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

Percentage Accurate: 88.6% → 98.3%

Time: 5.0s

Alternatives: 10

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: 88.6% 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: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14.5 \lor \neg \left(z \leq 1.35 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -14.5) (not (<= z 1.35e-16)))
   (- (* x (/ y z)) x)
   (/ (* x (+ 1.0 y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14.5) || !(z <= 1.35e-16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (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 <= (-14.5d0)) .or. (.not. (z <= 1.35d-16))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x * (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 <= -14.5) || !(z <= 1.35e-16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (1.0 + y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -14.5) or not (z <= 1.35e-16):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x * (1.0 + y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -14.5) || !(z <= 1.35e-16))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x * Float64(1.0 + y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -14.5) || ~((z <= 1.35e-16)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x * (1.0 + y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -14.5], N[Not[LessEqual[z, 1.35e-16]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -14.5 or 1.35e-16 < z

   1. Initial program 75.9%

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

   2. Taylor expanded in z around 0 88.6%

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

      1. neg-mul-1 88.6%

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

      2. +-commutative 88.6%

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

      3. unsub-neg 88.6%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in y around inf 87.7%

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

      1. associate-*r/ 99.0%

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

   7. Simplified 99.0%

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

   if -14.5 < z < 1.35e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14.5 \lor \neg \left(z \leq 1.35 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z}\\ \end{array} \]

Alternative 2: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+54}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)))
   (if (<= z -8.5e+54)
     (- x)
     (if (<= z -1.28e-123)
       t_0
       (if (<= z 2.8e-277)
         (/ x z)
         (if (<= z 6e-197)
           t_0
           (if (<= z 1.92e-83)
             (/ x z)
             (if (<= z 1.42e-56)
               t_0
               (if (<= z 8.5e-17)
                 (/ x z)
                 (if (<= z 9.8e+107) t_0 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (z <= -8.5e+54) {
		tmp = -x;
	} else if (z <= -1.28e-123) {
		tmp = t_0;
	} else if (z <= 2.8e-277) {
		tmp = x / z;
	} else if (z <= 6e-197) {
		tmp = t_0;
	} else if (z <= 1.92e-83) {
		tmp = x / z;
	} else if (z <= 1.42e-56) {
		tmp = t_0;
	} else if (z <= 8.5e-17) {
		tmp = x / z;
	} else if (z <= 9.8e+107) {
		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 / z) * y
    if (z <= (-8.5d+54)) then
        tmp = -x
    else if (z <= (-1.28d-123)) then
        tmp = t_0
    else if (z <= 2.8d-277) then
        tmp = x / z
    else if (z <= 6d-197) then
        tmp = t_0
    else if (z <= 1.92d-83) then
        tmp = x / z
    else if (z <= 1.42d-56) then
        tmp = t_0
    else if (z <= 8.5d-17) then
        tmp = x / z
    else if (z <= 9.8d+107) 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 / z) * y;
	double tmp;
	if (z <= -8.5e+54) {
		tmp = -x;
	} else if (z <= -1.28e-123) {
		tmp = t_0;
	} else if (z <= 2.8e-277) {
		tmp = x / z;
	} else if (z <= 6e-197) {
		tmp = t_0;
	} else if (z <= 1.92e-83) {
		tmp = x / z;
	} else if (z <= 1.42e-56) {
		tmp = t_0;
	} else if (z <= 8.5e-17) {
		tmp = x / z;
	} else if (z <= 9.8e+107) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	tmp = 0
	if z <= -8.5e+54:
		tmp = -x
	elif z <= -1.28e-123:
		tmp = t_0
	elif z <= 2.8e-277:
		tmp = x / z
	elif z <= 6e-197:
		tmp = t_0
	elif z <= 1.92e-83:
		tmp = x / z
	elif z <= 1.42e-56:
		tmp = t_0
	elif z <= 8.5e-17:
		tmp = x / z
	elif z <= 9.8e+107:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * y)
	tmp = 0.0
	if (z <= -8.5e+54)
		tmp = Float64(-x);
	elseif (z <= -1.28e-123)
		tmp = t_0;
	elseif (z <= 2.8e-277)
		tmp = Float64(x / z);
	elseif (z <= 6e-197)
		tmp = t_0;
	elseif (z <= 1.92e-83)
		tmp = Float64(x / z);
	elseif (z <= 1.42e-56)
		tmp = t_0;
	elseif (z <= 8.5e-17)
		tmp = Float64(x / z);
	elseif (z <= 9.8e+107)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * y;
	tmp = 0.0;
	if (z <= -8.5e+54)
		tmp = -x;
	elseif (z <= -1.28e-123)
		tmp = t_0;
	elseif (z <= 2.8e-277)
		tmp = x / z;
	elseif (z <= 6e-197)
		tmp = t_0;
	elseif (z <= 1.92e-83)
		tmp = x / z;
	elseif (z <= 1.42e-56)
		tmp = t_0;
	elseif (z <= 8.5e-17)
		tmp = x / z;
	elseif (z <= 9.8e+107)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -8.5e+54], (-x), If[LessEqual[z, -1.28e-123], t$95$0, If[LessEqual[z, 2.8e-277], N[(x / z), $MachinePrecision], If[LessEqual[z, 6e-197], t$95$0, If[LessEqual[z, 1.92e-83], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.42e-56], t$95$0, If[LessEqual[z, 8.5e-17], N[(x / z), $MachinePrecision], If[LessEqual[z, 9.8e+107], t$95$0, (-x)]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999995e54 or 9.8000000000000003e107 < z

