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

Percentage Accurate: 97.9% → 100.0%

Time: 3.1s

Alternatives: 6

Speedup: 1.3×

• 21.5% 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: 97.9% 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 98.0%

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

   2. sub-neg 98.0%

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

   3. distribute-rgt-in 98.0%

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

   4. associate-+r+ 98.0%

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

   5. metadata-eval 98.0%

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

   6. mul-1-neg 98.0%

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

   7. unsub-neg 98.0%

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

   8. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-68}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+182} \lor \neg \left(x \leq 1.85 \cdot 10^{+207}\right) \land x \leq 1.5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e+57)
   (* x z)
   (if (<= x -7.6e-25)
     (* x y)
     (if (<= x 5.8e-68)
       (- z)
       (if (<= x 1.8e-36)
         (* x y)
         (if (<= x 6e-12)
           (- z)
           (if (<= x 2.2e+73)
             (* x y)
             (if (or (<= x 1.8e+182)
                     (and (not (<= x 1.85e+207)) (<= x 1.5e+301)))
               (* x z)
               (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+57) {
		tmp = x * z;
	} else if (x <= -7.6e-25) {
		tmp = x * y;
	} else if (x <= 5.8e-68) {
		tmp = -z;
	} else if (x <= 1.8e-36) {
		tmp = x * y;
	} else if (x <= 6e-12) {
		tmp = -z;
	} else if (x <= 2.2e+73) {
		tmp = x * y;
	} else if ((x <= 1.8e+182) || (!(x <= 1.85e+207) && (x <= 1.5e+301))) {
		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 <= (-9d+57)) then
        tmp = x * z
    else if (x <= (-7.6d-25)) then
        tmp = x * y
    else if (x <= 5.8d-68) then
        tmp = -z
    else if (x <= 1.8d-36) then
        tmp = x * y
    else if (x <= 6d-12) then
        tmp = -z
    else if (x <= 2.2d+73) then
        tmp = x * y
    else if ((x <= 1.8d+182) .or. (.not. (x <= 1.85d+207)) .and. (x <= 1.5d+301)) 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 <= -9e+57) {
		tmp = x * z;
	} else if (x <= -7.6e-25) {
		tmp = x * y;
	} else if (x <= 5.8e-68) {
		tmp = -z;
	} else if (x <= 1.8e-36) {
		tmp = x * y;
	} else if (x <= 6e-12) {
		tmp = -z;
	} else if (x <= 2.2e+73) {
		tmp = x * y;
	} else if ((x <= 1.8e+182) || (!(x <= 1.85e+207) && (x <= 1.5e+301))) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e+57:
		tmp = x * z
	elif x <= -7.6e-25:
		tmp = x * y
	elif x <= 5.8e-68:
		tmp = -z
	elif x <= 1.8e-36:
		tmp = x * y
	elif x <= 6e-12:
		tmp = -z
	elif x <= 2.2e+73:
		tmp = x * y
	elif (x <= 1.8e+182) or (not (x <= 1.85e+207) and (x <= 1.5e+301)):
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e+57)
		tmp = Float64(x * z);
	elseif (x <= -7.6e-25)
		tmp = Float64(x * y);
	elseif (x <= 5.8e-68)
		tmp = Float64(-z);
	elseif (x <= 1.8e-36)
		tmp = Float64(x * y);
	elseif (x <= 6e-12)
		tmp = Float64(-z);
	elseif (x <= 2.2e+73)
		tmp = Float64(x * y);
	elseif ((x <= 1.8e+182) || (!(x <= 1.85e+207) && (x <= 1.5e+301)))
		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 <= -9e+57)
		tmp = x * z;
	elseif (x <= -7.6e-25)
		tmp = x * y;
	elseif (x <= 5.8e-68)
		tmp = -z;
	elseif (x <= 1.8e-36)
		tmp = x * y;
	elseif (x <= 6e-12)
		tmp = -z;
	elseif (x <= 2.2e+73)
		tmp = x * y;
	elseif ((x <= 1.8e+182) || (~((x <= 1.85e+207)) && (x <= 1.5e+301)))
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e+57], N[(x * z), $MachinePrecision], If[LessEqual[x, -7.6e-25], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.8e-68], (-z), If[LessEqual[x, 1.8e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-12], (-z), If[LessEqual[x, 2.2e+73], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 1.8e+182], And[N[Not[LessEqual[x, 1.85e+207]], $MachinePrecision], LessEqual[x, 1.5e+301]]], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999991e57 or 2.2e73 < x < 1.8e182 or 1.85e207 < x < 1.5e301

