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

Percentage Accurate: 97.9% → 100.0%

Time: 6.9s

Alternatives: 9

Speedup: 1.3×

• 21.6% 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: 97.9% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. distribute-lft-out-- 98.0%

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

   3. *-rgt-identity 98.0%

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

   4. cancel-sign-sub-inv 98.0%

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

   5. +-commutative 98.0%

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

   6. associate-+r+ 98.0%

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

   7. +-commutative 98.0%

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

   8. *-commutative 98.0%

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

   9. distribute-rgt-out 100.0%

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

   10. fma-define 100.0%

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

   11. +-commutative 100.0%

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

   12. unsub-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y - z, z\right) \]
6. Add Preprocessing

Alternative 2: 60.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+231}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+41} \lor \neg \left(x \leq 1.95 \cdot 10^{+76} \lor \neg \left(x \leq 7.5 \cdot 10^{+140}\right) \land \left(x \leq 1.3 \cdot 10^{+215} \lor \neg \left(x \leq 1.2 \cdot 10^{+278}\right) \land x \leq 2.5 \cdot 10^{+297}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -2.6e+231)
     (* x y)
     (if (<= x -1.05e+40)
       t_0
       (if (<= x -3e-109)
         (* x y)
         (if (<= x 6.2e-34)
           z
           (if (or (<= x 1.65e+41)
                   (not
                    (or (<= x 1.95e+76)
                        (and (not (<= x 7.5e+140))
                             (or (<= x 1.3e+215)
                                 (and (not (<= x 1.2e+278))
                                      (<= x 2.5e+297)))))))
             (* x y)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -2.6e+231) {
		tmp = x * y;
	} else if (x <= -1.05e+40) {
		tmp = t_0;
	} else if (x <= -3e-109) {
		tmp = x * y;
	} else if (x <= 6.2e-34) {
		tmp = z;
	} else if ((x <= 1.65e+41) || !((x <= 1.95e+76) || (!(x <= 7.5e+140) && ((x <= 1.3e+215) || (!(x <= 1.2e+278) && (x <= 2.5e+297)))))) {
		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 = x * -z
    if (x <= (-2.6d+231)) then
        tmp = x * y
    else if (x <= (-1.05d+40)) then
        tmp = t_0
    else if (x <= (-3d-109)) then
        tmp = x * y
    else if (x <= 6.2d-34) then
        tmp = z
    else if ((x <= 1.65d+41) .or. (.not. (x <= 1.95d+76) .or. (.not. (x <= 7.5d+140)) .and. (x <= 1.3d+215) .or. (.not. (x <= 1.2d+278)) .and. (x <= 2.5d+297))) 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 = x * -z;
	double tmp;
	if (x <= -2.6e+231) {
		tmp = x * y;
	} else if (x <= -1.05e+40) {
		tmp = t_0;
	} else if (x <= -3e-109) {
		tmp = x * y;
	} else if (x <= 6.2e-34) {
		tmp = z;
	} else if ((x <= 1.65e+41) || !((x <= 1.95e+76) || (!(x <= 7.5e+140) && ((x <= 1.3e+215) || (!(x <= 1.2e+278) && (x <= 2.5e+297)))))) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -2.6e+231:
		tmp = x * y
	elif x <= -1.05e+40:
		tmp = t_0
	elif x <= -3e-109:
		tmp = x * y
	elif x <= 6.2e-34:
		tmp = z
	elif (x <= 1.65e+41) or not ((x <= 1.95e+76) or (not (x <= 7.5e+140) and ((x <= 1.3e+215) or (not (x <= 1.2e+278) and (x <= 2.5e+297))))):
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (x <= -2.6e+231)
		tmp = Float64(x * y);
	elseif (x <= -1.05e+40)
		tmp = t_0;
	elseif (x <= -3e-109)
		tmp = Float64(x * y);
	elseif (x <= 6.2e-34)
		tmp = z;
	elseif ((x <= 1.65e+41) || !((x <= 1.95e+76) || (!(x <= 7.5e+140) && ((x <= 1.3e+215) || (!(x <= 1.2e+278) && (x <= 2.5e+297))))))
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (x <= -2.6e+231)
		tmp = x * y;
	elseif (x <= -1.05e+40)
		tmp = t_0;
	elseif (x <= -3e-109)
		tmp = x * y;
	elseif (x <= 6.2e-34)
		tmp = z;
	elseif ((x <= 1.65e+41) || ~(((x <= 1.95e+76) || (~((x <= 7.5e+140)) && ((x <= 1.3e+215) || (~((x <= 1.2e+278)) && (x <= 2.5e+297)))))))
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -2.6e+231], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.05e+40], t$95$0, If[LessEqual[x, -3e-109], N[(x * y), $MachinePrecision], If[LessEqual[x, 6.2e-34], z, If[Or[LessEqual[x, 1.65e+41], N[Not[Or[LessEqual[x, 1.95e+76], And[N[Not[LessEqual[x, 7.5e+140]], $MachinePrecision], Or[LessEqual[x, 1.3e+215], And[N[Not[LessEqual[x, 1.2e+278]], $MachinePrecision], LessEqual[x, 2.5e+297]]]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999999e231 or -1.05000000000000005e40 < x < -3.00000000000000021e-109 or 6.1999999999999996e-34 < x < 1.65e41 or 1.94999999999999995e76 < x < 7.4999999999999997e140 or 1.3e215 < x < 1.19999999999999992e278 or 2.4999999999999999e297 < x