   1. Initial program 70.3%

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

   2. Taylor expanded in z around inf 85.7%

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

      1. neg-mul-1 85.7%

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

   4. Simplified 85.7%

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

   if -8.4999999999999995e54 < z < -1.28000000000000002e-123 or 2.79999999999999976e-277 < z < 6.00000000000000051e-197 or 1.92000000000000014e-83 < z < 1.42e-56 or 8.5e-17 < z < 9.8000000000000003e107

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 70.9%

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

      2. associate-/r/ 73.7%

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

   4. Simplified 73.7%

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

   if -1.28000000000000002e-123 < z < 2.79999999999999976e-277 or 6.00000000000000051e-197 < z < 1.92000000000000014e-83 or 1.42e-56 < z < 8.5e-17

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

      4. associate-/l* 95.7%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 77.3%

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

   6. Taylor expanded in z around 0 77.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+54}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -14 \lor \neg \left(y \leq 6.5 \cdot 10^{+83}\right) \land \left(y \leq 1.22 \cdot 10^{+151} \lor \neg \left(y \leq 4.1 \cdot 10^{+193}\right)\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -14.0)
         (and (not (<= y 6.5e+83))
              (or (<= y 1.22e+151) (not (<= y 4.1e+193)))))
   (* (/ x z) y)
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -14.0) || (!(y <= 6.5e+83) && ((y <= 1.22e+151) || !(y <= 4.1e+193)))) {
		tmp = (x / z) * y;
	} 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 <= (-14.0d0)) .or. (.not. (y <= 6.5d+83)) .and. (y <= 1.22d+151) .or. (.not. (y <= 4.1d+193))) then
        tmp = (x / z) * y
    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 <= -14.0) || (!(y <= 6.5e+83) && ((y <= 1.22e+151) || !(y <= 4.1e+193)))) {
		tmp = (x / z) * y;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -14.0) or (not (y <= 6.5e+83) and ((y <= 1.22e+151) or not (y <= 4.1e+193))):
		tmp = (x / z) * y
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -14.0) || (!(y <= 6.5e+83) && ((y <= 1.22e+151) || !(y <= 4.1e+193))))
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -14.0) || (~((y <= 6.5e+83)) && ((y <= 1.22e+151) || ~((y <= 4.1e+193)))))
		tmp = (x / z) * y;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -14.0], And[N[Not[LessEqual[y, 6.5e+83]], $MachinePrecision], Or[LessEqual[y, 1.22e+151], N[Not[LessEqual[y, 4.1e+193]], $MachinePrecision]]]], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -14 or 6.5000000000000003e83 < y < 1.22000000000000005e151 or 4.0999999999999997e193 < y

   1. Initial program 88.8%

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

   2. Taylor expanded in y around inf 78.1%

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

      1. associate-/l* 76.2%

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

      2. associate-/r/ 79.4%

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

   4. Simplified 79.4%

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

   if -14 < y < 6.5000000000000003e83 or 1.22000000000000005e151 < y < 4.0999999999999997e193

