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

Percentage Accurate: 98.1% → 100.0%

Time: 6.2s

Alternatives: 8

Speedup: 1.3×

• 21.4% 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: 98.1% 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 98.8%

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

   1. distribute-lft-out-- 98.8%

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

   2. *-rgt-identity 98.8%

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

   3. cancel-sign-sub-inv 98.8%

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

   4. +-commutative 98.8%

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

   5. associate-+r+ 98.8%

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

   6. +-commutative 98.8%

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

   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: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1200:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -4e+147)
     t_0
     (if (<= y -1.85e-37)
       (* y x)
       (if (<= y 1200.0) z (if (<= y 9.6e+141) t_0 (* y x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -4e+147) {
		tmp = t_0;
	} else if (y <= -1.85e-37) {
		tmp = y * x;
	} else if (y <= 1200.0) {
		tmp = z;
	} else if (y <= 9.6e+141) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = y * -z
    if (y <= (-4d+147)) then
        tmp = t_0
    else if (y <= (-1.85d-37)) then
        tmp = y * x
    else if (y <= 1200.0d0) then
        tmp = z
    else if (y <= 9.6d+141) then
        tmp = t_0
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -4e+147) {
		tmp = t_0;
	} else if (y <= -1.85e-37) {
		tmp = y * x;
	} else if (y <= 1200.0) {
		tmp = z;
	} else if (y <= 9.6e+141) {
		tmp = t_0;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -4e+147:
		tmp = t_0
	elif y <= -1.85e-37:
		tmp = y * x
	elif y <= 1200.0:
		tmp = z
	elif y <= 9.6e+141:
		tmp = t_0
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -4e+147)
		tmp = t_0;
	elseif (y <= -1.85e-37)
		tmp = Float64(y * x);
	elseif (y <= 1200.0)
		tmp = z;
	elseif (y <= 9.6e+141)
		tmp = t_0;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (y <= -4e+147)
		tmp = t_0;
	elseif (y <= -1.85e-37)
		tmp = y * x;
	elseif (y <= 1200.0)
		tmp = z;
	elseif (y <= 9.6e+141)
		tmp = t_0;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -4e+147], t$95$0, If[LessEqual[y, -1.85e-37], N[(y * x), $MachinePrecision], If[LessEqual[y, 1200.0], z, If[LessEqual[y, 9.6e+141], t$95$0, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999999e147 or 1200 < y < 9.59999999999999989e141

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 97.6%

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

      1. mul-1-neg 97.6%

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

      2. sub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x around 0 62.1%

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

      1. associate-*r* 62.1%

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

      2. *-commutative 62.1%

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

      3. neg-mul-1 62.1%

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

   8. Simplified 62.1%

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

   if -3.9999999999999999e147 < y < -1.85e-37 or 9.59999999999999989e141 < y

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -1.85e-37 < y < 1200

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+147}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1200:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-37} \lor \neg \left(y \leq 5.2 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.06e-37) (not (<= y 5.2e-33))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.06e-37) || !(y <= 5.2e-33)) {
		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 <= (-1.06d-37)) .or. (.not. (y <= 5.2d-33))) 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 <= -1.06e-37) || !(y <= 5.2e-33)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.06e-37) or not (y <= 5.2e-33):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.06e-37) || !(y <= 5.2e-33))
		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 <= -1.06e-37) || ~((y <= 5.2e-33)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.06e-37], N[Not[LessEqual[y, 5.2e-33]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.06000000000000003e-37 or 5.19999999999999988e-33 < y

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 93.8%

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

      1. mul-1-neg 93.8%

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

      2. sub-neg 93.8%

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

   5. Simplified 93.8%

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

   if -1.06000000000000003e-37 < y < 5.19999999999999988e-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 78.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-37} \lor \neg \left(y \leq 5.2 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-37} \lor \neg \left(y \leq 700000000\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e-37) (not (<= y 700000000.0)))
   (* y (- x z))
   (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e-37) || !(y <= 700000000.0)) {
		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 ((y <= (-5.9d-37)) .or. (.not. (y <= 700000000.0d0))) 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 ((y <= -5.9e-37) || !(y <= 700000000.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e-37) or not (y <= 700000000.0):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e-37) || !(y <= 700000000.0))
		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 ((y <= -5.9e-37) || ~((y <= 700000000.0)))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e-37], N[Not[LessEqual[y, 700000000.0]], $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 y < -5.8999999999999996e-37 or 7e8 < y

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf 97.2%

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

      1. mul-1-neg 97.2%

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

      2. sub-neg 97.2%

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

   5. Simplified 97.2%

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

   if -5.8999999999999996e-37 < y < 7e8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-37} \lor \neg \left(y \leq 700000000\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
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 97.8%

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

   3. Taylor expanded in y around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. sub-neg 97.9%

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

   5. Simplified 97.9%

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

   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 98.3%

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

      1. mul-1-neg 98.3%

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

      2. distribute-lft-neg-out 98.3%

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

      3. *-commutative 98.3%

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

   7. Simplified 98.3%

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

      1. sub-neg 98.3%

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

      2. +-commutative 98.3%

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

      3. distribute-rgt-neg-out 98.3%

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

      4. remove-double-neg 98.3%

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

   9. Applied egg-rr 98.3%

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

4. Final simplification 98.1%

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

Alternative 6: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-38} \lor \neg \left(y \leq 5 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e-38) (not (<= y 5e-33))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e-38) || !(y <= 5e-33)) {
		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 <= (-5.5d-38)) .or. (.not. (y <= 5d-33))) 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 <= -5.5e-38) || !(y <= 5e-33)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e-38) or not (y <= 5e-33):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e-38) || !(y <= 5e-33))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e-38) || ~((y <= 5e-33)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e-38], N[Not[LessEqual[y, 5e-33]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000005e-38 or 5.00000000000000028e-33 < y

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   if -5.50000000000000005e-38 < y < 5.00000000000000028e-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 78.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-38} \lor \neg \left(y \leq 5 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
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 98.8%

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

   1. +-commutative 98.8%

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

   2. distribute-lft-out-- 98.8%

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

   3. *-rgt-identity 98.8%

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

   4. cancel-sign-sub-inv 98.8%

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

   5. +-commutative 98.8%

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

   6. +-commutative 98.8%

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

   7. associate-+l+ 98.8%

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

   8. distribute-lft-neg-out 98.8%

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

   9. remove-double-neg 98.8%

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

   10. distribute-rgt-neg-out 98.8%

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

   11. distribute-neg-out 98.8%

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

   12. sub-neg 98.8%

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

   13. distribute-rgt-neg-out 98.8%

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

   14. sub-neg 98.8%

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

   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: 35.3% 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 98.8%

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

3. Taylor expanded in y around 0 34.4%

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

4. Final simplification 34.4%

   \[\leadsto z \]
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 2024130 
(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))))