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

Percentage Accurate: 97.7% → 100.0%

Time: 3.7s

Alternatives: 7

Speedup: 1.3×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 97.7% 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 97.7%

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

   1. +-commutative 97.7%

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

   2. remove-double-neg 97.7%

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

   3. distribute-rgt-neg-out 97.7%

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

   4. neg-sub0 97.7%

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

   5. neg-sub0 97.7%

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

   6. *-commutative 97.7%

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

   7. distribute-lft-neg-in 97.7%

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

   8. remove-double-neg 97.7%

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

   9. distribute-rgt-out-- 97.6%

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

   10. *-lft-identity 97.6%

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

   11. associate-+l- 97.6%

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

   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: 55.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+205}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.47:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -2.7e+205)
     t_0
     (if (<= z -1.95e+170)
       z
       (if (<= z -5e+142)
         t_0
         (if (<= z -0.47) z (if (<= z 0.00017) (* x y) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -2.7e+205) {
		tmp = t_0;
	} else if (z <= -1.95e+170) {
		tmp = z;
	} else if (z <= -5e+142) {
		tmp = t_0;
	} else if (z <= -0.47) {
		tmp = z;
	} else if (z <= 0.00017) {
		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) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-2.7d+205)) then
        tmp = t_0
    else if (z <= (-1.95d+170)) then
        tmp = z
    else if (z <= (-5d+142)) then
        tmp = t_0
    else if (z <= (-0.47d0)) then
        tmp = z
    else if (z <= 0.00017d0) 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 t_0 = z * -x;
	double tmp;
	if (z <= -2.7e+205) {
		tmp = t_0;
	} else if (z <= -1.95e+170) {
		tmp = z;
	} else if (z <= -5e+142) {
		tmp = t_0;
	} else if (z <= -0.47) {
		tmp = z;
	} else if (z <= 0.00017) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -2.7e+205:
		tmp = t_0
	elif z <= -1.95e+170:
		tmp = z
	elif z <= -5e+142:
		tmp = t_0
	elif z <= -0.47:
		tmp = z
	elif z <= 0.00017:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -2.7e+205)
		tmp = t_0;
	elseif (z <= -1.95e+170)
		tmp = z;
	elseif (z <= -5e+142)
		tmp = t_0;
	elseif (z <= -0.47)
		tmp = z;
	elseif (z <= 0.00017)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -2.7e+205)
		tmp = t_0;
	elseif (z <= -1.95e+170)
		tmp = z;
	elseif (z <= -5e+142)
		tmp = t_0;
	elseif (z <= -0.47)
		tmp = z;
	elseif (z <= 0.00017)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -2.7e+205], t$95$0, If[LessEqual[z, -1.95e+170], z, If[LessEqual[z, -5e+142], t$95$0, If[LessEqual[z, -0.47], z, If[LessEqual[z, 0.00017], N[(x * y), $MachinePrecision], z]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000012e205 or -1.9500000000000001e170 < z < -5.0000000000000001e142

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 72.4%

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

      1. neg-mul-1 72.4%

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

      2. sub-neg 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. distribute-rgt-neg-out 72.4%

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

   8. Simplified 72.4%

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

   if -2.70000000000000012e205 < z < -1.9500000000000001e170 or -5.0000000000000001e142 < z < -0.46999999999999997 or 1.7e-4 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 57.0%

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

   if -0.46999999999999997 < z < 1.7e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+142}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -0.47:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{-83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-178}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -2e-83)
     t_0
     (if (<= x 1.22e-178)
       z
       (if (<= x 9e-124) (* x y) (if (<= x 2.5e-35) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -2e-83) {
		tmp = t_0;
	} else if (x <= 1.22e-178) {
		tmp = z;
	} else if (x <= 9e-124) {
		tmp = x * y;
	} else if (x <= 2.5e-35) {
		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 <= (-2d-83)) then
        tmp = t_0
    else if (x <= 1.22d-178) then
        tmp = z
    else if (x <= 9d-124) then
        tmp = x * y
    else if (x <= 2.5d-35) 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 <= -2e-83) {
		tmp = t_0;
	} else if (x <= 1.22e-178) {
		tmp = z;
	} else if (x <= 9e-124) {
		tmp = x * y;
	} else if (x <= 2.5e-35) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -2e-83:
		tmp = t_0
	elif x <= 1.22e-178:
		tmp = z
	elif x <= 9e-124:
		tmp = x * y
	elif x <= 2.5e-35:
		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 <= -2e-83)
		tmp = t_0;
	elseif (x <= 1.22e-178)
		tmp = z;
	elseif (x <= 9e-124)
		tmp = Float64(x * y);
	elseif (x <= 2.5e-35)
		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 <= -2e-83)
		tmp = t_0;
	elseif (x <= 1.22e-178)
		tmp = z;
	elseif (x <= 9e-124)
		tmp = x * y;
	elseif (x <= 2.5e-35)
		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, -2e-83], t$95$0, If[LessEqual[x, 1.22e-178], z, If[LessEqual[x, 9e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.5e-35], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0000000000000001e-83 or 2.49999999999999982e-35 < x

