Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 87.9% → 99.8%

Time: 6.4s

Alternatives: 12

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 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 - z) + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((y - z) + 1.0)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 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 - z) + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((y - z) + 1.0)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+35} \lor \neg \left(z \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+35) (not (<= z 5e+30)))
   (- (* x (/ y z)) x)
   (* (/ x z) (+ 1.0 (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+35) || !(z <= 5e+30)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * (1.0 + (y - 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 ((z <= (-1d+35)) .or. (.not. (z <= 5d+30))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) * (1.0d0 + (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+35) || !(z <= 5e+30)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+35) or not (z <= 5e+30):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) * (1.0 + (y - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+35) || !(z <= 5e+30))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+35) || ~((z <= 5e+30)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) * (1.0 + (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+35], N[Not[LessEqual[z, 5e+30]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999997e34 or 4.9999999999999998e30 < z

   1. Initial program 75.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 88.8%

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

      1. neg-mul-1 88.8%

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

      2. +-commutative 88.8%

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

      3. unsub-neg 88.8%

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

      4. associate-/l* 93.0%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 99.9%

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

   if -9.9999999999999997e34 < z < 4.9999999999999998e30

   1. Initial program 99.9%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+35} \lor \neg \left(z \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \]

Alternative 2: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+32}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+74}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -8.2e+32)
     (- x)
     (if (<= z -3.2e-66)
       t_0
       (if (<= z -4.5e-260)
         (/ x z)
         (if (<= z 1.2e-180)
           t_0
           (if (<= z 9e-17)
             (/ x z)
             (if (<= z 8.5e+37)
               t_0
               (if (<= z 1.66e+74)
                 (- x)
                 (if (<= z 5e+141) (* x (/ y z)) (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -8.2e+32) {
		tmp = -x;
	} else if (z <= -3.2e-66) {
		tmp = t_0;
	} else if (z <= -4.5e-260) {
		tmp = x / z;
	} else if (z <= 1.2e-180) {
		tmp = t_0;
	} else if (z <= 9e-17) {
		tmp = x / z;
	} else if (z <= 8.5e+37) {
		tmp = t_0;
	} else if (z <= 1.66e+74) {
		tmp = -x;
	} else if (z <= 5e+141) {
		tmp = x * (y / z);
	} else {
		tmp = -x;
	}
	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 = y * (x / z)
    if (z <= (-8.2d+32)) then
        tmp = -x
    else if (z <= (-3.2d-66)) then
        tmp = t_0
    else if (z <= (-4.5d-260)) then
        tmp = x / z
    else if (z <= 1.2d-180) then
        tmp = t_0
    else if (z <= 9d-17) then
        tmp = x / z
    else if (z <= 8.5d+37) then
        tmp = t_0
    else if (z <= 1.66d+74) then
        tmp = -x
    else if (z <= 5d+141) then
        tmp = x * (y / z)
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -8.2e+32) {
		tmp = -x;
	} else if (z <= -3.2e-66) {
		tmp = t_0;
	} else if (z <= -4.5e-260) {
		tmp = x / z;
	} else if (z <= 1.2e-180) {
		tmp = t_0;
	} else if (z <= 9e-17) {
		tmp = x / z;
	} else if (z <= 8.5e+37) {
		tmp = t_0;
	} else if (z <= 1.66e+74) {
		tmp = -x;
	} else if (z <= 5e+141) {
		tmp = x * (y / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -8.2e+32:
		tmp = -x
	elif z <= -3.2e-66:
		tmp = t_0
	elif z <= -4.5e-260:
		tmp = x / z
	elif z <= 1.2e-180:
		tmp = t_0
	elif z <= 9e-17:
		tmp = x / z
	elif z <= 8.5e+37:
		tmp = t_0
	elif z <= 1.66e+74:
		tmp = -x
	elif z <= 5e+141:
		tmp = x * (y / z)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -8.2e+32)
		tmp = Float64(-x);
	elseif (z <= -3.2e-66)
		tmp = t_0;
	elseif (z <= -4.5e-260)
		tmp = Float64(x / z);
	elseif (z <= 1.2e-180)
		tmp = t_0;
	elseif (z <= 9e-17)
		tmp = Float64(x / z);
	elseif (z <= 8.5e+37)
		tmp = t_0;
	elseif (z <= 1.66e+74)
		tmp = Float64(-x);
	elseif (z <= 5e+141)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -8.2e+32)
		tmp = -x;
	elseif (z <= -3.2e-66)
		tmp = t_0;
	elseif (z <= -4.5e-260)
		tmp = x / z;
	elseif (z <= 1.2e-180)
		tmp = t_0;
	elseif (z <= 9e-17)
		tmp = x / z;
	elseif (z <= 8.5e+37)
		tmp = t_0;
	elseif (z <= 1.66e+74)
		tmp = -x;
	elseif (z <= 5e+141)
		tmp = x * (y / z);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+32], (-x), If[LessEqual[z, -3.2e-66], t$95$0, If[LessEqual[z, -4.5e-260], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.2e-180], t$95$0, If[LessEqual[z, 9e-17], N[(x / z), $MachinePrecision], If[LessEqual[z, 8.5e+37], t$95$0, If[LessEqual[z, 1.66e+74], (-x), If[LessEqual[z, 5e+141], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], (-x)]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.19999999999999961e32 or 8.4999999999999999e37 < z < 1.66000000000000001e74 or 5.00000000000000025e141 < z

