 0.0
	if (y <= -4.3e+33)
		tmp = t_0;
	elseif (y <= -2.2e-96)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= -3.5e-102)
		tmp = Float64(y * x);
	elseif (y <= 1.5e-19)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	tmp = 0.0;
	if (y <= -4.3e+33)
		tmp = t_0;
	elseif (y <= -2.2e-96)
		tmp = z * (1.0 - y);
	elseif (y <= -3.5e-102)
		tmp = y * x;
	elseif (y <= 1.5e-19)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+33], t$95$0, If[LessEqual[y, -2.2e-96], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-102], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.5e-19], z, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.30000000000000028e33 or 1.49999999999999996e-19 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. sub-neg 99.0%

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

   5. Simplified 99.0%

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

   if -4.30000000000000028e33 < y < -2.19999999999999979e-96

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.8%

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

   if -2.19999999999999979e-96 < y < -3.49999999999999986e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.49999999999999986e-102 < y < 1.49999999999999996e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+33} \lor \neg \left(y \leq -2.9 \cdot 10^{-96} \lor \neg \left(y \leq -3.5 \cdot 10^{-102}\right) \land y \leq 1.25 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e+33)
         (not
          (or (<= y -2.9e-96) (and (not (<= y -3.5e-102)) (<= y 1.25e-18)))))
   (* y x)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+33) || !((y <= -2.9e-96) || (!(y <= -3.5e-102) && (y <= 1.25e-18)))) {
		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 <= (-4.3d+33)) .or. (.not. (y <= (-2.9d-96)) .or. (.not. (y <= (-3.5d-102))) .and. (y <= 1.25d-18))) 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 <= -4.3e+33) || !((y <= -2.9e-96) || (!(y <= -3.5e-102) && (y <= 1.25e-18)))) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e+33) or not ((y <= -2.9e-96) or (not (y <= -3.5e-102) and (y <= 1.25e-18))):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e+33) || !((y <= -2.9e-96) || (!(y <= -3.5e-102) && (y <= 1.25e-18))))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.3e+33) || ~(((y <= -2.9e-96) || (~((y <= -3.5e-102)) && (y <= 1.25e-18)))))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e+33], N[Not[Or[LessEqual[y, -2.9e-96], And[N[Not[LessEqual[y, -3.5e-102]], $MachinePrecision], LessEqual[y, 1.25e-18]]]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -4.30000000000000028e33 or -2.89999999999999994e-96 < y < -3.49999999999999986e-102 or 1.25000000000000009e-18 < y

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 53.6%

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

      1. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   if -4.30000000000000028e33 < y < -2.89999999999999994e-96 or -3.49999999999999986e-102 < y < 1.25000000000000009e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.8%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+33} \lor \neg \left(y \leq -2.9 \cdot 10^{-96} \lor \neg \left(y \leq -3.5 \cdot 10^{-102}\right) \land y \leq 1.25 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.2e-18))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.2e-18)) {
		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 <= 2.2d-18))) 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 <= 2.2e-18)) {
		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 <= 2.2e-18):
		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 <= 2.2e-18))
		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 <= 2.2e-18)))
		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, 2.2e-18]], $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 2.1999999999999998e-18 < y

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. sub-neg 98.7%

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

   5. Simplified 98.7%

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

   if -1 < y < 2.1999999999999998e-18

   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. +-lft-identity 100.0%

         \[\leadsto \color{blue}{\left(0 + z \cdot \left(1 - y\right)\right)} + x \cdot y \]

      3. cancel-sign-sub 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-z\right) \cdot \left(1 - y\right)\right)} + x \cdot y \]

      4. cancel-sign-sub 100.0%

         \[\leadsto \color{blue}{\left(0 + z \cdot \left(1 - y\right)\right)} + x \cdot y \]

      5. +-lft-identity 100.0%

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

      6. distribute-lft-out-- 100.0%

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

      7. *-rgt-identity 100.0%

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

      8. associate-+l- 100.0%

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

      9. 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 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.4% 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 97.7%

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

3. Taylor expanded in y around 0 33.2%

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

4. Final simplification 33.2%

   \[\leadsto z \]
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 2024077 
(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))))