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

Percentage Accurate: 97.8% → 100.0%

Time: 5.4s

Alternatives: 8

Speedup: 1.3×

• 21.0% 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: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. *-commutative N/A

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

   2. sub-neg N/A

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

   3. distribute-rgt-in N/A

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

   4. associate-+r+ N/A

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

   5. metadata-eval N/A

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

   6. mul-1-neg N/A

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

   7. unsub-neg N/A

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

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot y + x \cdot z\right), \color{blue}{z}\right) \]

   9. distribute-lft-out N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(y + z\right)\right), z\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(y + z\right)\right), z\right) \]

   11. +-lowering-+.f64 100.0%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, z\right)\right), z\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x \cdot \left(y + z\right) - z} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+217}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+220}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e+217)
   (* x z)
   (if (<= x -1.95e-16)
     (* x y)
     (if (<= x 1.0) (- 0.0 z) (if (<= x 1.55e+220) (* x z) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e+217) {
		tmp = x * z;
	} else if (x <= -1.95e-16) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = 0.0 - z;
	} else if (x <= 1.55e+220) {
		tmp = x * 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 <= (-3.6d+217)) then
        tmp = x * z
    else if (x <= (-1.95d-16)) then
        tmp = x * y
    else if (x <= 1.0d0) then
        tmp = 0.0d0 - z
    else if (x <= 1.55d+220) then
        tmp = x * 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 <= -3.6e+217) {
		tmp = x * z;
	} else if (x <= -1.95e-16) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = 0.0 - z;
	} else if (x <= 1.55e+220) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.6e+217:
		tmp = x * z
	elif x <= -1.95e-16:
		tmp = x * y
	elif x <= 1.0:
		tmp = 0.0 - z
	elif x <= 1.55e+220:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.6e+217)
		tmp = Float64(x * z);
	elseif (x <= -1.95e-16)
		tmp = Float64(x * y);
	elseif (x <= 1.0)
		tmp = Float64(0.0 - z);
	elseif (x <= 1.55e+220)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.6e+217)
		tmp = x * z;
	elseif (x <= -1.95e-16)
		tmp = x * y;
	elseif (x <= 1.0)
		tmp = 0.0 - z;
	elseif (x <= 1.55e+220)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e+217], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.95e-16], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.0], N[(0.0 - z), $MachinePrecision], If[LessEqual[x, 1.55e+220], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6000000000000002e217 or 1 < x < 1.55e220

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 98.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 98.4%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 65.0%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 65.0%

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

   if -3.6000000000000002e217 < x < -1.94999999999999989e-16 or 1.55e220 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 61.5%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 61.5%

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

   if -1.94999999999999989e-16 < 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

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 77.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 77.1%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 77.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 77.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+217}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+220}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		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 <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 1.0d0) 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 <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		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 <= -1.0:
		tmp = t_0
	elif x <= 1.0:
		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 <= -1.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(Float64(x * y) - 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 <= -1.0)
		tmp = t_0;
	elseif (x <= 1.0)
		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, -1.0], t$95$0, If[LessEqual[x, 1.0], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 98.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 98.5%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+r+ N/A

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

      5. metadata-eval N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot y + x \cdot z\right), \color{blue}{z}\right) \]

      9. distribute-lft-out N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(y + z\right)\right), z\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(y + z\right)\right), z\right) \]

      11. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, z\right)\right), z\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(x \cdot y\right)}, z\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 99.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Simplified 99.1%

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

4. Final simplification 98.8%

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

Alternative 4: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.36 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 750:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.36e-16) t_0 (if (<= x 750.0) (* z (+ x -1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.36e-16) {
		tmp = t_0;
	} else if (x <= 750.0) {
		tmp = z * (x + -1.0);
	} 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 <= (-1.36d-16)) then
        tmp = t_0
    else if (x <= 750.0d0) then
        tmp = z * (x + (-1.0d0))
    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 <= -1.36e-16) {
		tmp = t_0;
	} else if (x <= 750.0) {
		tmp = z * (x + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1.36e-16:
		tmp = t_0
	elif x <= 750.0:
		tmp = z * (x + -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.36e-16)
		tmp = t_0;
	elseif (x <= 750.0)
		tmp = Float64(z * Float64(x + -1.0));
	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 <= -1.36e-16)
		tmp = t_0;
	elseif (x <= 750.0)
		tmp = z * (x + -1.0);
	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, -1.36e-16], t$95$0, If[LessEqual[x, 750.0], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3599999999999999e-16 or 750 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 99.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 99.0%

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

   if -1.3599999999999999e-16 < x < 750

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x + -1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{x}\right)\right) \]

      5. +-lowering-+.f64 78.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{x}\right)\right) \]