   1. Initial program 72.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 76.1%

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

      1. neg-mul-1 76.1%

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

   6. Simplified 76.1%

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

   if -8.19999999999999961e32 < z < -3.19999999999999982e-66 or -4.4999999999999997e-260 < z < 1.1999999999999999e-180 or 8.99999999999999957e-17 < z < 8.4999999999999999e37

   1. Initial program 99.8%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-/l* 62.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   6. Simplified 62.2%

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

      1. associate-/r/ 73.4%

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

   8. Applied egg-rr 73.4%

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

   if -3.19999999999999982e-66 < z < -4.4999999999999997e-260 or 1.1999999999999999e-180 < z < 8.99999999999999957e-17

   1. Initial program 99.9%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 72.3%

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

   5. Taylor expanded in z around 0 72.3%

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

   if 1.66000000000000001e74 < z < 5.00000000000000025e141

   1. Initial program 92.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-/l* 44.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

      2. associate-/r/ 76.0%

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

   6. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+32}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+74}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-62}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 10^{-181}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -5.2e+32)
     (- x)
     (if (<= z -3.1e-62)
       t_0
       (if (<= z -1.6e-259)
         (/ x z)
         (if (<= z 1e-181)
           t_0
           (if (<= z 3.5e-16) (/ x z) (if (<= z 1.65e+38) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -5.2e+32) {
		tmp = -x;
	} else if (z <= -3.1e-62) {
		tmp = t_0;
	} else if (z <= -1.6e-259) {
		tmp = x / z;
	} else if (z <= 1e-181) {
		tmp = t_0;
	} else if (z <= 3.5e-16) {
		tmp = x / z;
	} else if (z <= 1.65e+38) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	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 = y * (x / z)
    if (z <= (-5.2d+32)) then
        tmp = -x
    else if (z <= (-3.1d-62)) then
        tmp = t_0
    else if (z <= (-1.6d-259)) then
        tmp = x / z
    else if (z <= 1d-181) then
        tmp = t_0
    else if (z <= 3.5d-16) then
        tmp = x / z
    else if (z <= 1.65d+38) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -5.2e+32) {
		tmp = -x;
	} else if (z <= -3.1e-62) {
		tmp = t_0;
	} else if (z <= -1.6e-259) {
		tmp = x / z;
	} else if (z <= 1e-181) {
		tmp = t_0;
	} else if (z <= 3.5e-16) {
		tmp = x / z;
	} else if (z <= 1.65e+38) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -5.2e+32:
		tmp = -x
	elif z <= -3.1e-62:
		tmp = t_0
	elif z <= -1.6e-259:
		tmp = x / z
	elif z <= 1e-181:
		tmp = t_0
	elif z <= 3.5e-16:
		tmp = x / z
	elif z <= 1.65e+38:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -5.2e+32)
		tmp = Float64(-x);
	elseif (z <= -3.1e-62)
		tmp = t_0;
	elseif (z <= -1.6e-259)
		tmp = Float64(x / z);
	elseif (z <= 1e-181)
		tmp = t_0;
	elseif (z <= 3.5e-16)
		tmp = Float64(x / z);
	elseif (z <= 1.65e+38)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -5.2e+32)
		tmp = -x;
	elseif (z <= -3.1e-62)
		tmp = t_0;
	elseif (z <= -1.6e-259)
		tmp = x / z;
	elseif (z <= 1e-181)
		tmp = t_0;
	elseif (z <= 3.5e-16)
		tmp = x / z;
	elseif (z <= 1.65e+38)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+32], (-x), If[LessEqual[z, -3.1e-62], t$95$0, If[LessEqual[z, -1.6e-259], N[(x / z), $MachinePrecision], If[LessEqual[z, 1e-181], t$95$0, If[LessEqual[z, 3.5e-16], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.65e+38], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000004e32 or 1.65e38 < z

