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

Percentage Accurate: 97.8% → 100.0%

Time: 3.5s

Alternatives: 6

Speedup: 1.3×

• 21.3% 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: 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. *-commutative 98.4%

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

   2. sub-neg 98.4%

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

   3. distribute-rgt-in 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. unsub-neg 98.4%

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

   8. +-commutative 98.4%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+255}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+303}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+93)
   (* x z)
   (if (<= x -9.5e-66)
     (* x y)
     (if (<= x 1.55e-138)
       (- z)
       (if (<= x 3.5e-79)
         (* x y)
         (if (<= x 1.0)
           (- z)
           (if (<= x 4.5e+255)
             (* x z)
             (if (<= x 1.6e+303) (* x y) (* x z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+93) {
		tmp = x * z;
	} else if (x <= -9.5e-66) {
		tmp = x * y;
	} else if (x <= 1.55e-138) {
		tmp = -z;
	} else if (x <= 3.5e-79) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 4.5e+255) {
		tmp = x * z;
	} else if (x <= 1.6e+303) {
		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 <= (-1.05d+93)) then
        tmp = x * z
    else if (x <= (-9.5d-66)) then
        tmp = x * y
    else if (x <= 1.55d-138) then
        tmp = -z
    else if (x <= 3.5d-79) then
        tmp = x * y
    else if (x <= 1.0d0) then
        tmp = -z
    else if (x <= 4.5d+255) then
        tmp = x * z
    else if (x <= 1.6d+303) 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 <= -1.05e+93) {
		tmp = x * z;
	} else if (x <= -9.5e-66) {
		tmp = x * y;
	} else if (x <= 1.55e-138) {
		tmp = -z;
	} else if (x <= 3.5e-79) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 4.5e+255) {
		tmp = x * z;
	} else if (x <= 1.6e+303) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e+93:
		tmp = x * z
	elif x <= -9.5e-66:
		tmp = x * y
	elif x <= 1.55e-138:
		tmp = -z
	elif x <= 3.5e-79:
		tmp = x * y
	elif x <= 1.0:
		tmp = -z
	elif x <= 4.5e+255:
		tmp = x * z
	elif x <= 1.6e+303:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+93)
		tmp = Float64(x * z);
	elseif (x <= -9.5e-66)
		tmp = Float64(x * y);
	elseif (x <= 1.55e-138)
		tmp = Float64(-z);
	elseif (x <= 3.5e-79)
		tmp = Float64(x * y);
	elseif (x <= 1.0)
		tmp = Float64(-z);
	elseif (x <= 4.5e+255)
		tmp = Float64(x * z);
	elseif (x <= 1.6e+303)
		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 <= -1.05e+93)
		tmp = x * z;
	elseif (x <= -9.5e-66)
		tmp = x * y;
	elseif (x <= 1.55e-138)
		tmp = -z;
	elseif (x <= 3.5e-79)
		tmp = x * y;
	elseif (x <= 1.0)
		tmp = -z;
	elseif (x <= 4.5e+255)
		tmp = x * z;
	elseif (x <= 1.6e+303)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+93], N[(x * z), $MachinePrecision], If[LessEqual[x, -9.5e-66], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.55e-138], (-z), If[LessEqual[x, 3.5e-79], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.0], (-z), If[LessEqual[x, 4.5e+255], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.6e+303], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0499999999999999e93 or 1 < x < 4.49999999999999964e255 or 1.6000000000000001e303 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 68.8%

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

      1. sub-neg 68.8%

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

      2. metadata-eval 68.8%

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

      3. distribute-rgt-in 68.8%

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

      4. neg-mul-1 68.8%

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

      5. sub-neg 68.8%

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

      6. *-commutative 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in x around inf 68.6%

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

      1. *-commutative 68.6%

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

   7. Simplified 68.6%

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

   if -1.0499999999999999e93 < x < -9.5000000000000004e-66 or 1.5499999999999999e-138 < x < 3.5000000000000003e-79 or 4.49999999999999964e255 < x < 1.6000000000000001e303