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 92.7%

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

      1. neg-mul-1 92.7%

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

      2. sub-neg 92.7%

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

   5. Simplified 92.7%

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

   if -2.0000000000000001e-83 < x < 1.21999999999999999e-178 or 8.9999999999999992e-124 < x < 2.49999999999999982e-35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.4%

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

   if 1.21999999999999999e-178 < x < 8.9999999999999992e-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 73.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-178}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-84} \lor \neg \left(x \leq 1.22 \cdot 10^{-178} \lor \neg \left(x \leq 3 \cdot 10^{-125}\right) \land x \leq 1.95 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.3e-84)
         (not (or (<= x 1.22e-178) (and (not (<= x 3e-125)) (<= x 1.95e-36)))))
   (* x y)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.3e-84) || !((x <= 1.22e-178) || (!(x <= 3e-125) && (x <= 1.95e-36)))) {
		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 <= (-7.3d-84)) .or. (.not. (x <= 1.22d-178) .or. (.not. (x <= 3d-125)) .and. (x <= 1.95d-36))) 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 <= -7.3e-84) || !((x <= 1.22e-178) || (!(x <= 3e-125) && (x <= 1.95e-36)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.3e-84) or not ((x <= 1.22e-178) or (not (x <= 3e-125) and (x <= 1.95e-36))):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.3e-84) || !((x <= 1.22e-178) || (!(x <= 3e-125) && (x <= 1.95e-36))))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.3e-84) || ~(((x <= 1.22e-178) || (~((x <= 3e-125)) && (x <= 1.95e-36)))))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.3e-84], N[Not[Or[LessEqual[x, 1.22e-178], And[N[Not[LessEqual[x, 3e-125]], $MachinePrecision], LessEqual[x, 1.95e-36]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -7.3000000000000004e-84 or 1.21999999999999999e-178 < x < 2.9999999999999999e-125 or 1.95e-36 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf 58.4%

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

   if -7.3000000000000004e-84 < x < 1.21999999999999999e-178 or 2.9999999999999999e-125 < x < 1.95e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-84} \lor \neg \left(x \leq 1.22 \cdot 10^{-178} \lor \neg \left(x \leq 3 \cdot 10^{-125}\right) \land x \leq 1.95 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.42 \lor \neg \left(z \leq 3.7\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.42) (not (<= z 3.7))) (* z (- 1.0 x)) (* x (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.42) || !(z <= 3.7)) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * (y - 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 ((z <= (-0.42d0)) .or. (.not. (z <= 3.7d0))) then
        tmp = z * (1.0d0 - x)
    else
        tmp = x * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.42) || !(z <= 3.7)) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.42) or not (z <= 3.7):
		tmp = z * (1.0 - x)
	else:
		tmp = x * (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.42) || !(z <= 3.7))
		tmp = Float64(z * Float64(1.0 - x));
	else
		tmp = Float64(x * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.42) || ~((z <= 3.7)))
		tmp = z * (1.0 - x);
	else
		tmp = x * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.42], N[Not[LessEqual[z, 3.7]], $MachinePrecision]], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.419999999999999984 or 3.7000000000000002 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 87.4%

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

   if -0.419999999999999984 < z < 3.7000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.2%

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

      1. neg-mul-1 80.2%

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

      2. sub-neg 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.42 \lor \neg \left(z \leq 3.7\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -82000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -82000000.0) (not (<= x 1.0))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -82000000.0) || !(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 <= (-82000000.0d0)) .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 <= -82000000.0) || !(x <= 1.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -82000000.0) 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 <= -82000000.0) || !(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 <= -82000000.0) || ~((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, -82000000.0], 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 < -8.2e7 or 1 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.3%

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

      2. sub-neg 98.3%

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

   5. Simplified 98.3%

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

   if -8.2e7 < 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 99.4%

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

      1. associate-*r* 99.4%

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

      2. neg-mul-1 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -82000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 97.7%

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

3. Taylor expanded in x around 0 35.6%

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

4. Final simplification 35.6%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))