   1. Initial program 74.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 71.1%

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

      1. neg-mul-1 71.1%

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

   6. Simplified 71.1%

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

   if -5.2000000000000004e32 < z < -3.0999999999999999e-62 or -1.59999999999999994e-259 < z < 1.00000000000000005e-181 or 3.50000000000000017e-16 < z < 1.65e38

   1. Initial program 99.8%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-/l* 62.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   6. Simplified 62.2%

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

      1. associate-/r/ 73.4%

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

   8. Applied egg-rr 73.4%

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

   if -3.0999999999999999e-62 < z < -1.59999999999999994e-259 or 1.00000000000000005e-181 < z < 3.50000000000000017e-16

   1. Initial program 99.9%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 72.3%

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

   5. Taylor expanded in z around 0 72.3%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 10^{-181}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 94.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.5 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.5e-43))) (- (* x (/ y z)) x) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.5e-43)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) - x;
	}
	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 ((y <= (-1.0d0)) .or. (.not. (y <= 2.5d-43))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.5e-43)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 2.5e-43):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 2.5e-43))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 2.5e-43)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 2.5e-43]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.50000000000000009e-43 < y

   1. Initial program 86.8%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 90.2%

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

      1. neg-mul-1 90.2%

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

      2. +-commutative 90.2%

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

      3. unsub-neg 90.2%

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

      4. associate-/l* 93.9%

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

      5. associate-/r/ 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in y around inf 94.2%

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

   if -1 < y < 2.50000000000000009e-43

   1. Initial program 90.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 99.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.5 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 5: 94.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (- (/ x (/ z y)) x)
   (if (<= y 2.5e-43) (- (/ x z) x) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = (x / (z / y)) - x;
	} else if (y <= 2.5e-43) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * (y / z)) - x;
	}
	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 (y <= (-1.0d0)) then
        tmp = (x / (z / y)) - x
    else if (y <= 2.5d-43) then
        tmp = (x / z) - x
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = (x / (z / y)) - x;
	} else if (y <= 2.5e-43) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = (x / (z / y)) - x
	elif y <= 2.5e-43:
		tmp = (x / z) - x
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	elseif (y <= 2.5e-43)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = (x / (z / y)) - x;
	elseif (y <= 2.5e-43)
		tmp = (x / z) - x;
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 2.5e-43], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 86.9%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 88.4%