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf 69.2%

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

   if -2.5999999999999999e231 < x < -1.05000000000000005e40 or 1.65e41 < x < 1.94999999999999995e76 or 7.4999999999999997e140 < x < 1.3e215 or 1.19999999999999992e278 < x < 2.4999999999999999e297

   1. Initial program 98.7%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   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. mul-1-neg 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 69.1%

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

      1. associate-*r* 69.1%

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

      2. mul-1-neg 69.1%

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

   8. Simplified 69.1%

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

   if -3.00000000000000021e-109 < x < 6.1999999999999996e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+231}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+41} \lor \neg \left(x \leq 1.95 \cdot 10^{+76} \lor \neg \left(x \leq 7.5 \cdot 10^{+140}\right) \land \left(x \leq 1.3 \cdot 10^{+215} \lor \neg \left(x \leq 1.2 \cdot 10^{+278}\right) \land x \leq 2.5 \cdot 10^{+297}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+230}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-41}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+76} \lor \neg \left(x \leq 3.1 \cdot 10^{+140}\right) \land \left(x \leq 1.5 \cdot 10^{+218} \lor \neg \left(x \leq 3.2 \cdot 10^{+281}\right) \land x \leq 3.8 \cdot 10^{+297}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -5.2e+230)
     (* x y)
     (if (<= x -1.1e+40)
       t_0
       (if (<= x -3e-109)
         (* x y)
         (if (<= x 7.2e-41)
           z
           (if (<= x 7.2e+36)
             (* x (+ y z))
             (if (or (<= x 8.8e+76)
                     (and (not (<= x 3.1e+140))
                          (or (<= x 1.5e+218)
                              (and (not (<= x 3.2e+281)) (<= x 3.8e+297)))))
               t_0
               (* x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -5.2e+230) {
		tmp = x * y;
	} else if (x <= -1.1e+40) {
		tmp = t_0;
	} else if (x <= -3e-109) {
		tmp = x * y;
	} else if (x <= 7.2e-41) {
		tmp = z;
	} else if (x <= 7.2e+36) {
		tmp = x * (y + z);
	} else if ((x <= 8.8e+76) || (!(x <= 3.1e+140) && ((x <= 1.5e+218) || (!(x <= 3.2e+281) && (x <= 3.8e+297))))) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (x <= (-5.2d+230)) then
        tmp = x * y
    else if (x <= (-1.1d+40)) then
        tmp = t_0
    else if (x <= (-3d-109)) then
        tmp = x * y
    else if (x <= 7.2d-41) then
        tmp = z
    else if (x <= 7.2d+36) then
        tmp = x * (y + z)
    else if ((x <= 8.8d+76) .or. (.not. (x <= 3.1d+140)) .and. (x <= 1.5d+218) .or. (.not. (x <= 3.2d+281)) .and. (x <= 3.8d+297)) then
        tmp = t_0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -5.2e+230) {
		tmp = x * y;
	} else if (x <= -1.1e+40) {
