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

Percentage Accurate: 98.0% → 100.0%

Time: 7.9s

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: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. distribute-lft-out-- 98.0%

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

   2. *-rgt-identity 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+r+ 98.0%

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

   6. 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: 60.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-89}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+250}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -6.5e+193)
     (* y x)
     (if (<= y -3.7e+109)
       t_0
       (if (<= y -2.9e-89)
         (* y x)
         (if (<= y 1.0) z (if (<= y 1.36e+250) t_0 (* y x))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -6.5e+193) {
		tmp = y * x;
	} else if (y <= -3.7e+109) {
		tmp = t_0;
	} else if (y <= -2.9e-89) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = z;
	} else if (y <= 1.36e+250) {
		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 <= (-6.5d+193)) then
        tmp = y * x
    else if (y <= (-3.7d+109)) then
        tmp = t_0
    else if (y <= (-2.9d-89)) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = z
    else if (y <= 1.36d+250) 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 <= -6.5e+193) {
		tmp = y * x;
	} else if (y <= -3.7e+109) {
		tmp = t_0;
	} else if (y <= -2.9e-89) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = z;
	} else if (y <= 1.36e+250) {
		tmp = t_0;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -6.5e+193:
		tmp = y * x
	elif y <= -3.7e+109:
		tmp = t_0
	elif y <= -2.9e-89:
		tmp = y * x
	elif y <= 1.0:
		tmp = z
	elif y <= 1.36e+250:
		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 <= -6.5e+193)
		tmp = Float64(y * x);
	elseif (y <= -3.7e+109)
		tmp = t_0;
	elseif (y <= -2.9e-89)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = z;
	elseif (y <= 1.36e+250)
		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 <= -6.5e+193)
		tmp = y * x;
	elseif (y <= -3.7e+109)
		tmp = t_0;
	elseif (y <= -2.9e-89)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = z;
	elseif (y <= 1.36e+250)
		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, -6.5e+193], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.7e+109], t$95$0, If[LessEqual[y, -2.9e-89], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], z, If[LessEqual[y, 1.36e+250], t$95$0, N[(y * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4999999999999997e193 or -3.7000000000000002e109 < y < -2.89999999999999992e-89 or 1.36000000000000005e250 < y

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   if -6.4999999999999997e193 < y < -3.7000000000000002e109 or 1 < y < 1.36000000000000005e250

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. neg-mul-1 99.7%

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

      2. sub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 66.0%

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

      1. neg-mul-1 66.0%

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

   8. Simplified 66.0%

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

   if -2.89999999999999992e-89 < 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 75.2%

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

Alternative 3: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -135 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -135.0) (not (<= y 1.0))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -135.0) || !(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 <= (-135.0d0)) .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 <= -135.0) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -135.0) 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 <= -135.0) || !(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 <= -135.0) || ~((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, -135.0], 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 < -135 or 1 < y

   1. Initial program 96.1%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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. neg-mul-1 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 -135 < 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. +-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 0 98.0%

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

      1. mul-1-neg 98.0%

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

      2. distribute-lft-neg-out 98.0%

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

      3. *-commutative 98.0%

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

   7. Simplified 98.0%

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

      1. sub-neg 98.0%

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

      2. distribute-rgt-neg-out 98.0%

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

      3. remove-double-neg 98.0%

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

      4. +-commutative 98.0%

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

      5. *-commutative 98.0%

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

   9. Applied egg-rr 98.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -135 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-89} \lor \neg \left(y \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e-89) (not (<= y 2e-10))) (* y (- x z)) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-89) || !(y <= 2e-10)) {
		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 <= (-2.9d-89)) .or. (.not. (y <= 2d-10))) 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 <= -2.9e-89) || !(y <= 2e-10)) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e-89) or not (y <= 2e-10):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e-89) || !(y <= 2e-10))
		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 <= -2.9e-89) || ~((y <= 2e-10)))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e-89], N[Not[LessEqual[y, 2e-10]], $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 < -2.89999999999999992e-89 or 2.00000000000000007e-10 < y

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 93.0%

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

      1. neg-mul-1 93.0%

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

      2. sub-neg 93.0%

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

   5. Simplified 93.0%

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

   if -2.89999999999999992e-89 < y < 2.00000000000000007e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-89} \lor \neg \left(y \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-89} \lor \neg \left(y \leq 2.3 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.42e-89) (not (<= y 2.3e-30))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42e-89) || !(y <= 2.3e-30)) {
		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 <= (-1.42d-89)) .or. (.not. (y <= 2.3d-30))) 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 <= -1.42e-89) || !(y <= 2.3e-30)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.42e-89) or not (y <= 2.3e-30):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.42e-89) || !(y <= 2.3e-30))
		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 <= -1.42e-89) || ~((y <= 2.3e-30)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.42e-89], N[Not[LessEqual[y, 2.3e-30]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.42e-89 or 2.29999999999999984e-30 < 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 91.5%

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

      1. neg-mul-1 91.5%

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

      2. sub-neg 91.5%

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

   5. Simplified 91.5%

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

   if -1.42e-89 < y < 2.29999999999999984e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-89} \lor \neg \left(y \leq 2.3 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-89} \lor \neg \left(y \leq 1.6 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.75e-89) (not (<= y 1.6e-31))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.75e-89) || !(y <= 1.6e-31)) {
		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 <= (-2.75d-89)) .or. (.not. (y <= 1.6d-31))) 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 <= -2.75e-89) || !(y <= 1.6e-31)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.75e-89) or not (y <= 1.6e-31):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.75e-89) || !(y <= 1.6e-31))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.75e-89) || ~((y <= 1.6e-31)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.75e-89], N[Not[LessEqual[y, 1.6e-31]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -2.75000000000000006e-89 or 1.60000000000000009e-31 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   if -2.75000000000000006e-89 < y < 1.60000000000000009e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-89} \lor \neg \left(y \leq 1.6 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. +-lft-identity 98.0%

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

   3. cancel-sign-sub 98.0%

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

   4. cancel-sign-sub 98.0%

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

   5. +-lft-identity 98.0%

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

   6. distribute-lft-out-- 98.0%

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

   7. *-rgt-identity 98.0%

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

   8. associate-+l- 98.0%

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

   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. Final simplification 100.0%

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

Alternative 8: 36.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in y around 0 34.7%

   \[\leadsto \color{blue}{z} \]
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 2024137 
(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))))