Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Percentage Accurate: 97.9% → 98.9%

Time: 5.5s

Alternatives: 8

Speedup: 0.8×

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

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * 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) + ((x - 1.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((x - 1.0) * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((x - 1.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * 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) + ((x - 1.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((x - 1.0) * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((x - 1.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x + -1\right)\\ \mathbf{if}\;x \cdot y + t\_0 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, x, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (+ x -1.0))))
   (if (<= (+ (* x y) t_0) INFINITY) (fma y x t_0) (* x y))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x + -1.0);
	double tmp;
	if (((x * y) + t_0) <= ((double) INFINITY)) {
		tmp = fma(y, x, t_0);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x + -1.0))
	tmp = 0.0
	if (Float64(Float64(x * y) + t_0) <= Inf)
		tmp = fma(y, x, t_0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x * y), $MachinePrecision] + t$95$0), $MachinePrecision], Infinity], N[(y * x + t$95$0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z)) < +inf.0

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 100.0

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot z\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot z\right) \]

      8. metadata-eval 100.0

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

   4. Applied rewrites 100.0%

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

   if +inf.0 < (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z))

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -0.00036:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{+187}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35e+143)
   (* x z)
   (if (<= x -0.00036)
     (* x y)
     (if (<= x 1.0)
       (- z)
       (if (<= x 6e+64) (* x z) (if (<= x 1.66e+187) (* x y) (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e+143) {
		tmp = x * z;
	} else if (x <= -0.00036) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 6e+64) {
		tmp = x * z;
	} else if (x <= 1.66e+187) {
		tmp = x * y;
	} else {
		tmp = x * 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+143)) then
        tmp = x * z
    else if (x <= (-0.00036d0)) then
        tmp = x * y
    else if (x <= 1.0d0) then
        tmp = -z
    else if (x <= 6d+64) then
        tmp = x * z
    else if (x <= 1.66d+187) then
        tmp = x * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e+143) {
		tmp = x * z;
	} else if (x <= -0.00036) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 6e+64) {
		tmp = x * z;
	} else if (x <= 1.66e+187) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35e+143:
		tmp = x * z
	elif x <= -0.00036:
		tmp = x * y
	elif x <= 1.0:
		tmp = -z
	elif x <= 6e+64:
		tmp = x * z
	elif x <= 1.66e+187:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35e+143)
		tmp = Float64(x * z);
	elseif (x <= -0.00036)
		tmp = Float64(x * y);
	elseif (x <= 1.0)
		tmp = Float64(-z);
	elseif (x <= 6e+64)
		tmp = Float64(x * z);
	elseif (x <= 1.66e+187)
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35e+143)
		tmp = x * z;
	elseif (x <= -0.00036)
		tmp = x * y;
	elseif (x <= 1.0)
		tmp = -z;
	elseif (x <= 6e+64)
		tmp = x * z;
	elseif (x <= 1.66e+187)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35e+143], N[(x * z), $MachinePrecision], If[LessEqual[x, -0.00036], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.0], (-z), If[LessEqual[x, 6e+64], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.66e+187], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001e143 or 1 < x < 6.0000000000000004e64 or 1.6600000000000001e187 < x

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

         \[\leadsto \color{blue}{x \cdot z + -1 \cdot z} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot x} + -1 \cdot z \]

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 53.7

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

   5. Applied rewrites 53.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 53.1%

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

   if -1.3500000000000001e143 < x < -3.60000000000000023e-4 or 6.0000000000000004e64 < x < 1.6600000000000001e187

   1. Initial program 98.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 50.2

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

   5. Applied rewrites 50.2%

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

   if -3.60000000000000023e-4 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 70.6

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

   5. Applied rewrites 70.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -0.00036:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{+187}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024228 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))