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

Percentage Accurate: 97.8% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.3×

• 20.2% 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: 97.8% 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 98.8%

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

   1. +-commutative 98.8%

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

   2. *-commutative 98.8%

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

   3. distribute-rgt-out-- 98.8%

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

   4. *-lft-identity 98.8%

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

   5. associate-+l- 98.8%

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

   6. 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: 58.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+159}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1860:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-79}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-58}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+107} \lor \neg \left(x \leq 1.25 \cdot 10^{+137}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -1.15e+159)
     t_0
     (if (<= x -1860.0)
       (* x y)
       (if (<= x -1.2e-79)
         z
         (if (<= x -1.2e-140)
           (* x y)
           (if (<= x 4.2e-58)
             z
             (if (or (<= x 1.42e+107) (not (<= x 1.25e+137)))
               (* x y)
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -1.15e+159) {
		tmp = t_0;
	} else if (x <= -1860.0) {
		tmp = x * y;
	} else if (x <= -1.2e-79) {
		tmp = z;
	} else if (x <= -1.2e-140) {
		tmp = x * y;
	} else if (x <= 4.2e-58) {
		tmp = z;
	} else if ((x <= 1.42e+107) || !(x <= 1.25e+137)) {
		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 <= (-1.15d+159)) then
        tmp = t_0
    else if (x <= (-1860.0d0)) then
        tmp = x * y
    else if (x <= (-1.2d-79)) then
        tmp = z
    else if (x <= (-1.2d-140)) then
        tmp = x * y
    else if (x <= 4.2d-58) then
        tmp = z
    else if ((x <= 1.42d+107) .or. (.not. (x <= 1.25d+137))) 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 <= -1.15e+159) {
		tmp = t_0;
	} else if (x <= -1860.0) {
		tmp = x * y;
	} else if (x <= -1.2e-79) {
		tmp = z;
	} else if (x <= -1.2e-140) {
		tmp = x * y;
	} else if (x <= 4.2e-58) {
		tmp = z;
	} else if ((x <= 1.42e+107) || !(x <= 1.25e+137)) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -1.15e+159:
		tmp = t_0
	elif x <= -1860.0:
		tmp = x * y
	elif x <= -1.2e-79:
		tmp = z
	elif x <= -1.2e-140:
		tmp = x * y
	elif x <= 4.2e-58:
		tmp = z
	elif (x <= 1.42e+107) or not (x <= 1.25e+137):
		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 <= -1.15e+159)
		tmp = t_0;
	elseif (x <= -1860.0)
		tmp = Float64(x * y);
	elseif (x <= -1.2e-79)
		tmp = z;
	elseif (x <= -1.2e-140)
		tmp = Float64(x * y);
	elseif (x <= 4.2e-58)
		tmp = z;
	elseif ((x <= 1.42e+107) || !(x <= 1.25e+137))
		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 <= -1.15e+159)
		tmp = t_0;
	elseif (x <= -1860.0)
		tmp = x * y;
	elseif (x <= -1.2e-79)
		tmp = z;
	elseif (x <= -1.2e-140)
		tmp = x * y;
	elseif (x <= 4.2e-58)
		tmp = z;
	elseif ((x <= 1.42e+107) || ~((x <= 1.25e+137)))
		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, -1.15e+159], t$95$0, If[LessEqual[x, -1860.0], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.2e-79], z, If[LessEqual[x, -1.2e-140], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.2e-58], z, If[Or[LessEqual[x, 1.42e+107], N[Not[LessEqual[x, 1.25e+137]], $MachinePrecision]], N[(x * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.14999999999999998e159 or 1.42000000000000006e107 < x < 1.25e137

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   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. unsub-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 75.6%

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

      1. associate-*r* 75.6%

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

      2. mul-1-neg 75.6%

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

   8. Simplified 75.6%

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

   if -1.14999999999999998e159 < x < -1860 or -1.20000000000000003e-79 < x < -1.19999999999999993e-140 or 4.19999999999999975e-58 < x < 1.42000000000000006e107 or 1.25e137 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf 67.1%

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

   if -1860 < x < -1.20000000000000003e-79 or -1.19999999999999993e-140 < x < 4.19999999999999975e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+159}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1860:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-79}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-58}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+107} \lor \neg \left(x \leq 1.25 \cdot 10^{+137}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-9} \lor \neg \left(x \leq -1.45 \cdot 10^{-79} \lor \neg \left(x \leq -1.2 \cdot 10^{-140}\right) \land x \leq 1.22 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-9)
         (not
          (or (<= x -1.45e-79) (and (not (<= x -1.2e-140)) (<= x 1.22e-32)))))
   (* x (- y z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-9) || !((x <= -1.45e-79) || (!(x <= -1.2e-140) && (x <= 1.22e-32)))) {
		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 <= (-1.5d-9)) .or. (.not. (x <= (-1.45d-79)) .or. (.not. (x <= (-1.2d-140))) .and. (x <= 1.22d-32))) 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 <= -1.5e-9) || !((x <= -1.45e-79) || (!(x <= -1.2e-140) && (x <= 1.22e-32)))) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-9) or not ((x <= -1.45e-79) or (not (x <= -1.2e-140) and (x <= 1.22e-32))):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-9) || !((x <= -1.45e-79) || (!(x <= -1.2e-140) && (x <= 1.22e-32))))
		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 <= -1.5e-9) || ~(((x <= -1.45e-79) || (~((x <= -1.2e-140)) && (x <= 1.22e-32)))))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-9], N[Not[Or[LessEqual[x, -1.45e-79], And[N[Not[LessEqual[x, -1.2e-140]], $MachinePrecision], LessEqual[x, 1.22e-32]]]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999999e-9 or -1.45e-79 < x < -1.19999999999999993e-140 or 1.22e-32 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 96.4%