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 98.7%

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

      1. neg-mul-1 98.7%

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

      2. +-commutative 98.7%

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

      3. unsub-neg 98.7%

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

      4. associate-/l* 99.4%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14 \lor \neg \left(y \leq 6.5 \cdot 10^{+83}\right) \land \left(y \leq 1.22 \cdot 10^{+151} \lor \neg \left(y \leq 4.1 \cdot 10^{+193}\right)\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 4: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ t_1 := \frac{x}{z} - x\\ \mathbf{if}\;y \leq -10:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)) (t_1 (- (/ x z) x)))
   (if (<= y -10.0)
     t_0
     (if (<= y 3.1e+84)
       t_1
       (if (<= y 1.22e+151) t_0 (if (<= y 4.1e+193) t_1 (/ x (/ z y))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double t_1 = (x / z) - x;
	double tmp;
	if (y <= -10.0) {
		tmp = t_0;
	} else if (y <= 3.1e+84) {
		tmp = t_1;
	} else if (y <= 1.22e+151) {
		tmp = t_0;
	} else if (y <= 4.1e+193) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x / z) * y
    t_1 = (x / z) - x
    if (y <= (-10.0d0)) then
        tmp = t_0
    else if (y <= 3.1d+84) then
        tmp = t_1
    else if (y <= 1.22d+151) then
        tmp = t_0
    else if (y <= 4.1d+193) then
        tmp = t_1
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double t_1 = (x / z) - x;
	double tmp;
	if (y <= -10.0) {
		tmp = t_0;
	} else if (y <= 3.1e+84) {
		tmp = t_1;
	} else if (y <= 1.22e+151) {
		tmp = t_0;
	} else if (y <= 4.1e+193) {
		tmp = t_1;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	t_1 = (x / z) - x
	tmp = 0
	if y <= -10.0:
		tmp = t_0
	elif y <= 3.1e+84:
		tmp = t_1
	elif y <= 1.22e+151:
		tmp = t_0
	elif y <= 4.1e+193:
		tmp = t_1
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * y)
	t_1 = Float64(Float64(x / z) - x)
	tmp = 0.0
	if (y <= -10.0)
		tmp = t_0;
	elseif (y <= 3.1e+84)
		tmp = t_1;
	elseif (y <= 1.22e+151)
		tmp = t_0;
	elseif (y <= 4.1e+193)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * y;
	t_1 = (x / z) - x;
	tmp = 0.0;
	if (y <= -10.0)
		tmp = t_0;
	elseif (y <= 3.1e+84)
		tmp = t_1;
	elseif (y <= 1.22e+151)
		tmp = t_0;
	elseif (y <= 4.1e+193)
		tmp = t_1;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -10.0], t$95$0, If[LessEqual[y, 3.1e+84], t$95$1, If[LessEqual[y, 1.22e+151], t$95$0, If[LessEqual[y, 4.1e+193], t$95$1, N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -10 or 3.10000000000000003e84 < y < 1.22000000000000005e151

   1. Initial program 91.4%

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

   2. Taylor expanded in y around inf 77.2%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 78.5%

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

   4. Simplified 78.5%

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

   if -10 < y < 3.10000000000000003e84 or 1.22000000000000005e151 < y < 4.0999999999999997e193

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 98.7%

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

      1. neg-mul-1 98.7%

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

      2. +-commutative 98.7%

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

      3. unsub-neg 98.7%

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

      4. associate-/l* 99.4%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.8%

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

   if 4.0999999999999997e193 < y

   1. Initial program 81.1%

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

   2. Taylor expanded in y around inf 81.1%

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

      1. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14.5 \lor \neg \left(z \leq 1.35 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -14.5) (not (<= z 1.35e-16)))
   (- (* x (/ y z)) x)
   (* (/ x z) (+ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14.5) || !(z <= 1.35e-16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * (1.0 + 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 ((z <= (-14.5d0)) .or. (.not. (z <= 1.35d-16))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) * (1.0d0 + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14.5) || !(z <= 1.35e-16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * (1.0 + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -14.5) or not (z <= 1.35e-16):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) * (1.0 + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -14.5) || !(z <= 1.35e-16))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -14.5) || ~((z <= 1.35e-16)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) * (1.0 + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -14.5], N[Not[LessEqual[z, 1.35e-16]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -14.5 or 1.35e-16 < z

   1. Initial program 75.9%

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

   2. Taylor expanded in z around 0 88.6%

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

      1. neg-mul-1 88.6%

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

      2. +-commutative 88.6%

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

      3. unsub-neg 88.6%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in y around inf 87.7%

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

      1. associate-*r/ 99.0%

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

   7. Simplified 99.0%

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

   if -14.5 < z < 1.35e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 94.9%

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

      2. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14.5 \lor \neg \left(z \leq 1.35 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right)\\ \end{array} \]

