Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 97.6% → 100.0%

Time: 5.7s

Alternatives: 6

Speedup: 1.3×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - 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 = (x * y) + ((1.0d0 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - 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 = (x * y) + ((1.0d0 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. remove-double-neg 98.0%

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

   3. distribute-rgt-neg-out 98.0%

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

   4. neg-sub0 98.0%

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

   5. neg-sub0 98.0%

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

   6. *-commutative 98.0%

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

   7. distribute-lft-neg-in 98.0%

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

   8. remove-double-neg 98.0%

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

   9. distribute-rgt-out-- 98.0%

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

   10. *-lft-identity 98.0%

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

   11. associate-+l- 98.0%

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

   12. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+266}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-60} \lor \neg \left(x \leq 3 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e+266)
   (* z (- x))
   (if (or (<= x -4.1e-60) (not (<= x 3e-65))) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+266) {
		tmp = z * -x;
	} else if ((x <= -4.1e-60) || !(x <= 3e-65)) {
		tmp = x * y;
	} 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 (x <= (-9d+266)) then
        tmp = z * -x
    else if ((x <= (-4.1d-60)) .or. (.not. (x <= 3d-65))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+266) {
		tmp = z * -x;
	} else if ((x <= -4.1e-60) || !(x <= 3e-65)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e+266:
		tmp = z * -x
	elif (x <= -4.1e-60) or not (x <= 3e-65):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e+266)
		tmp = Float64(z * Float64(-x));
	elseif ((x <= -4.1e-60) || !(x <= 3e-65))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e+266)
		tmp = z * -x;
	elseif ((x <= -4.1e-60) || ~((x <= 3e-65)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e+266], N[(z * (-x)), $MachinePrecision], If[Or[LessEqual[x, -4.1e-60], N[Not[LessEqual[x, 3e-65]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999999e266

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. *-commutative 75.3%

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

      3. distribute-rgt-neg-in 75.3%

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

   8. Simplified 75.3%

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

   if -8.99999999999999999e266 < x < -4.10000000000000013e-60 or 2.99999999999999998e-65 < x

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 59.1%

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

   if -4.10000000000000013e-60 < x < 2.99999999999999998e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around 0 84.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+266}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-60} \lor \neg \left(x \leq 3 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 10^{-14}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1e-14))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1e-14)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * 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 ((x <= (-1.0d0)) .or. (.not. (x <= 1d-14))) then
        tmp = x * (y - z)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1e-14)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.0) or not (x <= 1e-14):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1e-14))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1e-14)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1e-14]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 9.99999999999999999e-15 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. sub-neg 98.2%

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

   5. Simplified 98.2%

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

   if -1 < x < 9.99999999999999999e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 10^{-14}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-53} \lor \neg \left(x \leq 3.6 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.5e-53) (not (<= x 3.6e-65))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e-53) || !(x <= 3.6e-65)) {
		tmp = x * (y - 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 ((x <= (-4.5d-53)) .or. (.not. (x <= 3.6d-65))) then
        tmp = x * (y - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e-53) || !(x <= 3.6e-65)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.5e-53) or not (x <= 3.6e-65):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.5e-53) || !(x <= 3.6e-65))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.5e-53) || ~((x <= 3.6e-65)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.5e-53], N[Not[LessEqual[x, 3.6e-65]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999985e-53 or 3.5999999999999998e-65 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 92.4%

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

      1. neg-mul-1 92.4%

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

      2. sub-neg 92.4%

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

   5. Simplified 92.4%

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

   if -4.49999999999999985e-53 < x < 3.5999999999999998e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around 0 84.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-53} \lor \neg \left(x \leq 3.6 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-53} \lor \neg \left(x \leq 5.4 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-53) (not (<= x 5.4e-64))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-53) || !(x <= 5.4e-64)) {
		tmp = x * y;
	} 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 ((x <= (-5.8d-53)) .or. (.not. (x <= 5.4d-64))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-53) || !(x <= 5.4e-64)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-53) or not (x <= 5.4e-64):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-53) || !(x <= 5.4e-64))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e-53) || ~((x <= 5.4e-64)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-53], N[Not[LessEqual[x, 5.4e-64]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999996e-53 or 5.39999999999999971e-64 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 57.0%

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

   if -5.7999999999999996e-53 < x < 5.39999999999999971e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around 0 84.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-53} \lor \neg \left(x \leq 5.4 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
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 98.0%

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

3. Taylor expanded in x around 0 77.6%

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

4. Taylor expanded in x around 0 38.7%

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))