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

Percentage Accurate: 88.4% → 99.9%

Time: 7.5s

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: 88.4% 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: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+37} \lor \neg \left(z \leq 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (or (<= z -4.1e+37) (not (<= z 1e-16)))
     (* x (/ t_0 z))
     (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if ((z <= -4.1e+37) || !(z <= 1e-16)) {
		tmp = x * (t_0 / z);
	} else {
		tmp = t_0 * (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) :: t_0
    real(8) :: tmp
    t_0 = (y - z) + 1.0d0
    if ((z <= (-4.1d+37)) .or. (.not. (z <= 1d-16))) then
        tmp = x * (t_0 / z)
    else
        tmp = t_0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if ((z <= -4.1e+37) || !(z <= 1e-16)) {
		tmp = x * (t_0 / z);
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if (z <= -4.1e+37) or not (z <= 1e-16):
		tmp = x * (t_0 / z)
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if ((z <= -4.1e+37) || !(z <= 1e-16))
		tmp = Float64(x * Float64(t_0 / z));
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if ((z <= -4.1e+37) || ~((z <= 1e-16)))
		tmp = x * (t_0 / z);
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[Or[LessEqual[z, -4.1e+37], N[Not[LessEqual[z, 1e-16]], $MachinePrecision]], N[(x * N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0999999999999998e37 or 9.9999999999999998e-17 < z

   1. Initial program 72.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -4.0999999999999998e37 < z < 9.9999999999999998e-17

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+37} \lor \neg \left(z \leq 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-155}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -2.2e+58)
     (- x)
     (if (<= z -1.22e-155)
       t_0
       (if (<= z 1.6e-265)
         (/ x z)
         (if (<= z 2.8e-195)
           t_0
           (if (<= z 1.85e-26)
             (/ x z)
             (if (<= z 5e+67) (* x (/ y z)) (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2.2e+58) {
		tmp = -x;
	} else if (z <= -1.22e-155) {
		tmp = t_0;
	} else if (z <= 1.6e-265) {
		tmp = x / z;
	} else if (z <= 2.8e-195) {
		tmp = t_0;
	} else if (z <= 1.85e-26) {
		tmp = x / z;
	} else if (z <= 5e+67) {
		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 <= (-2.2d+58)) then
        tmp = -x
    else if (z <= (-1.22d-155)) then
        tmp = t_0
    else if (z <= 1.6d-265) then
        tmp = x / z
    else if (z <= 2.8d-195) then
        tmp = t_0
    else if (z <= 1.85d-26) then
        tmp = x / z
    else if (z <= 5d+67) 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 <= -2.2e+58) {
		tmp = -x;
	} else if (z <= -1.22e-155) {
		tmp = t_0;
	} else if (z <= 1.6e-265) {
		tmp = x / z;
	} else if (z <= 2.8e-195) {
		tmp = t_0;
	} else if (z <= 1.85e-26) {
		tmp = x / z;
	} else if (z <= 5e+67) {
		tmp = x * (y / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -2.2e+58:
		tmp = -x
	elif z <= -1.22e-155:
		tmp = t_0
	elif z <= 1.6e-265:
		tmp = x / z
	elif z <= 2.8e-195:
		tmp = t_0
	elif z <= 1.85e-26:
		tmp = x / z
	elif z <= 5e+67:
		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 <= -2.2e+58)
		tmp = Float64(-x);
	elseif (z <= -1.22e-155)
		tmp = t_0;
	elseif (z <= 1.6e-265)
		tmp = Float64(x / z);
	elseif (z <= 2.8e-195)
		tmp = t_0;
	elseif (z <= 1.85e-26)
		tmp = Float64(x / z);
	elseif (z <= 5e+67)
		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 <= -2.2e+58)
		tmp = -x;
	elseif (z <= -1.22e-155)
		tmp = t_0;
	elseif (z <= 1.6e-265)
		tmp = x / z;
	elseif (z <= 2.8e-195)
		tmp = t_0;
	elseif (z <= 1.85e-26)
		tmp = x / z;
	elseif (z <= 5e+67)
		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, -2.2e+58], (-x), If[LessEqual[z, -1.22e-155], t$95$0, If[LessEqual[z, 1.6e-265], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.8e-195], t$95$0, If[LessEqual[z, 1.85e-26], N[(x / z), $MachinePrecision], If[LessEqual[z, 5e+67], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], (-x)]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2000000000000001e58 or 4.99999999999999976e67 < z

   1. Initial program 70.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.9%

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

      1. neg-mul-1 78.9%

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

   7. Simplified 78.9%

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

   if -2.2000000000000001e58 < z < -1.22000000000000001e-155 or 1.6e-265 < z < 2.80000000000000003e-195

   1. Initial program 95.6%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-/l* 75.4%

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

   7. Applied egg-rr 75.4%

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

   if -1.22000000000000001e-155 < z < 1.6e-265 or 2.80000000000000003e-195 < z < 1.8499999999999999e-26

