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

Percentage Accurate: 97.8% → 99.7%

Time: 4.7s

Alternatives: 8

Speedup: 0.7×

• 21.8% 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: 97.8% 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: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot y + \left(x + -1\right) \cdot z\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x y) (* (+ x -1.0) z))))
   (if (<= t_0 2e+303) t_0 (* x (+ y z)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) + ((x + -1.0) * z);
	double tmp;
	if (t_0 <= 2e+303) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x * y) + ((x + (-1.0d0)) * z)
    if (t_0 <= 2d+303) then
        tmp = t_0
    else
        tmp = x * (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * y) + ((x + -1.0) * z);
	double tmp;
	if (t_0 <= 2e+303) {
		tmp = t_0;
	} else {
		tmp = x * (y + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) + ((x + -1.0) * z)
	tmp = 0
	if t_0 <= 2e+303:
		tmp = t_0
	else:
		tmp = x * (y + z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) + Float64(Float64(x + -1.0) * z))
	tmp = 0.0
	if (t_0 <= 2e+303)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) + ((x + -1.0) * z);
	tmp = 0.0;
	if (t_0 <= 2e+303)
		tmp = t_0;
	else
		tmp = x * (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+303], t$95$0, N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z)) < 2e303

   1. Initial program 100.0%

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

   if 2e303 < (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z))

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + \left(x + -1\right) \cdot z \leq 2 \cdot 10^{+303}:\\ \;\;\;\;x \cdot y + \left(x + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -320000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -320000000000.0)
   (* x z)
   (if (<= x -4.3e-16) (* x y) (if (<= x 1.9e-28) (- z) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -320000000000.0) {
		tmp = x * z;
	} else if (x <= -4.3e-16) {
		tmp = x * y;
	} else if (x <= 1.9e-28) {
		tmp = -z;
	} else {
		tmp = 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 <= (-320000000000.0d0)) then
        tmp = x * z
    else if (x <= (-4.3d-16)) then
        tmp = x * y
    else if (x <= 1.9d-28) then
        tmp = -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -320000000000.0) {
		tmp = x * z;
	} else if (x <= -4.3e-16) {
		tmp = x * y;
	} else if (x <= 1.9e-28) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -320000000000.0:
		tmp = x * z
	elif x <= -4.3e-16:
		tmp = x * y
	elif x <= 1.9e-28:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -320000000000.0)
		tmp = Float64(x * z);
	elseif (x <= -4.3e-16)
		tmp = Float64(x * y);
	elseif (x <= 1.9e-28)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -320000000000.0)
		tmp = x * z;
	elseif (x <= -4.3e-16)
		tmp = x * y;
	elseif (x <= 1.9e-28)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -320000000000.0], N[(x * z), $MachinePrecision], If[LessEqual[x, -4.3e-16], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.9e-28], (-z), N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e11

   1. Initial program 92.1%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 60.2

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 59.8%

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

   if -3.2e11 < x < -4.2999999999999999e-16 or 1.90000000000000005e-28 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 58.0

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

   5. Applied rewrites 58.0%

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

   if -4.2999999999999999e-16 < x < 1.90000000000000005e-28

   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 76.9

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

   5. Applied rewrites 76.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -320000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -205000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y + \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -205000000000.0) t_0 (if (<= x 3.3e-28) (+ (* x y) (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -205000000000.0) {
		tmp = t_0;
	} else if (x <= 3.3e-28) {
		tmp = (x * y) + -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 <= (-205000000000.0d0)) then
        tmp = t_0
    else if (x <= 3.3d-28) then
        tmp = (x * y) + -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 <= -205000000000.0) {
		tmp = t_0;
	} else if (x <= 3.3e-28) {
		tmp = (x * y) + -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -205000000000.0:
		tmp = t_0
	elif x <= 3.3e-28:
		tmp = (x * y) + -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 <= -205000000000.0)
		tmp = t_0;
	elseif (x <= 3.3e-28)
		tmp = Float64(Float64(x * y) + Float64(-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 <= -205000000000.0)
		tmp = t_0;
	elseif (x <= 3.3e-28)
		tmp = (x * y) + -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, -205000000000.0], t$95$0, If[LessEqual[x, 3.3e-28], N[(N[(x * y), $MachinePrecision] + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e11 or 3.3000000000000002e-28 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 99.2

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

   5. Applied rewrites 99.2%

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

   if -2.05e11 < x < 3.3000000000000002e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 98.6

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

   5. Applied rewrites 98.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -205000000000:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y + \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -4.3e-16) t_0 (if (<= x 1.9e-28) (fma z x (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -4.3e-16) {
		tmp = t_0;
	} else if (x <= 1.9e-28) {
		tmp = fma(z, x, -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 <= -4.3e-16)
		tmp = t_0;
	elseif (x <= 1.9e-28)
		tmp = fma(z, x, Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e-16], t$95$0, If[LessEqual[x, 1.9e-28], N[(z * x + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2999999999999999e-16 or 1.90000000000000005e-28 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 97.4

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

   5. Applied rewrites 97.4%

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

   if -4.2999999999999999e-16 < x < 1.90000000000000005e-28

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 76.9

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

   5. Applied rewrites 76.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -4.3e-16) t_0 (if (<= x 1.9e-28) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -4.3e-16) {
		tmp = t_0;
	} else if (x <= 1.9e-28) {
		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 <= (-4.3d-16)) then
        tmp = t_0
    else if (x <= 1.9d-28) 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 <= -4.3e-16) {
		tmp = t_0;
	} else if (x <= 1.9e-28) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -4.3e-16:
		tmp = t_0
	elif x <= 1.9e-28:
		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 <= -4.3e-16)
		tmp = t_0;
	elseif (x <= 1.9e-28)
		tmp = Float64(-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 <= -4.3e-16)
		tmp = t_0;
	elseif (x <= 1.9e-28)
		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, -4.3e-16], t$95$0, If[LessEqual[x, 1.9e-28], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2999999999999999e-16 or 1.90000000000000005e-28 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 97.4

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

   5. Applied rewrites 97.4%

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

   if -4.2999999999999999e-16 < x < 1.90000000000000005e-28

   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 76.9

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

   5. Applied rewrites 76.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -205000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -205000000000.0) (* x z) (if (<= x 7e-26) (- z) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -205000000000.0) {
		tmp = x * z;
	} else if (x <= 7e-26) {
		tmp = -z;
	} 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 <= (-205000000000.0d0)) then
        tmp = x * z
    else if (x <= 7d-26) then
        tmp = -z
    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 <= -205000000000.0) {
		tmp = x * z;
	} else if (x <= 7e-26) {
		tmp = -z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -205000000000.0:
		tmp = x * z
	elif x <= 7e-26:
		tmp = -z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -205000000000.0)
		tmp = Float64(x * z);
	elseif (x <= 7e-26)
		tmp = Float64(-z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -205000000000.0)
		tmp = x * z;
	elseif (x <= 7e-26)
		tmp = -z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -205000000000.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 7e-26], (-z), N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e11 or 6.9999999999999997e-26 < x

   1. Initial program 93.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 53.0%

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

   if -2.05e11 < x < 6.9999999999999997e-26

   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 72.0

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

   5. Applied rewrites 72.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -205000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.6% accurate, 5.7× 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 Float64(-z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 96.9%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 36.9

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

5. Applied rewrites 36.9%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 8: 2.7% accurate, 17.0× 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 96.9%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 36.9

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

5. Applied rewrites 36.9%

   \[\leadsto \color{blue}{-z} \]
6. Step-by-step derivation

7. Applied rewrites 2.5%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024234 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))