   5. Simplified 78.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 750:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -3.9e-16) t_0 (if (<= x 0.8) (- 0.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -3.9e-16) {
		tmp = t_0;
	} else if (x <= 0.8) {
		tmp = 0.0 - 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 <= (-3.9d-16)) then
        tmp = t_0
    else if (x <= 0.8d0) then
        tmp = 0.0d0 - 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 <= -3.9e-16) {
		tmp = t_0;
	} else if (x <= 0.8) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -3.9e-16:
		tmp = t_0
	elif x <= 0.8:
		tmp = 0.0 - 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 <= -3.9e-16)
		tmp = t_0;
	elseif (x <= 0.8)
		tmp = Float64(0.0 - 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 <= -3.9e-16)
		tmp = t_0;
	elseif (x <= 0.8)
		tmp = 0.0 - 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, -3.9e-16], t$95$0, If[LessEqual[x, 0.8], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999977e-16 or 0.80000000000000004 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 98.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 98.5%

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

   if -3.89999999999999977e-16 < x < 0.80000000000000004

   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

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 77.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 77.1%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 77.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 77.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e-16) (* x y) (if (<= x 0.8) (- 0.0 z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e-16) {
		tmp = x * y;
	} else if (x <= 0.8) {
		tmp = 0.0 - 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 <= (-1.85d-16)) then
        tmp = x * y
    else if (x <= 0.8d0) then
        tmp = 0.0d0 - 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 <= -1.85e-16) {
		tmp = x * y;
	} else if (x <= 0.8) {
		tmp = 0.0 - z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.85e-16:
		tmp = x * y
	elif x <= 0.8:
		tmp = 0.0 - z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e-16)
		tmp = Float64(x * y);
	elseif (x <= 0.8)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.85e-16)
		tmp = x * y;
	elseif (x <= 0.8)
		tmp = 0.0 - z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e-16], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.8], N[(0.0 - z), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e-16 or 0.80000000000000004 < x

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 52.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 52.8%

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

   if -1.85e-16 < x < 0.80000000000000004

   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

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 77.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 77.1%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 77.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 77.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ 0 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 0.0 z))

C

double code(double x, double y, double z) {
	return 0.0 - 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 = 0.0d0 - z
end function

Java

public static double code(double x, double y, double z) {
	return 0.0 - z;
}

Python

def code(x, y, z):
	return 0.0 - z

Julia

function code(x, y, z)
	return Float64(0.0 - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0 - z;
end

Wolfram

code[x_, y_, z_] := N[(0.0 - 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

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 37.9%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

5. Simplified 37.9%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 37.9%

      \[\leadsto \mathsf{neg.f64}\left(z\right) \]

7. Applied egg-rr 37.9%

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

8. Final simplification 37.9%

   \[\leadsto 0 - z \]
9. Add Preprocessing

Alternative 8: 2.6% 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

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

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

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 37.9%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

5. Simplified 37.9%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 37.9%

      \[\leadsto \mathsf{neg.f64}\left(z\right) \]

7. Applied egg-rr 37.9%

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

   1. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   2. flip3-- N/A

      \[\leadsto \frac{{0}^{3} - {z}^{3}}{\color{blue}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \frac{0 - {z}^{3}}{\color{blue}{0} \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   4. neg-sub0 N/A

      \[\leadsto \frac{\mathsf{neg}\left({z}^{3}\right)}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   5. cube-neg N/A

      \[\leadsto \frac{{\left(\mathsf{neg}\left(z\right)\right)}^{3}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   6. sqr-pow N/A

      \[\leadsto \frac{{\left(\mathsf{neg}\left(z\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   7. unpow-prod-down N/A

      \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   8. sqr-neg N/A

      \[\leadsto \frac{{\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0} \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   9. pow-prod-down N/A

      \[\leadsto \frac{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   10. sqr-pow N/A

       \[\leadsto \frac{{z}^{3}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   11. metadata-eval N/A

       \[\leadsto \frac{{z}^{3}}{0 + \left(\color{blue}{z \cdot z} + 0 \cdot z\right)} \]

   12. +-lft-identity N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot z + \color{blue}{0 \cdot z}} \]

   13. distribute-rgt-out N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot \color{blue}{\left(z + 0\right)}} \]

   14. +-commutative N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot \left(0 + \color{blue}{z}\right)} \]

   15. +-lft-identity N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot z} \]

   16. pow2 N/A

       \[\leadsto \frac{{z}^{3}}{{z}^{\color{blue}{2}}} \]

   17. pow-div N/A

       \[\leadsto {z}^{\color{blue}{\left(3 - 2\right)}} \]

   18. metadata-eval N/A

       \[\leadsto {z}^{1} \]

   19. unpow1 2.5%

       \[\leadsto z \]

9. Applied egg-rr 2.5%

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

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))