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

      1. neg-mul-1 88.4%

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

      2. +-commutative 88.4%

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

      3. unsub-neg 88.4%

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

      4. associate-/l* 95.5%

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

      5. associate-/r/ 96.9%

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

   6. Simplified 96.9%

      \[\leadsto \color{blue}{\frac{1 + y}{z} \cdot x - x} \]
   7. Step-by-step derivation

      1. *-commutative 96.9%

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

      2. clear-num 96.8%

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

      3. un-div-inv 97.3%

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

   8. Applied egg-rr 97.3%

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

   9. Taylor expanded in y around inf 94.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} - x \]

   if -1 < y < 2.50000000000000009e-43

   1. Initial program 90.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 99.1%

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

   if 2.50000000000000009e-43 < y

   1. Initial program 86.6%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 91.9%

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

      1. neg-mul-1 91.9%

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

      2. +-commutative 91.9%

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

      3. unsub-neg 91.9%

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

      4. associate-/l* 92.4%

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

      5. associate-/r/ 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in y around inf 94.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 6: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1)
   (- (* x (/ y z)) x)
   (if (<= z 5.2e-16) (/ (+ x (* x y)) z) (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 5.2e-16) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / (z / y)) - x;
	}
	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 (z <= (-1.1d0)) then
        tmp = (x * (y / z)) - x
    else if (z <= 5.2d-16) then
        tmp = (x + (x * y)) / z
    else
        tmp = (x / (z / y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 5.2e-16) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1:
		tmp = (x * (y / z)) - x
	elif z <= 5.2e-16:
		tmp = (x + (x * y)) / z
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (z <= 5.2e-16)
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	else
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1)
		tmp = (x * (y / z)) - x;
	elseif (z <= 5.2e-16)
		tmp = (x + (x * y)) / z;
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 5.2e-16], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001

   1. Initial program 79.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 87.3%

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

      1. neg-mul-1 87.3%

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

      2. +-commutative 87.3%

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

      3. unsub-neg 87.3%

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

      4. associate-/l* 96.2%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 98.8%

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

   if -1.1000000000000001 < z < 5.1999999999999997e-16

   1. Initial program 99.9%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 99.5%

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

      1. *-commutative 99.5%

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

      2. distribute-lft-in 99.5%

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

      3. *-rgt-identity 99.5%

         \[\leadsto \frac{\color{blue}{x} + x \cdot y}{z} \]

   6. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{x + x \cdot y}{z}} \]

   if 5.1999999999999997e-16 < z

   1. Initial program 76.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 92.1%

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

      1. neg-mul-1 92.1%

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

      2. +-commutative 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-/l* 91.6%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{1 + y}{z} \cdot x - x} \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in y around inf 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]

Alternative 7: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -320 \lor \neg \left(y \leq 4.7 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -320.0) (not (<= y 4.7e+39))) (* x (/ y z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -320.0) || !(y <= 4.7e+39)) {
		tmp = x * (y / z);
	} else {
		tmp = (x / z) - x;
	}
	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 ((y <= (-320.0d0)) .or. (.not. (y <= 4.7d+39))) then
        tmp = x * (y / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -320.0) || !(y <= 4.7e+39)) {
		tmp = x * (y / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -320.0) or not (y <= 4.7e+39):
		tmp = x * (y / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -320.0) || !(y <= 4.7e+39))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -320.0) || ~((y <= 4.7e+39)))
		tmp = x * (y / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -320.0], N[Not[LessEqual[y, 4.7e+39]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -320 or 4.6999999999999999e39 < y

   1. Initial program 87.6%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 72.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

