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

Percentage Accurate: 98.0% → 100.0%

Time: 4.2s

Alternatives: 6

Speedup: 1.3×

• 20.6% 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: 98.0% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. +-commutative 95.7%

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

   2. remove-double-neg 95.7%

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

   3. distribute-rgt-neg-out 95.7%

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

   4. neg-sub0 95.7%

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

   5. neg-sub0 95.7%

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

   6. *-commutative 95.7%

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

   7. distribute-lft-neg-in 95.7%

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

   8. remove-double-neg 95.7%

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

   9. distribute-rgt-out-- 95.7%

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

   10. *-lft-identity 95.7%

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

   11. associate-+l- 95.7%

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

   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. Final simplification 100.0%

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

Alternative 2: 59.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.46 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-89}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+31} \lor \neg \left(x \leq 1.85 \cdot 10^{+229}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -1.46e+75)
     t_0
     (if (<= x -1.6e-89)
       (* x y)
       (if (<= x 6e-179)
         z
         (if (<= x 7.5e-124)
           (* x y)
           (if (<= x 9.5e-44)
             z
             (if (or (<= x 1.02e+31) (not (<= x 1.85e+229)))
               (* x y)
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -1.46e+75) {
		tmp = t_0;
	} else if (x <= -1.6e-89) {
		tmp = x * y;
	} else if (x <= 6e-179) {
		tmp = z;
	} else if (x <= 7.5e-124) {
		tmp = x * y;
	} else if (x <= 9.5e-44) {
		tmp = z;
	} else if ((x <= 1.02e+31) || !(x <= 1.85e+229)) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (x <= (-1.46d+75)) then
        tmp = t_0
    else if (x <= (-1.6d-89)) then
        tmp = x * y
    else if (x <= 6d-179) then
        tmp = z
    else if (x <= 7.5d-124) then
        tmp = x * y
    else if (x <= 9.5d-44) then
        tmp = z
    else if ((x <= 1.02d+31) .or. (.not. (x <= 1.85d+229))) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -1.46e+75) {
		tmp = t_0;
	} else if (x <= -1.6e-89) {
		tmp = x * y;
	} else if (x <= 6e-179) {
		tmp = z;
	} else if (x <= 7.5e-124) {
		tmp = x * y;
	} else if (x <= 9.5e-44) {
		tmp = z;
	} else if ((x <= 1.02e+31) || !(x <= 1.85e+229)) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -1.46e+75:
		tmp = t_0
	elif x <= -1.6e-89:
		tmp = x * y
	elif x <= 6e-179:
		tmp = z
	elif x <= 7.5e-124:
		tmp = x * y
	elif x <= 9.5e-44:
		tmp = z
	elif (x <= 1.02e+31) or not (x <= 1.85e+229):
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (x <= -1.46e+75)
		tmp = t_0;
	elseif (x <= -1.6e-89)
		tmp = Float64(x * y);
	elseif (x <= 6e-179)
		tmp = z;
	elseif (x <= 7.5e-124)
		tmp = Float64(x * y);
	elseif (x <= 9.5e-44)
		tmp = z;
	elseif ((x <= 1.02e+31) || !(x <= 1.85e+229))
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (x <= -1.46e+75)
		tmp = t_0;
	elseif (x <= -1.6e-89)
		tmp = x * y;
	elseif (x <= 6e-179)
		tmp = z;
	elseif (x <= 7.5e-124)
		tmp = x * y;
	elseif (x <= 9.5e-44)
		tmp = z;
	elseif ((x <= 1.02e+31) || ~((x <= 1.85e+229)))
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[x, -1.46e+75], t$95$0, If[LessEqual[x, -1.6e-89], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-179], z, If[LessEqual[x, 7.5e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.5e-44], z, If[Or[LessEqual[x, 1.02e+31], N[Not[LessEqual[x, 1.85e+229]], $MachinePrecision]], N[(x * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4600000000000001e75 or 1.02000000000000007e31 < x < 1.85000000000000001e229

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. *-commutative 59.3%

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

      3. distribute-rgt-neg-in 59.3%

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

   8. Simplified 59.3%

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

   if -1.4600000000000001e75 < x < -1.59999999999999999e-89 or 6.00000000000000012e-179 < x < 7.4999999999999996e-124 or 9.49999999999999924e-44 < x < 1.02000000000000007e31 or 1.85000000000000001e229 < x

