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

Percentage Accurate: 97.8% → 100.0%

Time: 3.3s

Alternatives: 6

Speedup: 1.3×

• 21.7% 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: 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 97.3%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 100.0%

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

   1. neg-mul-1 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - z\right) \]

Alternative 2: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -5.5e+140)
     (* x y)
     (if (<= x -2.05e+30)
       t_0
       (if (<= x -3.8e-112) (* x y) (if (<= x 1.0) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -5.5e+140) {
		tmp = x * y;
	} else if (x <= -2.05e+30) {
		tmp = t_0;
	} else if (x <= -3.8e-112) {
		tmp = x * y;
	} else if (x <= 1.0) {
		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 = z * -x
    if (x <= (-5.5d+140)) then
        tmp = x * y
    else if (x <= (-2.05d+30)) then
        tmp = t_0
    else if (x <= (-3.8d-112)) then
        tmp = x * y
    else if (x <= 1.0d0) 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 = z * -x;
	double tmp;
	if (x <= -5.5e+140) {
		tmp = x * y;
	} else if (x <= -2.05e+30) {
		tmp = t_0;
	} else if (x <= -3.8e-112) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -5.5e+140:
		tmp = x * y
	elif x <= -2.05e+30:
		tmp = t_0
	elif x <= -3.8e-112:
		tmp = x * y
	elif x <= 1.0:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (x <= -5.5e+140)
		tmp = Float64(x * y);
	elseif (x <= -2.05e+30)
		tmp = t_0;
	elseif (x <= -3.8e-112)
		tmp = Float64(x * y);
	elseif (x <= 1.0)
		tmp = z;
	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 <= -5.5e+140)
		tmp = x * y;
	elseif (x <= -2.05e+30)
		tmp = t_0;
	elseif (x <= -3.8e-112)
		tmp = x * y;
	elseif (x <= 1.0)
		tmp = z;
	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, -5.5e+140], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.05e+30], t$95$0, If[LessEqual[x, -3.8e-112], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.0], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5e140 or -2.05000000000000003e30 < x < -3.79999999999999995e-112

   1. Initial program 92.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 70.8%

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

   if -5.5e140 < x < -2.05000000000000003e30 or 1 < x

   1. Initial program 96.9%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 99.2%

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

      1. neg-mul-1 99.2%

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

      2. unsub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. distribute-lft-neg-out 62.6%

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

      3. *-commutative 62.6%

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

   7. Simplified 62.6%

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

   if -3.79999999999999995e-112 < x < 1

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-112} \lor \neg \left(x \leq 7.5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-112) (not (<= x 7.5e-9))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-112) || !(x <= 7.5e-9)) {
		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 <= (-3.8d-112)) .or. (.not. (x <= 7.5d-9))) 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 <= -3.8e-112) || !(x <= 7.5e-9)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-112) or not (x <= 7.5e-9):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-112) || !(x <= 7.5e-9))
		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 <= -3.8e-112) || ~((x <= 7.5e-9)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-112], N[Not[LessEqual[x, 7.5e-9]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999995e-112 or 7.49999999999999933e-9 < x

   1. Initial program 95.2%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 95.1%

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

      1. neg-mul-1 95.1%

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

      2. unsub-neg 95.1%

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

   4. Simplified 95.1%

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

   if -3.79999999999999995e-112 < x < 7.49999999999999933e-9

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-112} \lor \neg \left(x \leq 7.5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-112} \lor \neg \left(x \leq 58000\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e-112) (not (<= x 58000.0))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-112) || !(x <= 58000.0)) {
		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 <= (-3.5d-112)) .or. (.not. (x <= 58000.0d0))) 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 <= -3.5e-112) || !(x <= 58000.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e-112) or not (x <= 58000.0):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e-112) || !(x <= 58000.0))
		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 <= -3.5e-112) || ~((x <= 58000.0)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-112], N[Not[LessEqual[x, 58000.0]], $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 < -3.49999999999999994e-112 or 58000 < x

   1. Initial program 95.2%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 95.6%

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

      1. neg-mul-1 95.6%

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

      2. unsub-neg 95.6%

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

   4. Simplified 95.6%

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

   if -3.49999999999999994e-112 < x < 58000

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around 0 78.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-112} \lor \neg \left(x \leq 58000\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-112} \lor \neg \left(x \leq 8.2 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e-112) (not (<= x 8.2e-7))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-112) || !(x <= 8.2e-7)) {
		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 <= (-3.5d-112)) .or. (.not. (x <= 8.2d-7))) 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 <= -3.5e-112) || !(x <= 8.2e-7)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e-112) or not (x <= 8.2e-7):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e-112) || !(x <= 8.2e-7))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.5e-112) || ~((x <= 8.2e-7)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-112], N[Not[LessEqual[x, 8.2e-7]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -3.49999999999999994e-112 or 8.1999999999999998e-7 < x

   1. Initial program 95.2%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 56.4%

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

   if -3.49999999999999994e-112 < x < 8.1999999999999998e-7

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-112} \lor \neg \left(x \leq 8.2 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 36.0% 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 97.3%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 37.0%

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

3. Final simplification 37.0%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023305 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))