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

Percentage Accurate: 97.8% → 100.0%

Time: 9.8s

Alternatives: 8

Speedup: 1.3×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.8% 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

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

FPCore

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

C

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

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 * (z - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. +-lft-identity 97.2%

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

   3. cancel-sign-sub 97.2%

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

   4. cancel-sign-sub 97.2%

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

   5. +-lft-identity 97.2%

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

   6. distribute-lft-out-- 97.2%

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

   7. *-rgt-identity 97.2%

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

   8. associate-+l- 97.2%

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

   9. distribute-rgt-out-- 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-5}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -3.15e+94)
     t_0
     (if (<= y -5.9e-5) (* y x) (if (<= y 1.35e-8) z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -3.15e+94) {
		tmp = t_0;
	} else if (y <= -5.9e-5) {
		tmp = y * x;
	} else if (y <= 1.35e-8) {
		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 = z * -y
    if (y <= (-3.15d+94)) then
        tmp = t_0
    else if (y <= (-5.9d-5)) then
        tmp = y * x
    else if (y <= 1.35d-8) 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 = z * -y;
	double tmp;
	if (y <= -3.15e+94) {
		tmp = t_0;
	} else if (y <= -5.9e-5) {
		tmp = y * x;
	} else if (y <= 1.35e-8) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -3.15e+94:
		tmp = t_0
	elif y <= -5.9e-5:
		tmp = y * x
	elif y <= 1.35e-8:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -3.15e+94)
		tmp = t_0;
	elseif (y <= -5.9e-5)
		tmp = Float64(y * x);
	elseif (y <= 1.35e-8)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	tmp = 0.0;
	if (y <= -3.15e+94)
		tmp = t_0;
	elseif (y <= -5.9e-5)
		tmp = y * x;
	elseif (y <= 1.35e-8)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -3.15e+94], t$95$0, If[LessEqual[y, -5.9e-5], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.35e-8], z, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.15e94 or 1.35000000000000001e-8 < y

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. sub-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0 59.3%

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

      1. associate-*r* 59.3%

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

      2. neg-mul-1 59.3%

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

      3. *-commutative 59.3%

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

   8. Simplified 59.3%

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

   if -3.15e94 < y < -5.8999999999999998e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if -5.8999999999999998e-5 < y < 1.35000000000000001e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

   4. Taylor expanded in x around 0 73.7%

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

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.35e-8))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.35e-8)) {
		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 <= 1.35d-8))) 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 <= 1.35e-8)) {
		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 <= 1.35e-8):
		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 <= 1.35e-8))
		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 <= 1.35e-8)))
		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, 1.35e-8]], $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 1.35000000000000001e-8 < y

   1. Initial program 94.4%

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

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

   if -1 < y < 1.35000000000000001e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2000000 \lor \neg \left(y \leq 1.32 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2000000.0) (not (<= y 1.32e-8)))
   (* y (- x z))
   (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2000000.0) || !(y <= 1.32e-8)) {
		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 <= (-2000000.0d0)) .or. (.not. (y <= 1.32d-8))) 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 <= -2000000.0) || !(y <= 1.32e-8)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2000000.0) or not (y <= 1.32e-8):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2000000.0) || !(y <= 1.32e-8))
		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 <= -2000000.0) || ~((y <= 1.32e-8)))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2000000.0], N[Not[LessEqual[y, 1.32e-8]], $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 < -2e6 or 1.32000000000000007e-8 < y

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. sub-neg 98.6%

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

   5. Simplified 98.6%

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

   if -2e6 < y < 1.32000000000000007e-8

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. +-lft-identity 100.0%

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

      3. cancel-sign-sub 100.0%

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

      4. cancel-sign-sub 100.0%

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

      5. +-lft-identity 100.0%

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

      6. distribute-lft-out-- 100.0%

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

      7. *-rgt-identity 100.0%

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

      8. associate-+l- 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 74.7%

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

      1. *-commutative 74.7%

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

   7. Simplified 74.7%

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

   8. Taylor expanded in z around 0 74.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2000000 \lor \neg \left(y \leq 1.32 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-6} \lor \neg \left(y \leq 2.3 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9e-6) (not (<= y 2.3e-23))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e-6) || !(y <= 2.3e-23)) {
		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 <= (-9d-6)) .or. (.not. (y <= 2.3d-23))) 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 <= -9e-6) || !(y <= 2.3e-23)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9e-6) or not (y <= 2.3e-23):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9e-6) || !(y <= 2.3e-23))
		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 <= -9e-6) || ~((y <= 2.3e-23)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9e-6], N[Not[LessEqual[y, 2.3e-23]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000023e-6 or 2.3000000000000001e-23 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf 95.5%

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

      1. mul-1-neg 95.5%

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

      2. sub-neg 95.5%

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

   5. Simplified 95.5%

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

   if -9.00000000000000023e-6 < y < 2.3000000000000001e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in x around 0 75.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-6} \lor \neg \left(y \leq 2.3 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-8} \lor \neg \left(y \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-8) (not (<= y 3.5e-79))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-8) || !(y <= 3.5e-79)) {
		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 <= (-1.15d-8)) .or. (.not. (y <= 3.5d-79))) 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 <= -1.15e-8) || !(y <= 3.5e-79)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-8) or not (y <= 3.5e-79):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-8) || !(y <= 3.5e-79))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e-8) || ~((y <= 3.5e-79)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-8], N[Not[LessEqual[y, 3.5e-79]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-8 or 3.5000000000000003e-79 < 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 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   if -1.15e-8 < y < 3.5000000000000003e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

   4. Taylor expanded in x around 0 78.5%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-8} \lor \neg \left(y \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% 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 97.2%

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

3. Taylor expanded in y around 0 72.9%

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

4. Taylor expanded in x around 0 38.7%

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

Alternative 8: 2.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.0)

C

double code(double x, double y, double z) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 0.0;
}

Python

def code(x, y, z):
	return 0.0

Julia

function code(x, y, z)
	return 0.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in y around inf 62.1%

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

   1. mul-1-neg 62.1%

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

   2. sub-neg 62.1%

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

5. Simplified 62.1%

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

6. Taylor expanded in x around 0 29.4%

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

   1. associate-*r* 29.4%

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

   2. neg-mul-1 29.4%

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

   3. *-commutative 29.4%

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

8. Simplified 29.4%

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

   1. add-log-exp 21.1%

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

   2. add-sqr-sqrt 21.1%

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

   3. sqrt-unprod 21.1%

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

   4. exp-prod 21.0%

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

   5. add-sqr-sqrt 9.0%

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

   6. sqrt-unprod 9.3%

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

   7. sqr-neg 9.3%

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

   8. sqrt-unprod 4.3%

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

   9. add-sqr-sqrt 4.5%

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

   10. pow-flip 4.5%

       \[\leadsto \log \left(\sqrt{e^{z \cdot \left(-y\right)} \cdot \color{blue}{\frac{1}{{\left(e^{z}\right)}^{\left(-y\right)}}}}\right) \]

   11. exp-prod 1.5%

       \[\leadsto \log \left(\sqrt{e^{z \cdot \left(-y\right)} \cdot \frac{1}{\color{blue}{e^{z \cdot \left(-y\right)}}}}\right) \]

   12. rgt-mult-inverse 2.5%

       \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

   13. metadata-eval 2.5%

       \[\leadsto \log \color{blue}{1} \]

   14. metadata-eval 2.5%

       \[\leadsto \color{blue}{0} \]

10. Applied egg-rr 2.5%

    \[\leadsto \color{blue}{0} \]
11. 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 2024132 
(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))))