   1. Initial program 95.1%

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

   2. Taylor expanded in y around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. distribute-lft-out-- 69.6%

         \[\leadsto \color{blue}{z \cdot x - z \cdot 1} \]

      3. *-rgt-identity 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in x around inf 69.6%

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

   if -8.99999999999999991e57 < x < -7.5999999999999996e-25 or 5.8000000000000001e-68 < x < 1.80000000000000016e-36 or 6.0000000000000003e-12 < x < 2.2e73 or 1.8e182 < x < 1.85e207 or 1.5e301 < x

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 76.2%

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

   if -7.5999999999999996e-25 < x < 5.8000000000000001e-68 or 1.80000000000000016e-36 < x < 6.0000000000000003e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.0%

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

      1. mul-1-neg 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-68}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+182} \lor \neg \left(x \leq 1.85 \cdot 10^{+207}\right) \land x \leq 1.5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -3.4e-25)
     t_0
     (if (<= x 6.2e-61)
       (- z)
       (if (<= x 3.8e-36) (* x y) (if (<= x 3.25e-12) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -3.4e-25) {
		tmp = t_0;
	} else if (x <= 6.2e-61) {
		tmp = -z;
	} else if (x <= 3.8e-36) {
		tmp = x * y;
	} else if (x <= 3.25e-12) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-3.4d-25)) then
        tmp = t_0
    else if (x <= 6.2d-61) then
        tmp = -z
    else if (x <= 3.8d-36) then
        tmp = x * y
    else if (x <= 3.25d-12) then
        tmp = -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -3.4e-25) {
		tmp = t_0;
	} else if (x <= 6.2e-61) {
		tmp = -z;
	} else if (x <= 3.8e-36) {
		tmp = x * y;
	} else if (x <= 3.25e-12) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -3.4e-25:
		tmp = t_0
	elif x <= 6.2e-61:
		tmp = -z
	elif x <= 3.8e-36:
		tmp = x * y
	elif x <= 3.25e-12:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -3.4e-25)
		tmp = t_0;
	elseif (x <= 6.2e-61)
		tmp = Float64(-z);
	elseif (x <= 3.8e-36)
		tmp = Float64(x * y);
	elseif (x <= 3.25e-12)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -3.4e-25)
		tmp = t_0;
	elseif (x <= 6.2e-61)
		tmp = -z;
	elseif (x <= 3.8e-36)
		tmp = x * y;
	elseif (x <= 3.25e-12)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-25], t$95$0, If[LessEqual[x, 6.2e-61], (-z), If[LessEqual[x, 3.8e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.25e-12], (-z), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000002e-25 or 3.2500000000000001e-12 < x

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   if -3.40000000000000002e-25 < x < 6.1999999999999999e-61 or 3.79999999999999971e-36 < x < 3.2500000000000001e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.0%

