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

Percentage Accurate: 98.0% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.3×

• 21.0% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x - z, z\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. distribute-lft-out-- 98.0%

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

   2. *-rgt-identity 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. distribute-rgt-out 100.0%

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

   8. fma-define 100.0%

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

   9. +-commutative 100.0%

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

   10. unsub-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, x - z, z\right) \]
6. Add Preprocessing

Alternative 2: 60.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+59}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e-15)
   (* y x)
   (if (<= y 1.5e-119)
     z
     (if (<= y 8.5e-52)
       (* y x)
       (if (<= y 1.12e-33) z (if (<= y 1.7e+59) (* y x) (* y (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-15) {
		tmp = y * x;
	} else if (y <= 1.5e-119) {
		tmp = z;
	} else if (y <= 8.5e-52) {
		tmp = y * x;
	} else if (y <= 1.12e-33) {
		tmp = z;
	} else if (y <= 1.7e+59) {
		tmp = y * x;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.8d-15)) then
        tmp = y * x
    else if (y <= 1.5d-119) then
        tmp = z
    else if (y <= 8.5d-52) then
        tmp = y * x
    else if (y <= 1.12d-33) then
        tmp = z
    else if (y <= 1.7d+59) then
        tmp = y * x
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-15) {
		tmp = y * x;
	} else if (y <= 1.5e-119) {
		tmp = z;
	} else if (y <= 8.5e-52) {
		tmp = y * x;
	} else if (y <= 1.12e-33) {
		tmp = z;
	} else if (y <= 1.7e+59) {
		tmp = y * x;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e-15:
		tmp = y * x
	elif y <= 1.5e-119:
		tmp = z
	elif y <= 8.5e-52:
		tmp = y * x
	elif y <= 1.12e-33:
		tmp = z
	elif y <= 1.7e+59:
		tmp = y * x
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e-15)
		tmp = Float64(y * x);
	elseif (y <= 1.5e-119)
		tmp = z;
	elseif (y <= 8.5e-52)
		tmp = Float64(y * x);
	elseif (y <= 1.12e-33)
		tmp = z;
	elseif (y <= 1.7e+59)
		tmp = Float64(y * x);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e-15)
		tmp = y * x;
	elseif (y <= 1.5e-119)
		tmp = z;
	elseif (y <= 8.5e-52)
		tmp = y * x;
	elseif (y <= 1.12e-33)
		tmp = z;
	elseif (y <= 1.7e+59)
		tmp = y * x;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e-15], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.5e-119], z, If[LessEqual[y, 8.5e-52], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.12e-33], z, If[LessEqual[y, 1.7e+59], N[(y * x), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999999e-15 or 1.5000000000000001e-119 < y < 8.50000000000000006e-52 or 1.11999999999999999e-33 < y < 1.70000000000000003e59

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if -4.7999999999999999e-15 < y < 1.5000000000000001e-119 or 8.50000000000000006e-52 < y < 1.11999999999999999e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.8%

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

   if 1.70000000000000003e59 < y

   1. Initial program 92.2%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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 66.4%

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

      1. associate-*r* 66.4%

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

      2. neg-mul-1 66.4%

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

   8. Simplified 66.4%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+59}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -2.6e-14)
     t_0
     (if (<= y 2.2e-119)
       z
       (if (<= y 9.5e-52) (* y x) (if (<= y 1.9e-33) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -2.6e-14) {
		tmp = t_0;
	} else if (y <= 2.2e-119) {
		tmp = z;
	} else if (y <= 9.5e-52) {
		tmp = y * x;
	} else if (y <= 1.9e-33) {
		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 <= (-2.6d-14)) then
        tmp = t_0
    else if (y <= 2.2d-119) then
        tmp = z
    else if (y <= 9.5d-52) then
        tmp = y * x
    else if (y <= 1.9d-33) 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 <= -2.6e-14) {
		tmp = t_0;
	} else if (y <= 2.2e-119) {
		tmp = z;
	} else if (y <= 9.5e-52) {
		tmp = y * x;
	} else if (y <= 1.9e-33) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -2.6e-14:
		tmp = t_0
	elif y <= 2.2e-119:
		tmp = z
	elif y <= 9.5e-52:
		tmp = y * x
	elif y <= 1.9e-33:
		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 <= -2.6e-14)
		tmp = t_0;
	elseif (y <= 2.2e-119)
		tmp = z;
	elseif (y <= 9.5e-52)
		tmp = Float64(y * x);
	elseif (y <= 1.9e-33)
		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 <= -2.6e-14)
		tmp = t_0;
	elseif (y <= 2.2e-119)
		tmp = z;
	elseif (y <= 9.5e-52)
		tmp = y * x;
	elseif (y <= 1.9e-33)
		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, -2.6e-14], t$95$0, If[LessEqual[y, 2.2e-119], z, If[LessEqual[y, 9.5e-52], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.9e-33], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999997e-14 or 1.89999999999999997e-33 < y

