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

Percentage Accurate: 98.0% → 100.0%

Time: 6.5s

Alternatives: 7

Speedup: 1.3×

• 20.2% 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, 1.3× 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 96.9%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-20)
   (* x y)
   (if (<= x 8.5e-49) (- 0.0 z) (if (<= x 4.6e+26) (* x y) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-20) {
		tmp = x * y;
	} else if (x <= 8.5e-49) {
		tmp = 0.0 - z;
	} else if (x <= 4.6e+26) {
		tmp = x * y;
	} 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 <= (-1.4d-20)) then
        tmp = x * y
    else if (x <= 8.5d-49) then
        tmp = 0.0d0 - z
    else if (x <= 4.6d+26) then
        tmp = x * y
    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 <= -1.4e-20) {
		tmp = x * y;
	} else if (x <= 8.5e-49) {
		tmp = 0.0 - z;
	} else if (x <= 4.6e+26) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-20:
		tmp = x * y
	elif x <= 8.5e-49:
		tmp = 0.0 - z
	elif x <= 4.6e+26:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-20)
		tmp = Float64(x * y);
	elseif (x <= 8.5e-49)
		tmp = Float64(0.0 - z);
	elseif (x <= 4.6e+26)
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e-20)
		tmp = x * y;
	elseif (x <= 8.5e-49)
		tmp = 0.0 - z;
	elseif (x <= 4.6e+26)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-20], N[(x * y), $MachinePrecision], If[LessEqual[x, 8.5e-49], N[(0.0 - z), $MachinePrecision], If[LessEqual[x, 4.6e+26], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4000000000000001e-20 or 8.50000000000000069e-49 < x < 4.6000000000000001e26

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 57.4%

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

   5. Simplified 57.4%

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

   if -1.4000000000000001e-20 < x < 8.50000000000000069e-49

   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 79.2%

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

   5. Simplified 79.2%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 79.2%

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

   7. Applied egg-rr 79.2%

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

   if 4.6000000000000001e26 < x

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

      1. *-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 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]
   7. Step-by-step derivation

   8. Simplified 65.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.6× speedup

Math

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

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 92.4%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 99.2%

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

   5. Simplified 99.2%

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

   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 99.2%

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

Alternative 4: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -2.8e-20) t_0 (if (<= x 1.8e-49) (* 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 <= -2.8e-20) {
		tmp = t_0;
	} else if (x <= 1.8e-49) {
		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 <= (-2.8d-20)) then
        tmp = t_0
    else if (x <= 1.8d-49) 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 <= -2.8e-20) {
		tmp = t_0;
	} else if (x <= 1.8e-49) {
		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 <= -2.8e-20:
		tmp = t_0
	elif x <= 1.8e-49:
		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 <= -2.8e-20)
		tmp = t_0;
	elseif (x <= 1.8e-49)
		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 <= -2.8e-20)
		tmp = t_0;
	elseif (x <= 1.8e-49)
		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, -2.8e-20], t$95$0, If[LessEqual[x, 1.8e-49], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000003e-20 or 1.79999999999999985e-49 < x

   1. Initial program 93.6%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-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 93.4%

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

   5. Simplified 93.4%

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

   if -2.8000000000000003e-20 < x < 1.79999999999999985e-49

   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 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-48}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -5.4e-22) t_0 (if (<= x 1.18e-48) (- 0.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -5.4e-22) {
		tmp = t_0;
	} else if (x <= 1.18e-48) {
		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 <= (-5.4d-22)) then
        tmp = t_0
    else if (x <= 1.18d-48) 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 <= -5.4e-22) {
		tmp = t_0;
	} else if (x <= 1.18e-48) {
		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 <= -5.4e-22:
		tmp = t_0
	elif x <= 1.18e-48:
		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 <= -5.4e-22)
		tmp = t_0;
	elseif (x <= 1.18e-48)
		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 <= -5.4e-22)
		tmp = t_0;
	elseif (x <= 1.18e-48)
		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, -5.4e-22], t$95$0, If[LessEqual[x, 1.18e-48], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4000000000000004e-22 or 1.18000000000000007e-48 < x

   1. Initial program 93.6%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-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 93.4%

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

   5. Simplified 93.4%

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

   if -5.4000000000000004e-22 < x < 1.18000000000000007e-48

   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 79.2%

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

   5. Simplified 79.2%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 79.2%

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

   7. Applied egg-rr 79.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-48}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-21}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8e-21) (* x y) (if (<= x 1.35e-52) (- 0.0 z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8e-21) {
		tmp = x * y;
	} else if (x <= 1.35e-52) {
		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 <= (-8d-21)) then
        tmp = x * y
    else if (x <= 1.35d-52) 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 <= -8e-21) {
		tmp = x * y;
	} else if (x <= 1.35e-52) {
		tmp = 0.0 - z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8e-21:
		tmp = x * y
	elif x <= 1.35e-52:
		tmp = 0.0 - z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8e-21)
		tmp = Float64(x * y);
	elseif (x <= 1.35e-52)
		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 <= -8e-21)
		tmp = x * y;
	elseif (x <= 1.35e-52)
		tmp = 0.0 - z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8e-21], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.35e-52], N[(0.0 - z), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999926e-21 or 1.35000000000000005e-52 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 51.4%

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

   5. Simplified 51.4%

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

   if -7.99999999999999926e-21 < x < 1.35000000000000005e-52

   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 79.2%

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

   5. Simplified 79.2%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 79.2%

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

   7. Applied egg-rr 79.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-21}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.8% 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 96.9%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 44.1%

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

5. Simplified 44.1%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 44.1%

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

7. Applied egg-rr 44.1%

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

8. Final simplification 44.1%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))