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

Percentage Accurate: 97.7% → 100.0%

Time: 7.0s

Alternatives: 8

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: 97.7% 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 99.2%

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

   1. distribute-lft-out-- 99.2%

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

   2. *-rgt-identity 99.2%

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

   3. cancel-sign-sub-inv 99.2%

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

   4. +-commutative 99.2%

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

   5. associate-+r+ 99.2%

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

   6. distribute-rgt-out 100.0%

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

   7. +-commutative 100.0%

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

   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. Add Preprocessing

Alternative 2: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.35 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.35e-13))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.35e-13)) {
		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-13))) 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-13)) {
		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-13):
		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-13))
		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-13)))
		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-13]], $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 1.35000000000000005e-13 < y

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 98.5%

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

      1. neg-mul-1 98.5%

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

      2. sub-neg 98.5%

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

   5. Simplified 98.5%

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

   if -1 < y < 1.35000000000000005e-13

   1. Initial program 99.9%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-rgt-out 100.0%

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

      7. +-commutative 100.0%

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

      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. Taylor expanded in x around inf 98.7%

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

      1. fma-undefine 98.7%

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

   7. Applied egg-rr 98.7%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.35 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4700000 \lor \neg \left(y \leq 4 \cdot 10^{-52}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4700000.0) (not (<= y 4e-52))) (* y (- x z)) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4700000.0) || !(y <= 4e-52)) {
		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 <= (-4700000.0d0)) .or. (.not. (y <= 4d-52))) 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 <= -4700000.0) || !(y <= 4e-52)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4700000.0) or not (y <= 4e-52):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4700000.0) || !(y <= 4e-52))
		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 <= -4700000.0) || ~((y <= 4e-52)))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4700000.0], N[Not[LessEqual[y, 4e-52]], $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 < -4.7e6 or 4e-52 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 96.3%

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

      1. neg-mul-1 96.3%

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

      2. sub-neg 96.3%

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

   5. Simplified 96.3%

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

   if -4.7e6 < y < 4e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4700000 \lor \neg \left(y \leq 4 \cdot 10^{-52}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-94} \lor \neg \left(y \leq 1.36 \cdot 10^{-52}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e-94) (not (<= y 1.36e-52))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e-94) || !(y <= 1.36e-52)) {
		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 <= (-6.8d-94)) .or. (.not. (y <= 1.36d-52))) 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 <= -6.8e-94) || !(y <= 1.36e-52)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.8e-94) or not (y <= 1.36e-52):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e-94) || !(y <= 1.36e-52))
		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 <= -6.8e-94) || ~((y <= 1.36e-52)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e-94], N[Not[LessEqual[y, 1.36e-52]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999996e-94 or 1.36e-52 < y

   1. Initial program 98.8%

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

   3. Taylor expanded in y around inf 89.8%

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

      1. neg-mul-1 89.8%

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

      2. sub-neg 89.8%

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

   5. Simplified 89.8%

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

   if -6.7999999999999996e-94 < y < 1.36e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-94} \lor \neg \left(y \leq 1.36 \cdot 10^{-52}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-47} \lor \neg \left(y \leq 1.25 \cdot 10^{-59}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e-47) (not (<= y 1.25e-59))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-47) || !(y <= 1.25e-59)) {
		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 <= (-1.5d-47)) .or. (.not. (y <= 1.25d-59))) 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 <= -1.5e-47) || !(y <= 1.25e-59)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e-47) or not (y <= 1.25e-59):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e-47) || !(y <= 1.25e-59))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5e-47) || ~((y <= 1.25e-59)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e-47], N[Not[LessEqual[y, 1.25e-59]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000008e-47 or 1.25e-59 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf 51.6%

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

      1. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   if -1.50000000000000008e-47 < y < 1.25e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-47} \lor \neg \left(y \leq 1.25 \cdot 10^{-59}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0) (* z (- y)) (if (<= y 1.25e-59) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = z * -y;
	} else if (y <= 1.25e-59) {
		tmp = z;
	} 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) :: tmp
    if (y <= (-1.0d0)) then
        tmp = z * -y
    else if (y <= 1.25d-59) then
        tmp = z
    else
        tmp = 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) {
		tmp = z * -y;
	} else if (y <= 1.25e-59) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = z * -y
	elif y <= 1.25e-59:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(z * Float64(-y));
	elseif (y <= 1.25e-59)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = z * -y;
	elseif (y <= 1.25e-59)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(z * (-y)), $MachinePrecision], If[LessEqual[y, 1.25e-59], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 98.6%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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. neg-mul-1 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 55.9%

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

      1. neg-mul-1 55.9%

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

      2. *-commutative 55.9%

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

      3. distribute-rgt-neg-in 55.9%

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

   8. Simplified 55.9%

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

   if -1 < y < 1.25e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.6%

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

   if 1.25e-59 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.
4. 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 99.2%

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

   1. +-commutative 99.2%

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

   2. +-lft-identity 99.2%

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

   3. cancel-sign-sub 99.2%

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

   4. cancel-sign-sub 99.2%

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

   5. +-lft-identity 99.2%

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

   6. distribute-lft-out-- 99.2%

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

   7. *-rgt-identity 99.2%

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

   8. associate-+l- 99.2%

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

   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. Final simplification 100.0%

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

Alternative 8: 35.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in y around 0 33.7%

   \[\leadsto \color{blue}{z} \]
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 2024114 
(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))))