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 67.8%

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

   if -1.59999999999999999e-89 < x < 6.00000000000000012e-179 or 7.4999999999999996e-124 < x < 9.49999999999999924e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-89}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+31} \lor \neg \left(x \leq 1.85 \cdot 10^{+229}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{-90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -1.75e-90)
     t_0
     (if (<= x 6e-179)
       z
       (if (<= x 7.5e-124) (* x y) (if (<= x 1.4e-49) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -1.75e-90) {
		tmp = t_0;
	} else if (x <= 6e-179) {
		tmp = z;
	} else if (x <= 7.5e-124) {
		tmp = x * y;
	} else if (x <= 1.4e-49) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y - z)
    if (x <= (-1.75d-90)) then
        tmp = t_0
    else if (x <= 6d-179) then
        tmp = z
    else if (x <= 7.5d-124) then
        tmp = x * y
    else if (x <= 1.4d-49) then
        tmp = z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -1.75e-90) {
		tmp = t_0;
	} else if (x <= 6e-179) {
		tmp = z;
	} else if (x <= 7.5e-124) {
		tmp = x * y;
	} else if (x <= 1.4e-49) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -1.75e-90:
		tmp = t_0
	elif x <= 6e-179:
		tmp = z
	elif x <= 7.5e-124:
		tmp = x * y
	elif x <= 1.4e-49:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - z))
	tmp = 0.0
	if (x <= -1.75e-90)
		tmp = t_0;
	elseif (x <= 6e-179)
		tmp = z;
	elseif (x <= 7.5e-124)
		tmp = Float64(x * y);
	elseif (x <= 1.4e-49)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y - z);
	tmp = 0.0;
	if (x <= -1.75e-90)
		tmp = t_0;
	elseif (x <= 6e-179)
		tmp = z;
	elseif (x <= 7.5e-124)
		tmp = x * y;
	elseif (x <= 1.4e-49)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e-90], t$95$0, If[LessEqual[x, 6e-179], z, If[LessEqual[x, 7.5e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.4e-49], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7499999999999999e-90 or 1.39999999999999999e-49 < x

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 92.1%

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

      1. neg-mul-1 92.1%

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

      2. sub-neg 92.1%

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

   5. Simplified 92.1%

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

   if -1.7499999999999999e-90 < x < 6.00000000000000012e-179 or 7.4999999999999996e-124 < x < 1.39999999999999999e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

   if 6.00000000000000012e-179 < x < 7.4999999999999996e-124

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-91} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 8.5 \cdot 10^{-124}\right) \land x \leq 1.3 \cdot 10^{-45}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e-91)
         (not (or (<= x 6e-179) (and (not (<= x 8.5e-124)) (<= x 1.3e-45)))))
   (* x y)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e-91) || !((x <= 6e-179) || (!(x <= 8.5e-124) && (x <= 1.3e-45)))) {
		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 <= (-1.45d-91)) .or. (.not. (x <= 6d-179) .or. (.not. (x <= 8.5d-124)) .and. (x <= 1.3d-45))) 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 <= -1.45e-91) || !((x <= 6e-179) || (!(x <= 8.5e-124) && (x <= 1.3e-45)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45e-91) or not ((x <= 6e-179) or (not (x <= 8.5e-124) and (x <= 1.3e-45))):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e-91) || !((x <= 6e-179) || (!(x <= 8.5e-124) && (x <= 1.3e-45))))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45e-91) || ~(((x <= 6e-179) || (~((x <= 8.5e-124)) && (x <= 1.3e-45)))))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e-91], N[Not[Or[LessEqual[x, 6e-179], And[N[Not[LessEqual[x, 8.5e-124]], $MachinePrecision], LessEqual[x, 1.3e-45]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e-91 or 6.00000000000000012e-179 < x < 8.5000000000000002e-124 or 1.29999999999999993e-45 < x

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 56.3%

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

   if -1.45e-91 < x < 6.00000000000000012e-179 or 8.5000000000000002e-124 < x < 1.29999999999999993e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-91} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 8.5 \cdot 10^{-124}\right) \land x \leq 1.3 \cdot 10^{-45}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 1 < x

   1. Initial program 91.2%

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

   3. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.6%

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

      2. sub-neg 98.6%

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

   5. Simplified 98.6%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. neg-sub0 100.0%

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

      5. neg-sub0 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-+l- 100.0%

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

      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. 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. associate-*r* 98.0%

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

      2. neg-mul-1 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 98.3%

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

Alternative 6: 37.1% 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 95.7%

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

3. Taylor expanded in x around 0 33.1%

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

4. Final simplification 33.1%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))