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 95.0%

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

      1. mul-1-neg 95.0%

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

      2. sub-neg 95.0%

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

   5. Simplified 95.0%

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

   if -2.59999999999999997e-14 < y < 2.2000000000000001e-119 or 9.50000000000000007e-52 < y < 1.89999999999999997e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.8%

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

   if 2.2000000000000001e-119 < y < 9.50000000000000007e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. *-commutative 62.7%

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

   5. Simplified 62.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-70} \lor \neg \left(x \leq 9 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-70) (not (<= x 9e-7))) (* y (- x z)) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-70) || !(x <= 9e-7)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	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 ((x <= (-1d-70)) .or. (.not. (x <= 9d-7))) then
        tmp = y * (x - z)
    else
        tmp = z * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-70) || !(x <= 9e-7)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-70) or not (x <= 9e-7):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-70) || !(x <= 9e-7))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = Float64(z * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e-70) || ~((x <= 9e-7)))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-70], N[Not[LessEqual[x, 9e-7]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999996e-71 or 8.99999999999999959e-7 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. sub-neg 83.9%

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

   5. Simplified 83.9%

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

   if -9.99999999999999996e-71 < x < 8.99999999999999959e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-70} \lor \neg \left(x \leq 9 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 < -1 or 1 < y

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. sub-neg 98.0%

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

   5. Simplified 98.0%

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

   if -1 < 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 98.1%

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

      1. mul-1-neg 98.1%

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

      2. distribute-lft-neg-out 98.1%

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

      3. *-commutative 98.1%

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

   7. Simplified 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-rgt-neg-out 98.1%

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

      3. remove-double-neg 98.1%

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

      4. +-commutative 98.1%

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

   9. Applied egg-rr 98.1%

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

4. Final simplification 98.0%

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

Alternative 6: 55.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-76} \lor \neg \left(x \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-76) (not (<= x 5.5e-16))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-76) || !(x <= 5.5e-16)) {
		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 ((x <= (-5.5d-76)) .or. (.not. (x <= 5.5d-16))) 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 ((x <= -5.5e-76) || !(x <= 5.5e-16)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-76) or not (x <= 5.5e-16):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-76) || !(x <= 5.5e-16))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e-76) || ~((x <= 5.5e-16)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-76], N[Not[LessEqual[x, 5.5e-16]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000014e-76 or 5.49999999999999964e-16 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -5.50000000000000014e-76 < x < 5.49999999999999964e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 51.4%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-76} \lor \neg \left(x \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. distribute-lft-out-- 98.0%

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

   3. *-rgt-identity 98.0%

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

   4. cancel-sign-sub-inv 98.0%

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

   5. +-commutative 98.0%

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

   6. +-commutative 98.0%

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

   7. associate-+l+ 98.0%

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

   8. distribute-lft-neg-out 98.0%

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

   9. remove-double-neg 98.0%

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

   10. distribute-rgt-neg-out 98.0%

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

   11. distribute-neg-out 98.0%

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

   12. sub-neg 98.0%

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

   13. distribute-rgt-neg-out 98.0%

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

   14. sub-neg 98.0%

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

   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. Final simplification 100.0%

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

Alternative 8: 35.9% 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 98.0%

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

3. Taylor expanded in y around 0 32.0%

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

4. Final simplification 32.0%

   \[\leadsto z \]
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 2024112 
(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))))