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

Percentage Accurate: 97.8% → 99.2%

Time: 5.4s

Alternatives: 9

Speedup: 0.7×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot y + \left(x + -1\right) \cdot z\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x y) (* (+ x -1.0) z))))
   (if (<= t_0 2e+288) 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+288) {
		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+288) 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+288) {
		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+288:
		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+288)
		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+288)
		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+288], 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)) < 2e288

   1. Initial program 100.0%

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

   if 2e288 < (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z))

   1. Initial program 88.9%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + \left(x + -1\right) \cdot z \leq 2 \cdot 10^{+288}:\\ \;\;\;\;x \cdot y + \left(x + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y + \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5)
   (* x (+ y z))
   (if (<= x 5.1e-20) (+ (* x y) (- z)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5) {
		tmp = x * (y + z);
	} else if (x <= 5.1e-20) {
		tmp = (x * y) + -z;
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5)
		tmp = Float64(x * Float64(y + z));
	elseif (x <= 5.1e-20)
		tmp = Float64(Float64(x * y) + Float64(-z));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-20], N[(N[(x * y), $MachinePrecision] + (-z)), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5

   1. Initial program 95.9%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 97.2

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

   5. Applied rewrites 97.2%

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

   if -6.5 < x < 5.10000000000000019e-20

   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 98.9

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

   5. Applied rewrites 98.9%

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

   if 5.10000000000000019e-20 < x

   1. Initial program 97.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 98.9

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

   5. Applied rewrites 98.9%

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

   7. Applied rewrites 98.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y + \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -6.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y + \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -6.5) t_0 (if (<= x 5.1e-20) (+ (* x y) (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -6.5) {
		tmp = t_0;
	} else if (x <= 5.1e-20) {
		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 <= (-6.5d0)) then
        tmp = t_0
    else if (x <= 5.1d-20) 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 <= -6.5) {
		tmp = t_0;
	} else if (x <= 5.1e-20) {
		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 <= -6.5:
		tmp = t_0
	elif x <= 5.1e-20:
		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 <= -6.5)
		tmp = t_0;
	elseif (x <= 5.1e-20)
		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 <= -6.5)
		tmp = t_0;
	elseif (x <= 5.1e-20)
		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, -6.5], t$95$0, If[LessEqual[x, 5.1e-20], N[(N[(x * y), $MachinePrecision] + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5 or 5.10000000000000019e-20 < x

   1. Initial program 96.6%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 98.2

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

   5. Applied rewrites 98.2%

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

   if -6.5 < x < 5.10000000000000019e-20

   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 98.9

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

   5. Applied rewrites 98.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y + \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -5.5e+26) t_0 (if (<= x 5.5e-59) (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 <= -5.5e+26) {
		tmp = t_0;
	} else if (x <= 5.5e-59) {
		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 <= -5.5e+26)
		tmp = t_0;
	elseif (x <= 5.5e-59)
		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, -5.5e+26], t$95$0, If[LessEqual[x, 5.5e-59], N[(z * x + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999997e26 or 5.50000000000000014e-59 < x

   1. Initial program 96.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 96.2

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

   5. Applied rewrites 96.2%

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

   if -5.4999999999999997e26 < x < 5.50000000000000014e-59

   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 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -0.022) t_0 (if (<= x 5.5e-59) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -0.022) {
		tmp = t_0;
	} else if (x <= 5.5e-59) {
		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 <= (-0.022d0)) then
        tmp = t_0
    else if (x <= 5.5d-59) 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 <= -0.022) {
		tmp = t_0;
	} else if (x <= 5.5e-59) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -0.022:
		tmp = t_0
	elif x <= 5.5e-59:
		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 <= -0.022)
		tmp = t_0;
	elseif (x <= 5.5e-59)
		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 <= -0.022)
		tmp = t_0;
	elseif (x <= 5.5e-59)
		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, -0.022], t$95$0, If[LessEqual[x, 5.5e-59], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.021999999999999999 or 5.50000000000000014e-59 < x

   1. Initial program 96.9%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 95.3

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

   5. Applied rewrites 95.3%

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

   if -0.021999999999999999 < x < 5.50000000000000014e-59

   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 79.3

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

   5. Applied rewrites 79.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-59}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.022) (* x y) (if (<= x 5.2e-59) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.022) {
		tmp = x * y;
	} else if (x <= 5.2e-59) {
		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 <= (-0.022d0)) then
        tmp = x * y
    else if (x <= 5.2d-59) 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 <= -0.022) {
		tmp = x * y;
	} else if (x <= 5.2e-59) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.022:
		tmp = x * y
	elif x <= 5.2e-59:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.022)
		tmp = Float64(x * y);
	elseif (x <= 5.2e-59)
		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 <= -0.022)
		tmp = x * y;
	elseif (x <= 5.2e-59)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.022], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.2e-59], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.021999999999999999 or 5.19999999999999996e-59 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

   if -0.021999999999999999 < x < 5.19999999999999996e-59

   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 79.3

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

   5. Applied rewrites 79.3%

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

Alternative 7: 61.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0) (* x z) (if (<= x 1.8e-13) (- z) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * z;
	} else if (x <= 1.8e-13) {
		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 <= (-1.0d0)) then
        tmp = x * z
    else if (x <= 1.8d-13) 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 <= -1.0) {
		tmp = x * z;
	} else if (x <= 1.8e-13) {
		tmp = -z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x * z
	elif x <= 1.8e-13:
		tmp = -z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * z);
	elseif (x <= 1.8e-13)
		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 <= -1.0)
		tmp = x * z;
	elseif (x <= 1.8e-13)
		tmp = -z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.8e-13], (-z), N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.7999999999999999e-13 < x

   1. Initial program 96.5%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 46.5

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

   5. Applied rewrites 46.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.7%

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

   if -1 < x < 1.7999999999999999e-13

   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 73.9

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

   5. Applied rewrites 73.9%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.5% 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 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 42.1

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

5. Applied rewrites 42.1%

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

Alternative 9: 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 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 42.1

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

5. Applied rewrites 42.1%

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

7. Applied rewrites 2.5%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024221 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))