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 67.9%

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

   if -9.5000000000000004e-66 < x < 1.5499999999999999e-138 or 3.5000000000000003e-79 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. neg-mul-1 76.1%

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

   4. Simplified 76.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+255}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+303}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -1.6e-65)
     t_0
     (if (<= x 1.55e-138)
       (- z)
       (if (<= x 3.3e-79) (* x y) (if (<= x 4.6e-10) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -1.6e-65) {
		tmp = t_0;
	} else if (x <= 1.55e-138) {
		tmp = -z;
	} else if (x <= 3.3e-79) {
		tmp = x * y;
	} else if (x <= 4.6e-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 * (z + y)
    if (x <= (-1.6d-65)) then
        tmp = t_0
    else if (x <= 1.55d-138) then
        tmp = -z
    else if (x <= 3.3d-79) then
        tmp = x * y
    else if (x <= 4.6d-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 * (z + y);
	double tmp;
	if (x <= -1.6e-65) {
		tmp = t_0;
	} else if (x <= 1.55e-138) {
		tmp = -z;
	} else if (x <= 3.3e-79) {
		tmp = x * y;
	} else if (x <= 4.6e-10) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -1.6e-65:
		tmp = t_0
	elif x <= 1.55e-138:
		tmp = -z
	elif x <= 3.3e-79:
		tmp = x * y
	elif x <= 4.6e-10:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -1.6e-65)
		tmp = t_0;
	elseif (x <= 1.55e-138)
		tmp = Float64(-z);
	elseif (x <= 3.3e-79)
		tmp = Float64(x * y);
	elseif (x <= 4.6e-10)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -1.6e-65)
		tmp = t_0;
	elseif (x <= 1.55e-138)
		tmp = -z;
	elseif (x <= 3.3e-79)
		tmp = x * y;
	elseif (x <= 4.6e-10)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e-65], t$95$0, If[LessEqual[x, 1.55e-138], (-z), If[LessEqual[x, 3.3e-79], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.6e-10], (-z), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e-65 or 4.60000000000000014e-10 < x

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 98.0%

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

      1. +-commutative 98.0%

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

   4. Simplified 98.0%

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

   if -1.6e-65 < x < 1.5499999999999999e-138 or 3.2999999999999998e-79 < x < 4.60000000000000014e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. neg-mul-1 76.1%

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

   4. Simplified 76.1%

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

   if 1.5499999999999999e-138 < x < 3.2999999999999998e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]

Alternative 4: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ t_1 := x \cdot z - z\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1020000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))) (t_1 (- (* x z) z)))
   (if (<= x -2.6e-65)
     t_0
     (if (<= x 1.55e-138)
       t_1
       (if (<= x 3.3e-79) (* x y) (if (<= x 1020000000000.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double t_1 = (x * z) - z;
	double tmp;
	if (x <= -2.6e-65) {
		tmp = t_0;
	} else if (x <= 1.55e-138) {
		tmp = t_1;
	} else if (x <= 3.3e-79) {
		tmp = x * y;
	} else if (x <= 1020000000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * (z + y)
    t_1 = (x * z) - z
    if (x <= (-2.6d-65)) then
        tmp = t_0
    else if (x <= 1.55d-138) then
        tmp = t_1
    else if (x <= 3.3d-79) then
        tmp = x * y
    else if (x <= 1020000000000.0d0) then
        tmp = t_1
    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 * (z + y);
	double t_1 = (x * z) - z;
	double tmp;
	if (x <= -2.6e-65) {
		tmp = t_0;
	} else if (x <= 1.55e-138) {
		tmp = t_1;
	} else if (x <= 3.3e-79) {
		tmp = x * y;
	} else if (x <= 1020000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	t_1 = (x * z) - z
	tmp = 0
	if x <= -2.6e-65:
		tmp = t_0
	elif x <= 1.55e-138:
		tmp = t_1
	elif x <= 3.3e-79:
		tmp = x * y
	elif x <= 1020000000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	t_1 = Float64(Float64(x * z) - z)
	tmp = 0.0
	if (x <= -2.6e-65)
		tmp = t_0;
	elseif (x <= 1.55e-138)
		tmp = t_1;
	elseif (x <= 3.3e-79)
		tmp = Float64(x * y);
	elseif (x <= 1020000000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	t_1 = (x * z) - z;
	tmp = 0.0;
	if (x <= -2.6e-65)
		tmp = t_0;
	elseif (x <= 1.55e-138)
		tmp = t_1;
	elseif (x <= 3.3e-79)
		tmp = x * y;
	elseif (x <= 1020000000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -2.6e-65], t$95$0, If[LessEqual[x, 1.55e-138], t$95$1, If[LessEqual[x, 3.3e-79], N[(x * y), $MachinePrecision], If[LessEqual[x, 1020000000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6000000000000001e-65 or 1.02e12 < x

