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

Percentage Accurate: 98.0% → 100.0%

Time: 6.2s

Alternatives: 6

Speedup: 1.3×

• 20.8% 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 97.3%

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

   1. +-commutative 97.3%

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

   2. distribute-lft-out-- 97.3%

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

   3. *-rgt-identity 97.3%

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

   4. cancel-sign-sub-inv 97.3%

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

   5. +-commutative 97.3%

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

   6. +-commutative 97.3%

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

   7. associate-+l+ 97.3%

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

   8. distribute-lft-neg-out 97.3%

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

   9. remove-double-neg 97.3%

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

   10. distribute-rgt-neg-out 97.3%

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

   11. distribute-neg-out 97.3%

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

   12. sub-neg 97.3%

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

   13. distribute-rgt-neg-out 97.3%

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

   14. sub-neg 97.3%

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

   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: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-73}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-47}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -1.6e+51)
     t_0
     (if (<= y -2.8e-73)
       (* y x)
       (if (<= y 8e-47) z (if (<= y 1.85e+22) (* y x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -1.6e+51) {
		tmp = t_0;
	} else if (y <= -2.8e-73) {
		tmp = y * x;
	} else if (y <= 8e-47) {
		tmp = z;
	} else if (y <= 1.85e+22) {
		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 <= (-1.6d+51)) then
        tmp = t_0
    else if (y <= (-2.8d-73)) then
        tmp = y * x
    else if (y <= 8d-47) then
        tmp = z
    else if (y <= 1.85d+22) 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 <= -1.6e+51) {
		tmp = t_0;
	} else if (y <= -2.8e-73) {
		tmp = y * x;
	} else if (y <= 8e-47) {
		tmp = z;
	} else if (y <= 1.85e+22) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -1.6e+51:
		tmp = t_0
	elif y <= -2.8e-73:
		tmp = y * x
	elif y <= 8e-47:
		tmp = z
	elif y <= 1.85e+22:
		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 <= -1.6e+51)
		tmp = t_0;
	elseif (y <= -2.8e-73)
		tmp = Float64(y * x);
	elseif (y <= 8e-47)
		tmp = z;
	elseif (y <= 1.85e+22)
		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 <= -1.6e+51)
		tmp = t_0;
	elseif (y <= -2.8e-73)
		tmp = y * x;
	elseif (y <= 8e-47)
		tmp = z;
	elseif (y <= 1.85e+22)
		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, -1.6e+51], t$95$0, If[LessEqual[y, -2.8e-73], N[(y * x), $MachinePrecision], If[LessEqual[y, 8e-47], z, If[LessEqual[y, 1.85e+22], N[(y * x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e51 or 1.8499999999999999e22 < y

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 100.0%

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

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 63.8%

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

      1. associate-*r* 63.8%

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

      2. neg-mul-1 63.8%

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

      3. *-commutative 63.8%

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

   8. Simplified 63.8%

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

   if -1.6000000000000001e51 < y < -2.80000000000000012e-73 or 7.9999999999999998e-47 < y < 1.8499999999999999e22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -2.80000000000000012e-73 < y < 7.9999999999999998e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -21000000000.0) (not (<= y 1.0))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -21000000000.0) || !(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 <= (-21000000000.0d0)) .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 <= -21000000000.0) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -21000000000.0) 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 <= -21000000000.0) || !(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 <= -21000000000.0) || ~((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, -21000000000.0], 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 < -2.1e10 or 1 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. sub-neg 99.1%

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

   5. Simplified 99.1%

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

   if -2.1e10 < y < 1

   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 0 98.2%

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

      1. mul-1-neg 98.2%

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

      2. distribute-lft-neg-out 98.2%

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

      3. *-commutative 98.2%

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

   7. Simplified 98.2%

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

      1. *-commutative 98.2%

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

      2. cancel-sign-sub 98.2%

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

      3. *-commutative 98.2%

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

      4. +-commutative 98.2%

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

   9. Applied egg-rr 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-73} \lor \neg \left(y \leq 8.8 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e-73) (not (<= y 8.8e-48))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e-73) || !(y <= 8.8e-48)) {
		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 <= (-1.7d-73)) .or. (.not. (y <= 8.8d-48))) 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 <= -1.7e-73) || !(y <= 8.8e-48)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.7e-73) or not (y <= 8.8e-48):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e-73) || !(y <= 8.8e-48))
		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 <= -1.7e-73) || ~((y <= 8.8e-48)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e-73], N[Not[LessEqual[y, 8.8e-48]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e-73 or 8.8000000000000005e-48 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 94.9%

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

      1. mul-1-neg 94.9%

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

      2. sub-neg 94.9%

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

   5. Simplified 94.9%

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

   if -1.7000000000000001e-73 < y < 8.8000000000000005e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-73} \lor \neg \left(y \leq 8.8 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-73} \lor \neg \left(y \leq 7 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e-73) (not (<= y 7e-47))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-73) || !(y <= 7e-47)) {
		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 <= (-1d-73)) .or. (.not. (y <= 7d-47))) 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 <= -1e-73) || !(y <= 7e-47)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e-73) or not (y <= 7e-47):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e-73) || !(y <= 7e-47))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e-73) || ~((y <= 7e-47)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e-73], N[Not[LessEqual[y, 7e-47]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999997e-74 or 6.9999999999999996e-47 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 50.8%

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

      1. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   if -9.99999999999999997e-74 < y < 6.9999999999999996e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-73} \lor \neg \left(y \leq 7 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.0% 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 97.3%

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

3. Taylor expanded in y around 0 37.5%

   \[\leadsto \color{blue}{z} \]
4. Add Preprocessing

Developer Target 1: 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 2024131 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- z (* (- z x) y)))

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