      2. associate-/r/ 74.8%

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

   6. Simplified 74.8%

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

   if -320 < y < 4.6999999999999999e39

   1. Initial program 89.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 99.3%

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

      1. neg-mul-1 99.3%

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

      2. +-commutative 99.3%

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

      3. unsub-neg 99.3%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 97.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -320 \lor \neg \left(y \leq 4.7 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 8: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -310:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -310.0)
   (/ x (/ z y))
   (if (<= y 3.6e+39) (- (/ x z) x) (* x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -310.0) {
		tmp = x / (z / y);
	} else if (y <= 3.6e+39) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / 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 (y <= (-310.0d0)) then
        tmp = x / (z / y)
    else if (y <= 3.6d+39) then
        tmp = (x / z) - x
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -310.0) {
		tmp = x / (z / y);
	} else if (y <= 3.6e+39) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -310.0:
		tmp = x / (z / y)
	elif y <= 3.6e+39:
		tmp = (x / z) - x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -310.0)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 3.6e+39)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -310.0)
		tmp = x / (z / y);
	elseif (y <= 3.6e+39)
		tmp = (x / z) - x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -310.0], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+39], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -310

   1. Initial program 86.5%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-/l* 74.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   6. Simplified 74.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   if -310 < y < 3.59999999999999984e39

   1. Initial program 89.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 99.3%

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

      1. neg-mul-1 99.3%

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

      2. +-commutative 99.3%

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

      3. unsub-neg 99.3%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 97.1%

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

   if 3.59999999999999984e39 < y

   1. Initial program 88.7%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 72.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

      2. associate-/r/ 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -310:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z}{1 + y}} - x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ x (/ z (+ 1.0 y))) x))

C

double code(double x, double y, double z) {
	return (x / (z / (1.0 + y))) - x;
}

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 / (1.0d0 + y))) - x
end function

Java

public static double code(double x, double y, double z) {
	return (x / (z / (1.0 + y))) - x;
}

Python

def code(x, y, z):
	return (x / (z / (1.0 + y))) - x

Julia

function code(x, y, z)
	return Float64(Float64(x / Float64(z / Float64(1.0 + y))) - x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x / (z / (1.0 + y))) - x;
end

Wolfram

code[x_, y_, z_] := N[(N[(x / N[(z / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 88.4%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in z around 0 94.7%

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

   1. neg-mul-1 94.7%

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

   2. +-commutative 94.7%

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

   3. unsub-neg 94.7%

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

   4. associate-/l* 96.6%

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

   5. associate-/r/ 98.0%

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

6. Simplified 98.0%

   \[\leadsto \color{blue}{\frac{1 + y}{z} \cdot x - x} \]
7. Step-by-step derivation

   1. *-commutative 98.0%

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

   2. clear-num 97.9%

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

   3. un-div-inv 98.2%

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

8. Applied egg-rr 98.2%

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

9. Final simplification 98.2%

   \[\leadsto \frac{x}{\frac{z}{1 + y}} - x \]

Alternative 10: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{1 + y}{z} - x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x (/ (+ 1.0 y) z)) x))

C

double code(double x, double y, double z) {
	return (x * ((1.0 + y) / z)) - x;
}

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 * ((1.0d0 + y) / z)) - x
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((1.0 + y) / z)) - x;
}

Python

def code(x, y, z):
	return (x * ((1.0 + y) / z)) - x

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(1.0 + y) / z)) - x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((1.0 + y) / z)) - x;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(1.0 + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 88.4%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in z around 0 94.7%

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

   1. neg-mul-1 94.7%

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

   2. +-commutative 94.7%

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

   3. unsub-neg 94.7%

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

   4. associate-/l* 96.6%

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

   5. associate-/r/ 98.0%

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

6. Simplified 98.0%

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

7. Final simplification 98.0%

   \[\leadsto x \cdot \frac{1 + y}{z} - x \]

Alternative 11: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 1.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	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 (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x;
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 77.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. neg-mul-1 65.8%

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

   6. Simplified 65.8%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 57.8%

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

   5. Taylor expanded in z around 0 57.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 12: 38.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 88.4%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in z around inf 34.7%

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

   1. neg-mul-1 34.7%

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

6. Simplified 34.7%

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

7. Final simplification 34.7%

   \[\leadsto -x \]

Developer target: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / 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 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / 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 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023258 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))