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 98.1%

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

      1. +-commutative 98.1%

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

   4. Simplified 98.1%

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

   if -2.6000000000000001e-65 < x < 1.5499999999999999e-138 or 3.2999999999999998e-79 < x < 1.02e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.8%

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

      1. sub-neg 76.8%

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

      2. metadata-eval 76.8%

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

      3. distribute-rgt-in 76.8%

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

      4. neg-mul-1 76.8%

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

      5. sub-neg 76.8%

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

      6. *-commutative 76.8%

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

   4. Simplified 76.8%

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

   if 1.5499999999999999e-138 < x < 3.2999999999999998e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.4%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1020000000000:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]

Alternative 5: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-65}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138} \lor \neg \left(x \leq 3.3 \cdot 10^{-79}\right) \land x \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.65e-65)
   (* x y)
   (if (or (<= x 1.55e-138) (and (not (<= x 3.3e-79)) (<= x 3.4e-9)))
     (- z)
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.65e-65) {
		tmp = x * y;
	} else if ((x <= 1.55e-138) || (!(x <= 3.3e-79) && (x <= 3.4e-9))) {
		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 <= (-2.65d-65)) then
        tmp = x * y
    else if ((x <= 1.55d-138) .or. (.not. (x <= 3.3d-79)) .and. (x <= 3.4d-9)) 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 <= -2.65e-65) {
		tmp = x * y;
	} else if ((x <= 1.55e-138) || (!(x <= 3.3e-79) && (x <= 3.4e-9))) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.65e-65:
		tmp = x * y
	elif (x <= 1.55e-138) or (not (x <= 3.3e-79) and (x <= 3.4e-9)):
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.65e-65)
		tmp = Float64(x * y);
	elseif ((x <= 1.55e-138) || (!(x <= 3.3e-79) && (x <= 3.4e-9)))
		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 <= -2.65e-65)
		tmp = x * y;
	elseif ((x <= 1.55e-138) || (~((x <= 3.3e-79)) && (x <= 3.4e-9)))
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.65e-65], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 1.55e-138], And[N[Not[LessEqual[x, 3.3e-79]], $MachinePrecision], LessEqual[x, 3.4e-9]]], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.65000000000000019e-65 or 1.5499999999999999e-138 < x < 3.2999999999999998e-79 or 3.3999999999999998e-9 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf 47.3%

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

   if -2.65000000000000019e-65 < x < 1.5499999999999999e-138 or 3.2999999999999998e-79 < x < 3.3999999999999998e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. neg-mul-1 76.1%

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

   4. Simplified 76.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-65}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138} \lor \neg \left(x \leq 3.3 \cdot 10^{-79}\right) \land x \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

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 98.4%

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

2. Taylor expanded in x around 0 36.1%

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

   1. neg-mul-1 36.1%

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

4. Simplified 36.1%

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

5. Final simplification 36.1%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))