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

Percentage Accurate: 97.8% → 100.0%

Time: 4.5s

Alternatives: 7

Speedup: 1.3×

• 21.1% 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, 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 61.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{+275}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+196}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-12}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48} \lor \neg \left(x \leq 2.95 \cdot 10^{+94}\right) \land \left(x \leq 1.08 \cdot 10^{+126} \lor \neg \left(x \leq 7 \cdot 10^{+158}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -5.3e+275)
     t_0
     (if (<= x -1.35e+196)
       (* x y)
       (if (<= x -4e+138)
         t_0
         (if (<= x -1.42e+38)
           (* x y)
           (if (<= x -5.4e+17)
             t_0
             (if (<= x -5.1e-11)
               (* x y)
               (if (<= x 2.1e-12)
                 z
                 (if (or (<= x 5e+48)
                         (and (not (<= x 2.95e+94))
                              (or (<= x 1.08e+126) (not (<= x 7e+158)))))
                   (* x y)
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -5.3e+275) {
		tmp = t_0;
	} else if (x <= -1.35e+196) {
		tmp = x * y;
	} else if (x <= -4e+138) {
		tmp = t_0;
	} else if (x <= -1.42e+38) {
		tmp = x * y;
	} else if (x <= -5.4e+17) {
		tmp = t_0;
	} else if (x <= -5.1e-11) {
		tmp = x * y;
	} else if (x <= 2.1e-12) {
		tmp = z;
	} else if ((x <= 5e+48) || (!(x <= 2.95e+94) && ((x <= 1.08e+126) || !(x <= 7e+158)))) {
		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 <= (-5.3d+275)) then
        tmp = t_0
    else if (x <= (-1.35d+196)) then
        tmp = x * y
    else if (x <= (-4d+138)) then
        tmp = t_0
    else if (x <= (-1.42d+38)) then
        tmp = x * y
    else if (x <= (-5.4d+17)) then
        tmp = t_0
    else if (x <= (-5.1d-11)) then
        tmp = x * y
    else if (x <= 2.1d-12) then
        tmp = z
    else if ((x <= 5d+48) .or. (.not. (x <= 2.95d+94)) .and. (x <= 1.08d+126) .or. (.not. (x <= 7d+158))) 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 <= -5.3e+275) {
		tmp = t_0;
	} else if (x <= -1.35e+196) {
		tmp = x * y;
	} else if (x <= -4e+138) {
		tmp = t_0;
	} else if (x <= -1.42e+38) {
		tmp = x * y;
	} else if (x <= -5.4e+17) {
		tmp = t_0;
	} else if (x <= -5.1e-11) {
		tmp = x * y;
	} else if (x <= 2.1e-12) {
		tmp = z;
	} else if ((x <= 5e+48) || (!(x <= 2.95e+94) && ((x <= 1.08e+126) || !(x <= 7e+158)))) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -5.3e+275:
		tmp = t_0
	elif x <= -1.35e+196:
		tmp = x * y
	elif x <= -4e+138:
		tmp = t_0
	elif x <= -1.42e+38:
		tmp = x * y
	elif x <= -5.4e+17:
		tmp = t_0
	elif x <= -5.1e-11:
		tmp = x * y
	elif x <= 2.1e-12:
		tmp = z
	elif (x <= 5e+48) or (not (x <= 2.95e+94) and ((x <= 1.08e+126) or not (x <= 7e+158))):
		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 <= -5.3e+275)
		tmp = t_0;
	elseif (x <= -1.35e+196)
		tmp = Float64(x * y);
	elseif (x <= -4e+138)
		tmp = t_0;
	elseif (x <= -1.42e+38)
		tmp = Float64(x * y);
	elseif (x <= -5.4e+17)
		tmp = t_0;
	elseif (x <= -5.1e-11)
		tmp = Float64(x * y);
	elseif (x <= 2.1e-12)
		tmp = z;
	elseif ((x <= 5e+48) || (!(x <= 2.95e+94) && ((x <= 1.08e+126) || !(x <= 7e+158))))
		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 <= -5.3e+275)
		tmp = t_0;
	elseif (x <= -1.35e+196)
		tmp = x * y;
	elseif (x <= -4e+138)
		tmp = t_0;
	elseif (x <= -1.42e+38)
		tmp = x * y;
	elseif (x <= -5.4e+17)
		tmp = t_0;
	elseif (x <= -5.1e-11)
		tmp = x * y;
	elseif (x <= 2.1e-12)
		tmp = z;
	elseif ((x <= 5e+48) || (~((x <= 2.95e+94)) && ((x <= 1.08e+126) || ~((x <= 7e+158)))))
		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, -5.3e+275], t$95$0, If[LessEqual[x, -1.35e+196], N[(x * y), $MachinePrecision], If[LessEqual[x, -4e+138], t$95$0, If[LessEqual[x, -1.42e+38], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.4e+17], t$95$0, If[LessEqual[x, -5.1e-11], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.1e-12], z, If[Or[LessEqual[x, 5e+48], And[N[Not[LessEqual[x, 2.95e+94]], $MachinePrecision], Or[LessEqual[x, 1.08e+126], N[Not[LessEqual[x, 7e+158]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-11} \lor \neg \left(x \leq 1.6 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.35e-11) (not (<= x 1.6e-12))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.35e-11) || !(x <= 1.6e-12)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.35d-11)) .or. (.not. (x <= 1.6d-12))) then
        tmp = x * (y - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.35e-11) || !(x <= 1.6e-12)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.35e-11) or not (x <= 1.6e-12):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.35e-11) || !(x <= 1.6e-12))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.35e-11) || ~((x <= 1.6e-12)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-11], N[Not[LessEqual[x, 1.6e-12]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -25000000000000 \lor \neg \left(x \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -25000000000000.0) (not (<= x 4.8e-11)))
   (* x (- y z))
   (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -25000000000000.0) || !(x <= 4.8e-11)) {
		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 <= (-25000000000000.0d0)) .or. (.not. (x <= 4.8d-11))) 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 <= -25000000000000.0) || !(x <= 4.8e-11)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -25000000000000.0) or not (x <= 4.8e-11):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -25000000000000.0) || !(x <= 4.8e-11))
		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 <= -25000000000000.0) || ~((x <= 4.8e-11)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -25000000000000.0], N[Not[LessEqual[x, 4.8e-11]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.3 \cdot 10^{-13} \lor \neg \left(x \leq 3.3 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.3e-13) (not (<= x 3.3e-11))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.3e-13) || !(x <= 3.3e-11)) {
		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 <= (-8.3d-13)) .or. (.not. (x <= 3.3d-11))) 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 <= -8.3e-13) || !(x <= 3.3e-11)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.3e-13) or not (x <= 3.3e-11):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.3e-13) || !(x <= 3.3e-11))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.3e-13) || ~((x <= 3.3e-11)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.3e-13], N[Not[LessEqual[x, 3.3e-11]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 36.6% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023348 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))