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

Percentage Accurate: 98.0% → 100.0%

Time: 4.8s

Alternatives: 8

Speedup: 1.4×

• 20.3% 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: 98.0% 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: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z + y, x, -z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (+ z y) x (- z)))

C

double code(double x, double y, double z) {
	return fma((z + y), x, -z);
}

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. lower-+.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 100.0

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z + y, x, -z\right)} \]
6. Add Preprocessing

Alternative 2: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{-10}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-90}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{+81}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.55e-10)
   (* y x)
   (if (<= x 4.2e-90) (- z) (if (<= x 6.9e+81) (* y x) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.55e-10) {
		tmp = y * x;
	} else if (x <= 4.2e-90) {
		tmp = -z;
	} else if (x <= 6.9e+81) {
		tmp = y * x;
	} else {
		tmp = z * 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 <= (-3.55d-10)) then
        tmp = y * x
    else if (x <= 4.2d-90) then
        tmp = -z
    else if (x <= 6.9d+81) then
        tmp = y * x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.55e-10) {
		tmp = y * x;
	} else if (x <= 4.2e-90) {
		tmp = -z;
	} else if (x <= 6.9e+81) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.55e-10:
		tmp = y * x
	elif x <= 4.2e-90:
		tmp = -z
	elif x <= 6.9e+81:
		tmp = y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.55e-10)
		tmp = Float64(y * x);
	elseif (x <= 4.2e-90)
		tmp = Float64(-z);
	elseif (x <= 6.9e+81)
		tmp = Float64(y * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.55e-10)
		tmp = y * x;
	elseif (x <= 4.2e-90)
		tmp = -z;
	elseif (x <= 6.9e+81)
		tmp = y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.55e-10], N[(y * x), $MachinePrecision], If[LessEqual[x, 4.2e-90], (-z), If[LessEqual[x, 6.9e+81], N[(y * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5500000000000001e-10 or 4.1999999999999998e-90 < x < 6.8999999999999996e81

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.5

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

   8. Applied rewrites 60.5%

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

   if -3.5500000000000001e-10 < x < 4.1999999999999998e-90

   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 74.6

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

   5. Applied rewrites 74.6%

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

   if 6.8999999999999996e81 < x

   1. Initial program 94.9%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.1

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 60.1%

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

Alternative 3: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-9} \lor \neg \left(x \leq 7800\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e-9) (not (<= x 7800.0))) (* (+ z y) x) (- (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-9) || !(x <= 7800.0)) {
		tmp = (z + y) * x;
	} else {
		tmp = (z * 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 <= (-6.5d-9)) .or. (.not. (x <= 7800.0d0))) then
        tmp = (z + y) * x
    else
        tmp = (z * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-9) || !(x <= 7800.0)) {
		tmp = (z + y) * x;
	} else {
		tmp = (z * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e-9) or not (x <= 7800.0):
		tmp = (z + y) * x
	else:
		tmp = (z * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e-9) || !(x <= 7800.0))
		tmp = Float64(Float64(z + y) * x);
	else
		tmp = Float64(Float64(z * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e-9) || ~((x <= 7800.0)))
		tmp = (z + y) * x;
	else
		tmp = (z * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e-9], N[Not[LessEqual[x, 7800.0]], $MachinePrecision]], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000003e-9 or 7800 < x

   1. Initial program 97.3%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -6.5000000000000003e-9 < x < 7800

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.3

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

   5. Applied rewrites 71.3%

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

   7. Applied rewrites 71.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-9} \lor \neg \left(x \leq 7800\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-9} \lor \neg \left(x \leq 7800\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x - 1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e-9) (not (<= x 7800.0))) (* (+ z y) x) (* (- x 1.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-9) || !(x <= 7800.0)) {
		tmp = (z + y) * x;
	} else {
		tmp = (x - 1.0) * 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 <= (-6.5d-9)) .or. (.not. (x <= 7800.0d0))) then
        tmp = (z + y) * x
    else
        tmp = (x - 1.0d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-9) || !(x <= 7800.0)) {
		tmp = (z + y) * x;
	} else {
		tmp = (x - 1.0) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e-9) or not (x <= 7800.0):
		tmp = (z + y) * x
	else:
		tmp = (x - 1.0) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e-9) || !(x <= 7800.0))
		tmp = Float64(Float64(z + y) * x);
	else
		tmp = Float64(Float64(x - 1.0) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e-9) || ~((x <= 7800.0)))
		tmp = (z + y) * x;
	else
		tmp = (x - 1.0) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e-9], N[Not[LessEqual[x, 7800.0]], $MachinePrecision]], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000003e-9 or 7800 < x

   1. Initial program 97.3%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -6.5000000000000003e-9 < x < 7800

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.3

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

   5. Applied rewrites 71.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-9} \lor \neg \left(x \leq 7800\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x - 1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-10} \lor \neg \left(x \leq 4.2 \cdot 10^{-90}\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e-10) (not (<= x 4.2e-90))) (* (+ z y) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-10) || !(x <= 4.2e-90)) {
		tmp = (z + y) * x;
	} 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-10)) .or. (.not. (x <= 4.2d-90))) then
        tmp = (z + y) * x
    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-10) || !(x <= 4.2e-90)) {
		tmp = (z + y) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e-10) or not (x <= 4.2e-90):
		tmp = (z + y) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e-10) || !(x <= 4.2e-90))
		tmp = Float64(Float64(z + y) * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.5e-10) || ~((x <= 4.2e-90)))
		tmp = (z + y) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-10], N[Not[LessEqual[x, 4.2e-90]], $MachinePrecision]], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999998e-10 or 4.1999999999999998e-90 < x

   1. Initial program 97.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 89.8

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

   5. Applied rewrites 89.8%

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

   if -3.4999999999999998e-10 < x < 4.1999999999999998e-90

   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 74.6

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

   5. Applied rewrites 74.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-10} \lor \neg \left(x \leq 4.2 \cdot 10^{-90}\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = z * x;
	} 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 <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = z * x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(z * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 97.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.9

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 49.1%

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

   if -1 < 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 68.1

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

   5. Applied rewrites 68.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.0% 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 98.8%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 40.4

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

5. Applied rewrites 40.4%

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

Alternative 8: 2.6% 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 98.8%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 40.4

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

5. Applied rewrites 40.4%

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

7. Applied rewrites 2.4%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024318 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))