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

Percentage Accurate: 98.0% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.3×

• 20.7% 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 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: 58.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+139}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+82} \lor \neg \left(x \leq 3.5 \cdot 10^{+144}\right) \land x \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -9.2e+176)
     (* x y)
     (if (<= x -2.7e+139)
       t_0
       (if (<= x -7e+14)
         (* x y)
         (if (<= x 1.8e-152)
           z
           (if (or (<= x 1.25e+82) (and (not (<= x 3.5e+144)) (<= x 2.3e+179)))
             (* x y)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -9.2e+176) {
		tmp = x * y;
	} else if (x <= -2.7e+139) {
		tmp = t_0;
	} else if (x <= -7e+14) {
		tmp = x * y;
	} else if (x <= 1.8e-152) {
		tmp = z;
	} else if ((x <= 1.25e+82) || (!(x <= 3.5e+144) && (x <= 2.3e+179))) {
		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 <= (-9.2d+176)) then
        tmp = x * y
    else if (x <= (-2.7d+139)) then
        tmp = t_0
    else if (x <= (-7d+14)) then
        tmp = x * y
    else if (x <= 1.8d-152) then
        tmp = z
    else if ((x <= 1.25d+82) .or. (.not. (x <= 3.5d+144)) .and. (x <= 2.3d+179)) 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 <= -9.2e+176) {
		tmp = x * y;
	} else if (x <= -2.7e+139) {
		tmp = t_0;
	} else if (x <= -7e+14) {
		tmp = x * y;
	} else if (x <= 1.8e-152) {
		tmp = z;
	} else if ((x <= 1.25e+82) || (!(x <= 3.5e+144) && (x <= 2.3e+179))) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -9.2e+176:
		tmp = x * y
	elif x <= -2.7e+139:
		tmp = t_0
	elif x <= -7e+14:
		tmp = x * y
	elif x <= 1.8e-152:
		tmp = z
	elif (x <= 1.25e+82) or (not (x <= 3.5e+144) and (x <= 2.3e+179)):
		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 <= -9.2e+176)
		tmp = Float64(x * y);
	elseif (x <= -2.7e+139)
		tmp = t_0;
	elseif (x <= -7e+14)
		tmp = Float64(x * y);
	elseif (x <= 1.8e-152)
		tmp = z;
	elseif ((x <= 1.25e+82) || (!(x <= 3.5e+144) && (x <= 2.3e+179)))
		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 <= -9.2e+176)
		tmp = x * y;
	elseif (x <= -2.7e+139)
		tmp = t_0;
	elseif (x <= -7e+14)
		tmp = x * y;
	elseif (x <= 1.8e-152)
		tmp = z;
	elseif ((x <= 1.25e+82) || (~((x <= 3.5e+144)) && (x <= 2.3e+179)))
		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, -9.2e+176], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.7e+139], t$95$0, If[LessEqual[x, -7e+14], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.8e-152], z, If[Or[LessEqual[x, 1.25e+82], And[N[Not[LessEqual[x, 3.5e+144]], $MachinePrecision], LessEqual[x, 2.3e+179]]], N[(x * y), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999984e176 or -2.6999999999999998e139 < x < -7e14 or 1.8e-152 < x < 1.25000000000000004e82 or 3.4999999999999998e144 < x < 2.29999999999999994e179

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf 63.8%

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

   if -9.19999999999999984e176 < x < -2.6999999999999998e139 or 1.25000000000000004e82 < x < 3.4999999999999998e144 or 2.29999999999999994e179 < 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 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 72.0%