   1. Initial program 99.9%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 94.9%

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

   7. Simplified 94.9%

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

   8. Taylor expanded in y around 0 70.0%

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

   if 1.8499999999999999e-26 < z < 4.99999999999999976e67

   1. Initial program 93.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 59.7%

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

      1. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+59}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-148}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -1.55e+59)
     (- x)
     (if (<= z -8e-148)
       t_0
       (if (<= z 3.5e-36) (/ x z) (if (<= z 4.5e+67) t_0 (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -1.55e+59) {
		tmp = -x;
	} else if (z <= -8e-148) {
		tmp = t_0;
	} else if (z <= 3.5e-36) {
		tmp = x / z;
	} else if (z <= 4.5e+67) {
		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 = x * (y / z)
    if (z <= (-1.55d+59)) then
        tmp = -x
    else if (z <= (-8d-148)) then
        tmp = t_0
    else if (z <= 3.5d-36) then
        tmp = x / z
    else if (z <= 4.5d+67) 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 = x * (y / z);
	double tmp;
	if (z <= -1.55e+59) {
		tmp = -x;
	} else if (z <= -8e-148) {
		tmp = t_0;
	} else if (z <= 3.5e-36) {
		tmp = x / z;
	} else if (z <= 4.5e+67) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -1.55e+59:
		tmp = -x
	elif z <= -8e-148:
		tmp = t_0
	elif z <= 3.5e-36:
		tmp = x / z
	elif z <= 4.5e+67:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -1.55e+59)
		tmp = Float64(-x);
	elseif (z <= -8e-148)
		tmp = t_0;
	elseif (z <= 3.5e-36)
		tmp = Float64(x / z);
	elseif (z <= 4.5e+67)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -1.55e+59)
		tmp = -x;
	elseif (z <= -8e-148)
		tmp = t_0;
	elseif (z <= 3.5e-36)
		tmp = x / z;
	elseif (z <= 4.5e+67)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+59], (-x), If[LessEqual[z, -8e-148], t$95$0, If[LessEqual[z, 3.5e-36], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.5e+67], t$95$0, (-x)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000007e59 or 4.4999999999999998e67 < z

   1. Initial program 70.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.9%

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

      1. neg-mul-1 78.9%

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

   7. Simplified 78.9%

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

   if -1.55000000000000007e59 < z < -7.99999999999999949e-148 or 3.5e-36 < z < 4.4999999999999998e67

   1. Initial program 93.7%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 71.5%

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

   7. Simplified 71.5%

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

   if -7.99999999999999949e-148 < z < 3.5e-36

   1. Initial program 99.9%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 91.9%

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

   7. Simplified 91.9%

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

   8. Taylor expanded in y around 0 65.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+59}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+44)
   (* y (/ x z))
   (if (<= y 2.5e+22) (- (/ x z) x) (* x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+44) {
		tmp = y * (x / z);
	} else if (y <= 2.5e+22) {
		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 <= (-2.8d+44)) then
        tmp = y * (x / z)
    else if (y <= 2.5d+22) 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 <= -2.8e+44) {
		tmp = y * (x / z);
	} else if (y <= 2.5e+22) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+44:
		tmp = y * (x / z)
	elif y <= 2.5e+22:
		tmp = (x / z) - x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+44)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 2.5e+22)
		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 <= -2.8e+44)
		tmp = y * (x / z);
	elseif (y <= 2.5e+22)
		tmp = (x / z) - x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+44], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+22], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e44

   1. Initial program 87.1%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 77.2%

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

   7. Applied egg-rr 77.2%

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

   if -2.8000000000000001e44 < y < 2.4999999999999998e22

   1. Initial program 82.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 96.6%

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

   8. Taylor expanded in z around 0 96.6%

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

      1. neg-mul-1 96.6%

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

      2. +-commutative 96.6%

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

      3. unsub-neg 96.6%

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

   10. Simplified 96.6%

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

   if 2.4999999999999998e22 < y

   1. Initial program 96.4%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around inf 86.9%

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

      1. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+44)
   (* y (/ x z))
   (if (<= y 3e+23) (- (/ x z) x) (/ x (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+44) {
		tmp = y * (x / z);
	} else if (y <= 3e+23) {
		tmp = (x / z) - x;
	} else {
		tmp = x / (z / 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 (y <= (-2.8d+44)) then
        tmp = y * (x / z)
    else if (y <= 3d+23) then
        tmp = (x / z) - x
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+44) {
		tmp = y * (x / z);
	} else if (y <= 3e+23) {
		tmp = (x / z) - x;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+44:
		tmp = y * (x / z)
	elif y <= 3e+23:
		tmp = (x / z) - x
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+44)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3e+23)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+44)
		tmp = y * (x / z);
	elseif (y <= 3e+23)
		tmp = (x / z) - x;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+44], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+23], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e44