		tmp = t_0;
	} else if (x <= -3e-109) {
		tmp = x * y;
	} else if (x <= 7.2e-41) {
		tmp = z;
	} else if (x <= 7.2e+36) {
		tmp = x * (y + z);
	} else if ((x <= 8.8e+76) || (!(x <= 3.1e+140) && ((x <= 1.5e+218) || (!(x <= 3.2e+281) && (x <= 3.8e+297))))) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -5.2e+230:
		tmp = x * y
	elif x <= -1.1e+40:
		tmp = t_0
	elif x <= -3e-109:
		tmp = x * y
	elif x <= 7.2e-41:
		tmp = z
	elif x <= 7.2e+36:
		tmp = x * (y + z)
	elif (x <= 8.8e+76) or (not (x <= 3.1e+140) and ((x <= 1.5e+218) or (not (x <= 3.2e+281) and (x <= 3.8e+297)))):
		tmp = t_0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (x <= -5.2e+230)
		tmp = Float64(x * y);
	elseif (x <= -1.1e+40)
		tmp = t_0;
	elseif (x <= -3e-109)
		tmp = Float64(x * y);
	elseif (x <= 7.2e-41)
		tmp = z;
	elseif (x <= 7.2e+36)
		tmp = Float64(x * Float64(y + z));
	elseif ((x <= 8.8e+76) || (!(x <= 3.1e+140) && ((x <= 1.5e+218) || (!(x <= 3.2e+281) && (x <= 3.8e+297)))))
		tmp = t_0;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (x <= -5.2e+230)
		tmp = x * y;
	elseif (x <= -1.1e+40)
		tmp = t_0;
	elseif (x <= -3e-109)
		tmp = x * y;
	elseif (x <= 7.2e-41)
		tmp = z;
	elseif (x <= 7.2e+36)
		tmp = x * (y + z);
	elseif ((x <= 8.8e+76) || (~((x <= 3.1e+140)) && ((x <= 1.5e+218) || (~((x <= 3.2e+281)) && (x <= 3.8e+297)))))
		tmp = t_0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -5.2e+230], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.1e+40], t$95$0, If[LessEqual[x, -3e-109], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.2e-41], z, If[LessEqual[x, 7.2e+36], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8.8e+76], And[N[Not[LessEqual[x, 3.1e+140]], $MachinePrecision], Or[LessEqual[x, 1.5e+218], And[N[Not[LessEqual[x, 3.2e+281]], $MachinePrecision], LessEqual[x, 3.8e+297]]]]], t$95$0, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.1999999999999997e230 or -1.0999999999999999e40 < x < -3.00000000000000021e-109 or 8.8000000000000002e76 < x < 3.1e140 or 1.5e218 < x < 3.2000000000000001e281 or 3.7999999999999999e297 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 72.9%

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

   if -5.1999999999999997e230 < x < -1.0999999999999999e40 or 7.1999999999999995e36 < x < 8.8000000000000002e76 or 3.1e140 < x < 1.5e218 or 3.2000000000000001e281 < x < 3.7999999999999999e297

   1. Initial program 98.7%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   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. mul-1-neg 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 69.1%

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

      1. associate-*r* 69.1%

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

      2. mul-1-neg 69.1%

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

   8. Simplified 69.1%

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

   if -3.00000000000000021e-109 < x < 7.2e-41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

