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

Percentage Accurate: 98.1% → 100.0%

Time: 6.6s

Alternatives: 6

Speedup: 1.3×

• 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: 98.1% 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 98.0%

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

Alternative 2: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-13}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.35e+21)
   (* x z)
   (if (<= x -1.05e-46) (* x y) (if (<= x 1.52e-13) (- 0.0 z) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.35e+21) {
		tmp = x * z;
	} else if (x <= -1.05e-46) {
		tmp = x * y;
	} else if (x <= 1.52e-13) {
		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 <= (-2.35d+21)) then
        tmp = x * z
    else if (x <= (-1.05d-46)) then
        tmp = x * y
    else if (x <= 1.52d-13) 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 <= -2.35e+21) {
		tmp = x * z;
	} else if (x <= -1.05e-46) {
		tmp = x * y;
	} else if (x <= 1.52e-13) {
		tmp = 0.0 - z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.35e+21:
		tmp = x * z
	elif x <= -1.05e-46:
		tmp = x * y
	elif x <= 1.52e-13:
		tmp = 0.0 - z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.35e+21)
		tmp = Float64(x * z);
	elseif (x <= -1.05e-46)
		tmp = Float64(x * y);
	elseif (x <= 1.52e-13)
		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 <= -2.35e+21)
		tmp = x * z;
	elseif (x <= -1.05e-46)
		tmp = x * y;
	elseif (x <= 1.52e-13)
		tmp = 0.0 - z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.35e+21], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.05e-46], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.52e-13], N[(0.0 - z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.35e21

   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. *-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 100.0%

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

   5. Simplified 100.0%

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

   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 62.8%

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

   8. Simplified 62.8%

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

   if -2.35e21 < x < -1.04999999999999994e-46 or 1.5200000000000001e-13 < x

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 55.0%

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

   5. Simplified 55.0%

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

   if -1.04999999999999994e-46 < x < 1.5200000000000001e-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

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 74.1%

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

   5. Simplified 74.1%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 74.1%

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

   7. Applied egg-rr 74.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-13}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -7.8e+15) 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 <= -7.8e+15) {
		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 <= (-7.8d+15)) 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 <= -7.8e+15) {
		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 <= -7.8e+15:
		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 <= -7.8e+15)
		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 <= -7.8e+15)
		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, -7.8e+15], 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 < -7.8e15 or 1 < x

   1. Initial program 96.1%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 99.6%

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

   5. Simplified 99.6%

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

   if -7.8e15 < 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 99.0%

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

   7. Simplified 99.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-11}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -6.2e-45) t_0 (if (<= x 9.6e-11) (- 0.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -6.2e-45) {
		tmp = t_0;
	} else if (x <= 9.6e-11) {
		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 <= (-6.2d-45)) then
        tmp = t_0
    else if (x <= 9.6d-11) 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 <= -6.2e-45) {
		tmp = t_0;
	} else if (x <= 9.6e-11) {
		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 <= -6.2e-45:
		tmp = t_0
	elif x <= 9.6e-11:
		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 <= -6.2e-45)
		tmp = t_0;
	elseif (x <= 9.6e-11)
		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 <= -6.2e-45)
		tmp = t_0;
	elseif (x <= 9.6e-11)
		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, -6.2e-45], t$95$0, If[LessEqual[x, 9.6e-11], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000002e-45 or 9.6000000000000005e-11 < x

   1. Initial program 96.4%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 97.8%

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

   5. Simplified 97.8%

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

   if -6.2000000000000002e-45 < x < 9.6000000000000005e-11

   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 74.1%

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

   5. Simplified 74.1%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 74.1%

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

   7. Applied egg-rr 74.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-11}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-15}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e-40) (* x y) (if (<= x 9.2e-15) (- 0.0 z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-40) {
		tmp = x * y;
	} else if (x <= 9.2e-15) {
		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 <= (-1.45d-40)) then
        tmp = x * y
    else if (x <= 9.2d-15) 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 <= -1.45e-40) {
		tmp = x * y;
	} else if (x <= 9.2e-15) {
		tmp = 0.0 - z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e-40:
		tmp = x * y
	elif x <= 9.2e-15:
		tmp = 0.0 - z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e-40)
		tmp = Float64(x * y);
	elseif (x <= 9.2e-15)
		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 <= -1.45e-40)
		tmp = x * y;
	elseif (x <= 9.2e-15)
		tmp = 0.0 - z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e-40], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.2e-15], N[(0.0 - z), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e-40 or 9.19999999999999961e-15 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 51.9%

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

   5. Simplified 51.9%

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

   if -1.4499999999999999e-40 < x < 9.19999999999999961e-15

   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 74.1%

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

   5. Simplified 74.1%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 74.1%

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

   7. Applied egg-rr 74.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-15}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.1% 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 98.0%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 35.8%

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

5. Simplified 35.8%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 35.8%

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

7. Applied egg-rr 35.8%

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

8. Final simplification 35.8%

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))