   1. Initial program 87.1%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 77.2%

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

   7. Applied egg-rr 77.2%

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

   if -2.8000000000000001e44 < y < 3.0000000000000001e23

   1. Initial program 82.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 96.6%

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

   8. Taylor expanded in z around 0 96.6%

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

      1. neg-mul-1 96.6%

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

      2. +-commutative 96.6%

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

      3. unsub-neg 96.6%

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

   10. Simplified 96.6%

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

   if 3.0000000000000001e23 < y

   1. Initial program 96.4%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

      1. clear-num 93.0%

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

      2. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in y around inf 81.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+44)
   (* y (/ x z))
   (if (<= y 3.3e+22) (- (/ x z) x) (/ (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+44) {
		tmp = y * (x / z);
	} else if (y <= 3.3e+22) {
		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 <= (-2.8d+44)) then
        tmp = y * (x / z)
    else if (y <= 3.3d+22) 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 <= -2.8e+44) {
		tmp = y * (x / z);
	} else if (y <= 3.3e+22) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+44:
		tmp = y * (x / z)
	elif y <= 3.3e+22:
		tmp = (x / z) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+44)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3.3e+22)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+44)
		tmp = y * (x / z);
	elseif (y <= 3.3e+22)
		tmp = (x / z) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+44], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+22], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e44

   1. Initial program 87.1%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 77.2%

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

   7. Applied egg-rr 77.2%

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

   if -2.8000000000000001e44 < y < 3.2999999999999998e22

   1. Initial program 82.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 96.6%

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

   8. Taylor expanded in z around 0 96.6%

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

      1. neg-mul-1 96.6%

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

      2. +-commutative 96.6%

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

      3. unsub-neg 96.6%

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

   10. Simplified 96.6%

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

   if 3.2999999999999998e22 < y

   1. Initial program 96.4%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around inf 86.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;x \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= x 3.2e+21) (/ (* x t_0) z) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 3.2e+21) {
		tmp = (x * t_0) / z;
	} else {
		tmp = x / (z / 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 = (y - z) + 1.0d0
    if (x <= 3.2d+21) then
        tmp = (x * t_0) / z
    else
        tmp = x / (z / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 3.2e+21) {
		tmp = (x * t_0) / z;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if x <= 3.2e+21:
		tmp = (x * t_0) / z
	else:
		tmp = x / (z / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (x <= 3.2e+21)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(x / Float64(z / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (x <= 3.2e+21)
		tmp = (x * t_0) / z;
	else
		tmp = x / (z / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, 3.2e+21], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 3.2e21

   1. Initial program 91.8%

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

   if 3.2e21 < x

   1. Initial program 69.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00024 \lor \neg \left(z \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.00024) (not (<= z 5e-17))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00024) || !(z <= 5e-17)) {
		tmp = -x;
	} 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 ((z <= (-0.00024d0)) .or. (.not. (z <= 5d-17))) then
        tmp = -x
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00024) || !(z <= 5e-17)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.00024) or not (z <= 5e-17):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.00024) || !(z <= 5e-17))
		tmp = Float64(-x);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.00024) || ~((z <= 5e-17)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.00024], N[Not[LessEqual[z, 5e-17]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000006e-4 or 4.9999999999999999e-17 < z

   1. Initial program 74.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.9%

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

      1. neg-mul-1 65.9%

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

   7. Simplified 65.9%

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

   if -2.40000000000000006e-4 < z < 4.9999999999999999e-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* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 92.8%

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

   7. Simplified 92.8%

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

   8. Taylor expanded in y around 0 57.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00024 \lor \neg \left(z \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.9% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.8%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

   \[\leadsto x \cdot \frac{\left(y - z\right) + 1}{z} \]
6. Add Preprocessing

Alternative 10: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.8%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

   1. clear-num 96.4%

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

   2. un-div-inv 96.9%

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

6. Applied egg-rr 96.9%

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

7. Final simplification 96.9%

   \[\leadsto \frac{x}{\frac{z}{\left(y - z\right) + 1}} \]
8. Add Preprocessing

Alternative 11: 38.4% 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 86.8%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in z around inf 35.9%

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

   1. neg-mul-1 35.9%

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

7. Simplified 35.9%

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

8. Final simplification 35.9%

   \[\leadsto -x \]
9. Add Preprocessing

Alternative 12: 3.0% accurate, 9.0× 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 x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.8%

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

3. Taylor expanded in z around inf 25.6%

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

   1. mul-1-neg 25.6%

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

   2. distribute-rgt-neg-in 25.6%

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

5. Simplified 25.6%

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

   1. associate-/l* 35.9%

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

   2. add-sqr-sqrt 18.3%

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

   3. sqrt-unprod 10.8%

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

   4. sqr-neg 10.8%

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

   5. sqrt-unprod 1.8%

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

   6. add-sqr-sqrt 3.1%

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

7. Applied egg-rr 3.1%

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

   1. *-inverses 3.1%

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

   2. *-rgt-identity 3.1%

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

9. Simplified 3.1%

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

10. Final simplification 3.1%

    \[\leadsto x \]
11. Add Preprocessing

Developer target: 99.5% accurate, 0.4× 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 2024040 
(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))