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

      1. mul-1-neg 78.0%

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

   4. Simplified 78.0%

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

   if 6.1999999999999999e-61 < x < 3.79999999999999971e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.25e-24)
     t_0
     (if (<= x 3.4e-61)
       (- (* x z) z)
       (if (<= x 1.8e-36) (* x y) (if (<= x 1.45e-10) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.25e-24) {
		tmp = t_0;
	} else if (x <= 3.4e-61) {
		tmp = (x * z) - z;
	} else if (x <= 1.8e-36) {
		tmp = x * y;
	} else if (x <= 1.45e-10) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-1.25d-24)) then
        tmp = t_0
    else if (x <= 3.4d-61) then
        tmp = (x * z) - z
    else if (x <= 1.8d-36) then
        tmp = x * y
    else if (x <= 1.45d-10) then
        tmp = -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.25e-24) {
		tmp = t_0;
	} else if (x <= 3.4e-61) {
		tmp = (x * z) - z;
	} else if (x <= 1.8e-36) {
		tmp = x * y;
	} else if (x <= 1.45e-10) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1.25e-24:
		tmp = t_0
	elif x <= 3.4e-61:
		tmp = (x * z) - z
	elif x <= 1.8e-36:
		tmp = x * y
	elif x <= 1.45e-10:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.25e-24)
		tmp = t_0;
	elseif (x <= 3.4e-61)
		tmp = Float64(Float64(x * z) - z);
	elseif (x <= 1.8e-36)
		tmp = Float64(x * y);
	elseif (x <= 1.45e-10)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -1.25e-24)
		tmp = t_0;
	elseif (x <= 3.4e-61)
		tmp = (x * z) - z;
	elseif (x <= 1.8e-36)
		tmp = x * y;
	elseif (x <= 1.45e-10)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e-24], t$95$0, If[LessEqual[x, 3.4e-61], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 1.8e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.45e-10], (-z), t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.24999999999999995e-24 or 1.4499999999999999e-10 < x

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   if -1.24999999999999995e-24 < x < 3.3999999999999998e-61

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.0%

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

      1. *-commutative 77.0%

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

      2. distribute-lft-out-- 77.0%

         \[\leadsto \color{blue}{z \cdot x - z \cdot 1} \]

      3. *-rgt-identity 77.0%

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

   4. Simplified 77.0%

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

   if 3.3999999999999998e-61 < x < 1.80000000000000016e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.7%

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

   if 1.80000000000000016e-36 < x < 1.4499999999999999e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]

Alternative 5: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-61} \lor \neg \left(x \leq 4.4 \cdot 10^{-36}\right) \land x \leq 1.32 \cdot 10^{-14}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e-24)
   (* x y)
   (if (or (<= x 6.5e-61) (and (not (<= x 4.4e-36)) (<= x 1.32e-14)))
     (- z)
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-24) {
		tmp = x * y;
	} else if ((x <= 6.5e-61) || (!(x <= 4.4e-36) && (x <= 1.32e-14))) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.3d-24)) then
        tmp = x * y
    else if ((x <= 6.5d-61) .or. (.not. (x <= 4.4d-36)) .and. (x <= 1.32d-14)) then
        tmp = -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-24) {
		tmp = x * y;
	} else if ((x <= 6.5e-61) || (!(x <= 4.4e-36) && (x <= 1.32e-14))) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e-24:
		tmp = x * y
	elif (x <= 6.5e-61) or (not (x <= 4.4e-36) and (x <= 1.32e-14)):
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e-24)
		tmp = Float64(x * y);
	elseif ((x <= 6.5e-61) || (!(x <= 4.4e-36) && (x <= 1.32e-14)))
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e-24)
		tmp = x * y;
	elseif ((x <= 6.5e-61) || (~((x <= 4.4e-36)) && (x <= 1.32e-14)))
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e-24], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 6.5e-61], And[N[Not[LessEqual[x, 4.4e-36]], $MachinePrecision], LessEqual[x, 1.32e-14]]], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e-24 or 6.4999999999999994e-61 < x < 4.3999999999999999e-36 or 1.32e-14 < x

   1. Initial program 96.3%

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

   2. Taylor expanded in y around inf 51.1%

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

   if -1.3e-24 < x < 6.4999999999999994e-61 or 4.3999999999999999e-36 < x < 1.32e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.0%

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

      1. mul-1-neg 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-61} \lor \neg \left(x \leq 4.4 \cdot 10^{-36}\right) \land x \leq 1.32 \cdot 10^{-14}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 36.2% accurate, 4.5× 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 98.0%

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

2. Taylor expanded in x around 0 38.8%

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

   1. mul-1-neg 38.8%

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

4. Simplified 38.8%

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

5. Final simplification 38.8%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))