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

Percentage Accurate: 98.0% → 100.0%

Time: 4.0s

Alternatives: 6

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 96.9%

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

   1. +-commutative 96.9%

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

   2. distribute-lft-out-- 96.9%

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

   3. *-rgt-identity 96.9%

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

   4. associate-+l- 96.9%

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

   5. 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. Final simplification 100.0%

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

Alternative 2: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+95} \lor \neg \left(y \leq 2.3 \cdot 10^{+194}\right) \land y \leq 2.15 \cdot 10^{+226}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -1.16e+160)
     t_0
     (if (<= y -2.3e+30)
       (* y x)
       (if (<= y -4e+14)
         t_0
         (if (<= y -8.5e-20)
           (* y x)
           (if (<= y 8e-44)
             z
             (if (or (<= y 3.8e+95)
                     (and (not (<= y 2.3e+194)) (<= y 2.15e+226)))
               (* y x)
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -1.16e+160) {
		tmp = t_0;
	} else if (y <= -2.3e+30) {
		tmp = y * x;
	} else if (y <= -4e+14) {
		tmp = t_0;
	} else if (y <= -8.5e-20) {
		tmp = y * x;
	} else if (y <= 8e-44) {
		tmp = z;
	} else if ((y <= 3.8e+95) || (!(y <= 2.3e+194) && (y <= 2.15e+226))) {
		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 <= (-1.16d+160)) then
        tmp = t_0
    else if (y <= (-2.3d+30)) then
        tmp = y * x
    else if (y <= (-4d+14)) then
        tmp = t_0
    else if (y <= (-8.5d-20)) then
        tmp = y * x
    else if (y <= 8d-44) then
        tmp = z
    else if ((y <= 3.8d+95) .or. (.not. (y <= 2.3d+194)) .and. (y <= 2.15d+226)) 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 <= -1.16e+160) {
		tmp = t_0;
	} else if (y <= -2.3e+30) {
		tmp = y * x;
	} else if (y <= -4e+14) {
		tmp = t_0;
	} else if (y <= -8.5e-20) {
		tmp = y * x;
	} else if (y <= 8e-44) {
		tmp = z;
	} else if ((y <= 3.8e+95) || (!(y <= 2.3e+194) && (y <= 2.15e+226))) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -1.16e+160:
		tmp = t_0
	elif y <= -2.3e+30:
		tmp = y * x
	elif y <= -4e+14:
		tmp = t_0
	elif y <= -8.5e-20:
		tmp = y * x
	elif y <= 8e-44:
		tmp = z
	elif (y <= 3.8e+95) or (not (y <= 2.3e+194) and (y <= 2.15e+226)):
		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 <= -1.16e+160)
		tmp = t_0;
	elseif (y <= -2.3e+30)
		tmp = Float64(y * x);
	elseif (y <= -4e+14)
		tmp = t_0;
	elseif (y <= -8.5e-20)
		tmp = Float64(y * x);
	elseif (y <= 8e-44)
		tmp = z;
	elseif ((y <= 3.8e+95) || (!(y <= 2.3e+194) && (y <= 2.15e+226)))
		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 <= -1.16e+160)
		tmp = t_0;
	elseif (y <= -2.3e+30)
		tmp = y * x;
	elseif (y <= -4e+14)
		tmp = t_0;
	elseif (y <= -8.5e-20)
		tmp = y * x;
	elseif (y <= 8e-44)
		tmp = z;
	elseif ((y <= 3.8e+95) || (~((y <= 2.3e+194)) && (y <= 2.15e+226)))
		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, -1.16e+160], t$95$0, If[LessEqual[y, -2.3e+30], N[(y * x), $MachinePrecision], If[LessEqual[y, -4e+14], t$95$0, If[LessEqual[y, -8.5e-20], N[(y * x), $MachinePrecision], If[LessEqual[y, 8e-44], z, If[Or[LessEqual[y, 3.8e+95], And[N[Not[LessEqual[y, 2.3e+194]], $MachinePrecision], LessEqual[y, 2.15e+226]]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.16000000000000006e160 or -2.3e30 < y < -4e14 or 3.7999999999999999e95 < y < 2.30000000000000005e194 or 2.14999999999999994e226 < y

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. 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 69.9%

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

      1. associate-*r* 69.9%

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

      2. neg-mul-1 69.9%

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

      3. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   if -1.16000000000000006e160 < y < -2.3e30 or -4e14 < y < -8.5000000000000005e-20 or 7.99999999999999962e-44 < y < 3.7999999999999999e95 or 2.30000000000000005e194 < y < 2.14999999999999994e226

   1. Initial program 98.5%

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

   2. Taylor expanded in x around inf 70.6%

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

      1. *-commutative 70.6%

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

   4. Simplified 70.6%

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

   if -8.5000000000000005e-20 < y < 7.99999999999999962e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+95} \lor \neg \left(y \leq 2.3 \cdot 10^{+194}\right) \land y \leq 2.15 \cdot 10^{+226}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-19} \lor \neg \left(y \leq 8.8 \cdot 10^{-42}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e-19) (not (<= y 8.8e-42))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e-19) || !(y <= 8.8e-42)) {
		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 <= (-2.1d-19)) .or. (.not. (y <= 8.8d-42))) 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 <= -2.1e-19) || !(y <= 8.8e-42)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e-19) or not (y <= 8.8e-42):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e-19) || !(y <= 8.8e-42))
		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 <= -2.1e-19) || ~((y <= 8.8e-42)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e-19], N[Not[LessEqual[y, 8.8e-42]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -2.0999999999999999e-19 or 8.8000000000000002e-42 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. sub-neg 97.7%

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

   4. Simplified 97.7%

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

   if -2.0999999999999999e-19 < y < 8.8000000000000002e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-19} \lor \neg \left(y \leq 8.8 \cdot 10^{-42}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.035))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.035)) {
		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 <= 0.035d0))) 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 <= 0.035)) {
		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 <= 0.035):
		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 <= 0.035))
		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 <= 0.035)))
		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, 0.035]], $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 0.035000000000000003 < y

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. sub-neg 99.5%

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

   4. Simplified 99.5%

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

   if -1 < y < 0.035000000000000003

   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. associate-+l- 100.0%

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

      5. 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. Taylor expanded in z around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-lft-neg-out 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

      1. sub-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. distribute-rgt-neg-out 99.4%

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

      4. remove-double-neg 99.4%

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

   8. Applied egg-rr 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 5: 62.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-19} \lor \neg \left(y \leq 2.15 \cdot 10^{-42}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.45e-19) (not (<= y 2.15e-42))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e-19) || !(y <= 2.15e-42)) {
		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 <= (-1.45d-19)) .or. (.not. (y <= 2.15d-42))) 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 <= -1.45e-19) || !(y <= 2.15e-42)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.45e-19) or not (y <= 2.15e-42):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.45e-19) || !(y <= 2.15e-42))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.45e-19) || ~((y <= 2.15e-42)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.45e-19], N[Not[LessEqual[y, 2.15e-42]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e-19 or 2.1500000000000001e-42 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 54.0%

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

      1. *-commutative 54.0%

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

   4. Simplified 54.0%

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

   if -1.45e-19 < y < 2.1500000000000001e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-19} \lor \neg \left(y \leq 2.15 \cdot 10^{-42}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 36.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in y around 0 32.0%

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

3. Final simplification 32.0%

   \[\leadsto z \]

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 2023334 
(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))))