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

Percentage Accurate: 97.7% → 100.0%

Time: 10.0s

Alternatives: 7

Speedup: 1.3×

• 20.7% 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, 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 98.4%

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

   1. +-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. +-commutative 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+l+ 98.4%

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

   8. distribute-lft-neg-out 98.4%

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

   9. remove-double-neg 98.4%

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

   10. distribute-rgt-neg-out 98.4%

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

   11. distribute-neg-out 98.4%

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

   12. sub-neg 98.4%

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

   13. distribute-rgt-neg-out 98.4%

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

   14. sub-neg 98.4%

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

   15. distribute-rgt-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -140000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -140000000000.0) (not (<= y 1.0))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -140000000000.0) || !(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 <= (-140000000000.0d0)) .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 <= -140000000000.0) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -140000000000.0) 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 <= -140000000000.0) || !(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 <= -140000000000.0) || ~((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, -140000000000.0], 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 < -1.4e11 or 1 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. sub-neg 99.3%

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

   5. Simplified 99.3%

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

   if -1.4e11 < y < 1

   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%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -140000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-6} \lor \neg \left(y \leq 1.75 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-6) (not (<= y 1.75e-26))) (* y (- x z)) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-6) || !(y <= 1.75e-26)) {
		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 <= (-1.15d-6)) .or. (.not. (y <= 1.75d-26))) 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 <= -1.15e-6) || !(y <= 1.75e-26)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-6) or not (y <= 1.75e-26):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-6) || !(y <= 1.75e-26))
		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 <= -1.15e-6) || ~((y <= 1.75e-26)))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-6], N[Not[LessEqual[y, 1.75e-26]], $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 < -1.15e-6 or 1.74999999999999992e-26 < y

   1. Initial program 97.1%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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 -1.15e-6 < y < 1.74999999999999992e-26

   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 inf 80.1%

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

      1. *-commutative 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0 80.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-6} \lor \neg \left(y \leq 1.75 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-12} \lor \neg \left(y \leq 1.8 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e-12) (not (<= y 1.8e-26))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e-12) || !(y <= 1.8e-26)) {
		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 <= (-2.1d-12)) .or. (.not. (y <= 1.8d-26))) 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 <= -2.1e-12) || !(y <= 1.8e-26)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e-12) or not (y <= 1.8e-26):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e-12) || !(y <= 1.8e-26))
		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 <= -2.1e-12) || ~((y <= 1.8e-26)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e-12], N[Not[LessEqual[y, 1.8e-26]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999994e-12 or 1.8000000000000001e-26 < y

   1. Initial program 97.1%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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 -2.09999999999999994e-12 < y < 1.8000000000000001e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around 0 79.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-12} \lor \neg \left(y \leq 1.8 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-11} \lor \neg \left(y \leq 1.6 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e-11) (not (<= y 1.6e-26))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e-11) || !(y <= 1.6e-26)) {
		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 <= (-2.2d-11)) .or. (.not. (y <= 1.6d-26))) 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 <= -2.2e-11) || !(y <= 1.6e-26)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e-11) or not (y <= 1.6e-26):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.2e-11) || !(y <= 1.6e-26))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.2e-11) || ~((y <= 1.6e-26)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.2e-11], N[Not[LessEqual[y, 1.6e-26]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000002e-11 or 1.6000000000000001e-26 < y

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   if -2.2000000000000002e-11 < y < 1.6000000000000001e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around 0 79.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-11} \lor \neg \left(y \leq 1.6 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in y around 0 77.2%

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

4. Taylor expanded in x around 0 37.9%

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

Alternative 7: 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 98.4%

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

3. Taylor expanded in y around inf 64.5%

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

   1. mul-1-neg 64.5%

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

   2. sub-neg 64.5%

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

5. Simplified 64.5%

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

6. Taylor expanded in x around 0 26.2%

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

   1. neg-mul-1 26.2%

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

   2. *-commutative 26.2%

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

   3. distribute-rgt-neg-in 26.2%

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

8. Simplified 26.2%

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

   1. add-log-exp 16.4%

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

   2. add-sqr-sqrt 16.4%

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

   3. sqrt-unprod 16.4%

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

   4. exp-prod 16.3%

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

   5. add-sqr-sqrt 9.9%

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

   6. sqrt-unprod 10.2%

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

   7. sqr-neg 10.2%

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

   8. sqrt-unprod 3.4%

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

   9. add-sqr-sqrt 3.8%

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

   10. pow-flip 3.8%

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

   11. exp-prod 1.7%

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

   12. rgt-mult-inverse 2.6%

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

   13. metadata-eval 2.6%

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

   14. metadata-eval 2.6%

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

10. Applied egg-rr 2.6%

    \[\leadsto \color{blue}{0} \]
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 2024180 
(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))))