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

      1. neg-mul-1 96.4%

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

      2. unsub-neg 96.4%

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

   5. Simplified 96.4%

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

   if -1.49999999999999999e-9 < x < -1.45e-79 or -1.19999999999999993e-140 < x < 1.22e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.7%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-9} \lor \neg \left(x \leq -1.45 \cdot 10^{-79} \lor \neg \left(x \leq -1.2 \cdot 10^{-140}\right) \land x \leq 1.22 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12000 \lor \neg \left(x \leq -2 \cdot 10^{-79}\right) \land \left(x \leq -1.2 \cdot 10^{-140} \lor \neg \left(x \leq 1.8 \cdot 10^{-26}\right)\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -12000.0)
         (and (not (<= x -2e-79)) (or (<= x -1.2e-140) (not (<= x 1.8e-26)))))
   (* x (- y z))
   (- z (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -12000.0) || (!(x <= -2e-79) && ((x <= -1.2e-140) || !(x <= 1.8e-26)))) {
		tmp = x * (y - z);
	} else {
		tmp = z - (z * 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 ((x <= (-12000.0d0)) .or. (.not. (x <= (-2d-79))) .and. (x <= (-1.2d-140)) .or. (.not. (x <= 1.8d-26))) then
        tmp = x * (y - z)
    else
        tmp = z - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -12000.0) || (!(x <= -2e-79) && ((x <= -1.2e-140) || !(x <= 1.8e-26)))) {
		tmp = x * (y - z);
	} else {
		tmp = z - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -12000.0) or (not (x <= -2e-79) and ((x <= -1.2e-140) or not (x <= 1.8e-26))):
		tmp = x * (y - z)
	else:
		tmp = z - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -12000.0) || (!(x <= -2e-79) && ((x <= -1.2e-140) || !(x <= 1.8e-26))))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -12000.0) || (~((x <= -2e-79)) && ((x <= -1.2e-140) || ~((x <= 1.8e-26)))))
		tmp = x * (y - z);
	else
		tmp = z - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -12000.0], And[N[Not[LessEqual[x, -2e-79]], $MachinePrecision], Or[LessEqual[x, -1.2e-140], N[Not[LessEqual[x, 1.8e-26]], $MachinePrecision]]]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -12000 or -2e-79 < x < -1.19999999999999993e-140 or 1.8000000000000001e-26 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 96.8%

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

      1. neg-mul-1 96.8%

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

      2. unsub-neg 96.8%

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

   5. Simplified 96.8%

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

   if -12000 < x < -2e-79 or -1.19999999999999993e-140 < x < 1.8000000000000001e-26

   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. *-commutative 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l- 100.0%

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

      6. 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 inf 83.5%

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

      1. *-commutative 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12000 \lor \neg \left(x \leq -2 \cdot 10^{-79}\right) \land \left(x \leq -1.2 \cdot 10^{-140} \lor \neg \left(x \leq 1.8 \cdot 10^{-26}\right)\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1860 \lor \neg \left(x \leq -2.4 \cdot 10^{-78}\right) \land \left(x \leq -1.2 \cdot 10^{-140} \lor \neg \left(x \leq 5.5 \cdot 10^{-58}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1860.0)
         (and (not (<= x -2.4e-78))
              (or (<= x -1.2e-140) (not (<= x 5.5e-58)))))
   (* x y)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1860.0) || (!(x <= -2.4e-78) && ((x <= -1.2e-140) || !(x <= 5.5e-58)))) {
		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 <= (-1860.0d0)) .or. (.not. (x <= (-2.4d-78))) .and. (x <= (-1.2d-140)) .or. (.not. (x <= 5.5d-58))) 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 <= -1860.0) || (!(x <= -2.4e-78) && ((x <= -1.2e-140) || !(x <= 5.5e-58)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1860.0) or (not (x <= -2.4e-78) and ((x <= -1.2e-140) or not (x <= 5.5e-58))):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1860.0) || (!(x <= -2.4e-78) && ((x <= -1.2e-140) || !(x <= 5.5e-58))))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1860.0) || (~((x <= -2.4e-78)) && ((x <= -1.2e-140) || ~((x <= 5.5e-58)))))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1860.0], And[N[Not[LessEqual[x, -2.4e-78]], $MachinePrecision], Or[LessEqual[x, -1.2e-140], N[Not[LessEqual[x, 5.5e-58]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1860 or -2.4e-78 < x < -1.19999999999999993e-140 or 5.49999999999999996e-58 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in y around inf 58.1%

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

   if -1860 < x < -2.4e-78 or -1.19999999999999993e-140 < x < 5.49999999999999996e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1860 \lor \neg \left(x \leq -2.4 \cdot 10^{-78}\right) \land \left(x \leq -1.2 \cdot 10^{-140} \lor \neg \left(x \leq 5.5 \cdot 10^{-58}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.66\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.66))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.66)) {
		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 <= 0.66d0))) 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 <= 0.66)) {
		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 <= 0.66):
		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 <= 0.66))
		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 <= 0.66)))
		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, 0.66]], $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 0.660000000000000031 < x

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 99.3%

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

      1. neg-mul-1 99.3%

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

      2. unsub-neg 99.3%

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

   5. Simplified 99.3%

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

   if -1 < x < 0.660000000000000031

   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. *-commutative 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l- 100.0%

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

      6. 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 99.0%

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

      1. associate-*r* 99.0%

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

      2. neg-mul-1 99.0%

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

      3. *-commutative 99.0%

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

   7. Simplified 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.66\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.9% 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 98.8%

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

3. Taylor expanded in x around 0 34.2%

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

4. Final simplification 34.2%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))