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

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

      3. *-commutative 72.0%

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

   8. Simplified 72.0%

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

   if -7e14 < x < 1.8e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+82} \lor \neg \left(x \leq 3.5 \cdot 10^{+144}\right) \land x \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -6.6e-15)
     t_0
     (if (<= x 1.8e-152)
       z
       (if (<= x 2.5e-88) (* x y) (if (<= x 7.2e-24) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -6.6e-15) {
		tmp = t_0;
	} else if (x <= 1.8e-152) {
		tmp = z;
	} else if (x <= 2.5e-88) {
		tmp = x * y;
	} else if (x <= 7.2e-24) {
		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 <= (-6.6d-15)) then
        tmp = t_0
    else if (x <= 1.8d-152) then
        tmp = z
    else if (x <= 2.5d-88) then
        tmp = x * y
    else if (x <= 7.2d-24) 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 <= -6.6e-15) {
		tmp = t_0;
	} else if (x <= 1.8e-152) {
		tmp = z;
	} else if (x <= 2.5e-88) {
		tmp = x * y;
	} else if (x <= 7.2e-24) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -6.6e-15:
		tmp = t_0
	elif x <= 1.8e-152:
		tmp = z
	elif x <= 2.5e-88:
		tmp = x * y
	elif x <= 7.2e-24:
		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 <= -6.6e-15)
		tmp = t_0;
	elseif (x <= 1.8e-152)
		tmp = z;
	elseif (x <= 2.5e-88)
		tmp = Float64(x * y);
	elseif (x <= 7.2e-24)
		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 <= -6.6e-15)
		tmp = t_0;
	elseif (x <= 1.8e-152)
		tmp = z;
	elseif (x <= 2.5e-88)
		tmp = x * y;
	elseif (x <= 7.2e-24)
		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, -6.6e-15], t$95$0, If[LessEqual[x, 1.8e-152], z, If[LessEqual[x, 2.5e-88], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.2e-24], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.6e-15 or 7.2000000000000002e-24 < x

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 95.2%

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

      1. mul-1-neg 95.2%

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

      2. sub-neg 95.2%

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

   5. Simplified 95.2%

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

   if -6.6e-15 < x < 1.8e-152 or 2.50000000000000004e-88 < x < 7.2000000000000002e-24

   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 1.8e-152 < x < 2.50000000000000004e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-23}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -7e+14)
     t_0
     (if (<= x 1.8e-152)
       (* z (- 1.0 x))
       (if (<= x 3.2e-88) (* x y) (if (<= x 1.5e-23) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 1.8e-152) {
		tmp = z * (1.0 - x);
	} else if (x <= 3.2e-88) {
		tmp = x * y;
	} else if (x <= 1.5e-23) {
		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 <= (-7d+14)) then
        tmp = t_0
    else if (x <= 1.8d-152) then
        tmp = z * (1.0d0 - x)
    else if (x <= 3.2d-88) then
        tmp = x * y
    else if (x <= 1.5d-23) 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 <= -7e+14) {
		tmp = t_0;
	} else if (x <= 1.8e-152) {
		tmp = z * (1.0 - x);
	} else if (x <= 3.2e-88) {
		tmp = x * y;
	} else if (x <= 1.5e-23) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -7e+14:
		tmp = t_0
	elif x <= 1.8e-152:
		tmp = z * (1.0 - x)
	elif x <= 3.2e-88:
		tmp = x * y
	elif x <= 1.5e-23:
		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 <= -7e+14)
		tmp = t_0;
	elseif (x <= 1.8e-152)
		tmp = Float64(z * Float64(1.0 - x));
	elseif (x <= 3.2e-88)
		tmp = Float64(x * y);
	elseif (x <= 1.5e-23)
		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 <= -7e+14)
		tmp = t_0;
	elseif (x <= 1.8e-152)
		tmp = z * (1.0 - x);
	elseif (x <= 3.2e-88)
		tmp = x * y;
	elseif (x <= 1.5e-23)
		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, -7e+14], t$95$0, If[LessEqual[x, 1.8e-152], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-88], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.5e-23], z, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e14 or 1.50000000000000001e-23 < 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 96.9%

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

      1. mul-1-neg 96.9%

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

      2. sub-neg 96.9%

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

   5. Simplified 96.9%

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

   if -7e14 < x < 1.8e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.7%

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

   if 1.8e-152 < x < 3.20000000000000012e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.5%

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

   if 3.20000000000000012e-88 < x < 1.50000000000000001e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.9%

      \[\leadsto \color{blue}{z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-23}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 97.7%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. sub-neg 98.9%

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

   5. Simplified 98.9%

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

   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. *-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 97.9%

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

      1. mul-1-neg 97.9%

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

      2. distribute-rgt-neg-out 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 98.4%

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

Alternative 6: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 1.7 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+14) (not (<= x 1.7e-152))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 1.7e-152)) {
		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 <= (-7d+14)) .or. (.not. (x <= 1.7d-152))) 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 <= -7e+14) || !(x <= 1.7e-152)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+14) or not (x <= 1.7e-152):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+14) || !(x <= 1.7e-152))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+14) || ~((x <= 1.7e-152)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+14], N[Not[LessEqual[x, 1.7e-152]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -7e14 or 1.69999999999999992e-152 < 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 54.1%

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

   if -7e14 < x < 1.69999999999999992e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 1.7 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.8% 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 35.1%

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

4. Final simplification 35.1%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))