Alternative 6: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+56}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+56)
   (- x)
   (if (<= z 9.8e+107) (* (/ x z) (+ 1.0 y)) (- (/ x z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+56) {
		tmp = -x;
	} else if (z <= 9.8e+107) {
		tmp = (x / z) * (1.0 + y);
	} 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 (z <= (-4d+56)) then
        tmp = -x
    else if (z <= 9.8d+107) then
        tmp = (x / z) * (1.0d0 + y)
    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 (z <= -4e+56) {
		tmp = -x;
	} else if (z <= 9.8e+107) {
		tmp = (x / z) * (1.0 + y);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+56:
		tmp = -x
	elif z <= 9.8e+107:
		tmp = (x / z) * (1.0 + y)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+56)
		tmp = Float64(-x);
	elseif (z <= 9.8e+107)
		tmp = Float64(Float64(x / z) * Float64(1.0 + y));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e+56)
		tmp = -x;
	elseif (z <= 9.8e+107)
		tmp = (x / z) * (1.0 + y);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+56], (-x), If[LessEqual[z, 9.8e+107], N[(N[(x / z), $MachinePrecision] * N[(1.0 + y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000037e56

   1. Initial program 69.7%

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

   2. Taylor expanded in z around inf 84.4%

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

      1. neg-mul-1 84.4%

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

   4. Simplified 84.4%

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

   if -4.00000000000000037e56 < z < 9.8000000000000003e107

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 93.9%

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

      1. associate-/l* 90.3%

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

      2. associate-/r/ 93.9%

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

   4. Simplified 93.9%

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

   if 9.8000000000000003e107 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in z around 0 93.3%

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

      1. neg-mul-1 93.3%

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

      2. +-commutative 93.3%

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

      3. unsub-neg 93.3%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in y around 0 88.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+56}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 7: 98.1% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 88.7%

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

2. Taylor expanded in z around 0 94.6%

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

   1. neg-mul-1 94.6%

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

   2. +-commutative 94.6%

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

   3. unsub-neg 94.6%

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

   4. associate-/l* 97.3%

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

   5. associate-/r/ 98.9%

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

4. Simplified 98.9%

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

5. Final simplification 98.9%

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

Alternative 8: 63.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14.5:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -14.5) (- x) (if (<= z 1.35e-16) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -14.5) {
		tmp = -x;
	} else if (z <= 1.35e-16) {
		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 <= (-14.5d0)) then
        tmp = -x
    else if (z <= 1.35d-16) 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 <= -14.5) {
		tmp = -x;
	} else if (z <= 1.35e-16) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -14.5:
		tmp = -x
	elif z <= 1.35e-16:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -14.5)
		tmp = Float64(-x);
	elseif (z <= 1.35e-16)
		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 <= -14.5)
		tmp = -x;
	elseif (z <= 1.35e-16)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -14.5], (-x), If[LessEqual[z, 1.35e-16], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -14.5 or 1.35e-16 < z

   1. Initial program 75.9%

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

   2. Taylor expanded in z around inf 74.4%

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

      1. neg-mul-1 74.4%

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

   4. Simplified 74.4%

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

   if -14.5 < z < 1.35e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

      4. associate-/l* 94.9%

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

      5. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 59.1%

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

   6. Taylor expanded in z around 0 59.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14.5:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 9: 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 88.7%

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

2. Taylor expanded in z around inf 36.5%

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

   1. neg-mul-1 36.5%

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

4. Simplified 36.5%

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

5. Final simplification 36.5%

   \[\leadsto -x \]

Alternative 10: 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 88.7%

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

2. Taylor expanded in z around inf 28.0%

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

   1. associate-*r* 28.0%

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

   2. neg-mul-1 28.0%

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

4. Simplified 28.0%

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

   1. div-inv 27.9%

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

   2. associate-*l* 36.4%

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

   3. div-inv 36.5%

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

   4. *-inverses 36.5%

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

   5. *-commutative 36.5%

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

   6. *-un-lft-identity 36.5%

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

   7. neg-sub0 36.5%

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

   8. metadata-eval 36.5%

      \[\leadsto \color{blue}{\log 1} - x \]

   9. sub-neg 36.5%

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

   10. metadata-eval 36.5%

       \[\leadsto \color{blue}{0} + \left(-x\right) \]

   11. add-sqr-sqrt 15.7%

       \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   12. sqrt-unprod 17.3%

       \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   13. sqr-neg 17.3%

       \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   14. sqrt-unprod 1.5%

       \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   15. add-sqr-sqrt 3.1%

       \[\leadsto 0 + \color{blue}{x} \]

6. Applied egg-rr 3.1%

   \[\leadsto \color{blue}{0 + x} \]
7. Step-by-step derivation

   1. +-lft-identity 3.1%

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

8. Simplified 3.1%

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

9. Final simplification 3.1%

   \[\leadsto x \]

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 2023293 
(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))