   if 7.2e-41 < x < 7.1999999999999995e36

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. sub-neg 66.1%

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

   5. Simplified 66.1%

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

      1. sub-neg 66.1%

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

      2. distribute-rgt-in 66.1%

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

      3. *-commutative 66.1%

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

      4. add-sqr-sqrt 66.1%

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

      5. sqrt-unprod 66.1%

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

      6. sqr-neg 66.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 57.6%

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

      9. cancel-sign-sub-inv 57.6%

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

      10. *-commutative 57.6%

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

      11. cancel-sign-sub 57.6%

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

   7. Applied egg-rr 57.6%

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

      1. +-commutative 57.6%

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

      2. distribute-lft-out 57.6%

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

   9. Simplified 57.6%

      \[\leadsto \color{blue}{x \cdot \left(z + y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+230}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-41}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+76} \lor \neg \left(x \leq 3.1 \cdot 10^{+140}\right) \land \left(x \leq 1.5 \cdot 10^{+218} \lor \neg \left(x \leq 3.2 \cdot 10^{+281}\right) \land x \leq 3.8 \cdot 10^{+297}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{-112} \lor \neg \left(x \leq 8.5 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.25e-112) (not (<= x 8.5e-33))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.25e-112) || !(x <= 8.5e-33)) {
		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 <= (-3.25d-112)) .or. (.not. (x <= 8.5d-33))) 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 <= -3.25e-112) || !(x <= 8.5e-33)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.25e-112) or not (x <= 8.5e-33):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.25e-112) || !(x <= 8.5e-33))
		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 <= -3.25e-112) || ~((x <= 8.5e-33)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.25e-112], N[Not[LessEqual[x, 8.5e-33]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -3.24999999999999978e-112 or 8.49999999999999945e-33 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 91.2%

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

      1. mul-1-neg 91.2%

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

      2. sub-neg 91.2%

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

   5. Simplified 91.2%

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

   if -3.24999999999999978e-112 < x < 8.49999999999999945e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{-112} \lor \neg \left(x \leq 8.5 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-109} \lor \neg \left(x \leq 280\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-109) (not (<= x 280.0))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-109) || !(x <= 280.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - 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 <= (-3d-109)) .or. (.not. (x <= 280.0d0))) then
        tmp = x * (y - z)
    else
        tmp = z * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-109) || !(x <= 280.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-109) or not (x <= 280.0):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-109) || !(x <= 280.0))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3e-109) || ~((x <= 280.0)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-109], N[Not[LessEqual[x, 280.0]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000021e-109 or 280 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 94.9%

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

      1. mul-1-neg 94.9%

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

      2. sub-neg 94.9%

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

   5. Simplified 94.9%

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

   if -3.00000000000000021e-109 < x < 280

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-109} \lor \neg \left(x \leq 280\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% 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 96.4%

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

   3. Taylor expanded in x around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. sub-neg 99.1%

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

   5. Simplified 99.1%

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

   if -1 < x < 1

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-rgt-neg-out 99.9%

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

      4. neg-sub0 99.9%

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

      5. neg-sub0 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-neg-in 99.9%

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

      8. remove-double-neg 99.9%

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

      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 98.1%

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

      1. mul-1-neg 98.1%

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

      2. distribute-rgt-neg-out 98.1%

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

   7. Simplified 98.1%

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

      1. sub-neg 98.1%

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

      2. +-commutative 98.1%

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

      3. distribute-rgt-neg-out 98.1%

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

      4. remove-double-neg 98.1%

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

   9. Applied egg-rr 98.1%

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

4. Final simplification 98.6%

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

Alternative 7: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-109} \lor \neg \left(x \leq 2.75 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-109) (not (<= x 2.75e-33))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-109) || !(x <= 2.75e-33)) {
		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 <= (-3d-109)) .or. (.not. (x <= 2.75d-33))) 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 <= -3e-109) || !(x <= 2.75e-33)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-109) or not (x <= 2.75e-33):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-109) || !(x <= 2.75e-33))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3e-109) || ~((x <= 2.75e-33)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-109], N[Not[LessEqual[x, 2.75e-33]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000021e-109 or 2.75e-33 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 51.9%

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

   if -3.00000000000000021e-109 < x < 2.75e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-109} \lor \neg \left(x \leq 2.75 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 98.0%

   \[x \cdot y + \left(1 - x\right) \cdot z \]
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. Final simplification 100.0%

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

Alternative 9: 35.3% 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 30.9%

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

4. Final simplification 30.9%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))