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

Percentage Accurate: 88.3% → 97.8%

Time: 6.2s

Alternatives: 9

Speedup: 0.7×

• 21.3% 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: 88.3% 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: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;\frac{x \cdot t_0}{z} \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= (/ (* x t_0) z) -2e+41) (* t_0 (/ x 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 * t_0) / z) <= -2e+41) {
		tmp = t_0 * (x / 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 * t_0) / z) <= (-2d+41)) then
        tmp = t_0 * (x / 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 * t_0) / z) <= -2e+41) {
		tmp = t_0 * (x / 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 * t_0) / z) <= -2e+41:
		tmp = t_0 * (x / 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 (Float64(Float64(x * t_0) / z) <= -2e+41)
		tmp = Float64(t_0 * Float64(x / 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 * t_0) / z) <= -2e+41)
		tmp = t_0 * (x / 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[N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], -2e+41], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < -2.00000000000000001e41

   1. Initial program 79.9%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -2.00000000000000001e41 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

   1. Initial program 89.8%

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

      1. distribute-lft-in 89.8%

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

      2. *-rgt-identity 89.8%

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

   3. Applied egg-rr 89.8%

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

   4. Taylor expanded in x around 0 89.8%

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

      1. associate-/l* 97.8%

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

      2. associate--l+ 97.8%

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

   6. Simplified 97.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]

Alternative 2: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+65}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.9e+65)
     (- x)
     (if (<= z -1.65e-5)
       t_0
       (if (<= z -1e-63)
         (/ x z)
         (if (<= z -5.2e-218)
           t_0
           (if (<= z 7.8e-200)
             (/ x z)
             (if (<= z 5.2e-160)
               t_0
               (if (<= z 1.75e-53)
                 (/ x z)
                 (if (<= z 2.3e+94) t_0 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.9e+65) {
		tmp = -x;
	} else if (z <= -1.65e-5) {
		tmp = t_0;
	} else if (z <= -1e-63) {
		tmp = x / z;
	} else if (z <= -5.2e-218) {
		tmp = t_0;
	} else if (z <= 7.8e-200) {
		tmp = x / z;
	} else if (z <= 5.2e-160) {
		tmp = t_0;
	} else if (z <= 1.75e-53) {
		tmp = x / z;
	} else if (z <= 2.3e+94) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-1.9d+65)) then
        tmp = -x
    else if (z <= (-1.65d-5)) then
        tmp = t_0
    else if (z <= (-1d-63)) then
        tmp = x / z
    else if (z <= (-5.2d-218)) then
        tmp = t_0
    else if (z <= 7.8d-200) then
        tmp = x / z
    else if (z <= 5.2d-160) then
        tmp = t_0
    else if (z <= 1.75d-53) then
        tmp = x / z
    else if (z <= 2.3d+94) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.9e+65) {
		tmp = -x;
	} else if (z <= -1.65e-5) {
		tmp = t_0;
	} else if (z <= -1e-63) {
		tmp = x / z;
	} else if (z <= -5.2e-218) {
		tmp = t_0;
	} else if (z <= 7.8e-200) {
		tmp = x / z;
	} else if (z <= 5.2e-160) {
		tmp = t_0;
	} else if (z <= 1.75e-53) {
		tmp = x / z;
	} else if (z <= 2.3e+94) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.9e+65:
		tmp = -x
	elif z <= -1.65e-5:
		tmp = t_0
	elif z <= -1e-63:
		tmp = x / z
	elif z <= -5.2e-218:
		tmp = t_0
	elif z <= 7.8e-200:
		tmp = x / z
	elif z <= 5.2e-160:
		tmp = t_0
	elif z <= 1.75e-53:
		tmp = x / z
	elif z <= 2.3e+94:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -1.9e+65)
		tmp = Float64(-x);
	elseif (z <= -1.65e-5)
		tmp = t_0;
	elseif (z <= -1e-63)
		tmp = Float64(x / z);
	elseif (z <= -5.2e-218)
		tmp = t_0;
	elseif (z <= 7.8e-200)
		tmp = Float64(x / z);
	elseif (z <= 5.2e-160)
		tmp = t_0;
	elseif (z <= 1.75e-53)
		tmp = Float64(x / z);
	elseif (z <= 2.3e+94)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -1.9e+65)
		tmp = -x;
	elseif (z <= -1.65e-5)
		tmp = t_0;
	elseif (z <= -1e-63)
		tmp = x / z;
	elseif (z <= -5.2e-218)
		tmp = t_0;
	elseif (z <= 7.8e-200)
		tmp = x / z;
	elseif (z <= 5.2e-160)
		tmp = t_0;
	elseif (z <= 1.75e-53)
		tmp = x / z;
	elseif (z <= 2.3e+94)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+65], (-x), If[LessEqual[z, -1.65e-5], t$95$0, If[LessEqual[z, -1e-63], N[(x / z), $MachinePrecision], If[LessEqual[z, -5.2e-218], t$95$0, If[LessEqual[z, 7.8e-200], N[(x / z), $MachinePrecision], If[LessEqual[z, 5.2e-160], t$95$0, If[LessEqual[z, 1.75e-53], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.3e+94], t$95$0, (-x)]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000006e65 or 2.3e94 < z

   1. Initial program 70.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.7%

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

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   if -1.90000000000000006e65 < z < -1.6500000000000001e-5 or -1.00000000000000007e-63 < z < -5.19999999999999966e-218 or 7.79999999999999998e-200 < z < 5.20000000000000007e-160 or 1.74999999999999997e-53 < z < 2.3e94

   1. Initial program 94.7%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 67.3%

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

      1. associate-/r/ 73.6%

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

   6. Applied egg-rr 73.6%

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

   if -1.6500000000000001e-5 < z < -1.00000000000000007e-63 or -5.19999999999999966e-218 < z < 7.79999999999999998e-200 or 5.20000000000000007e-160 < z < 1.74999999999999997e-53

   1. Initial program 99.9%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 73.2%

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

   5. Taylor expanded in z around 0 72.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+65}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+69}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))) (t_1 (* x (/ y z))))
   (if (<= z -4.2e+69)
     (- x)
     (if (<= z -1.42e-5)
       t_1
       (if (<= z -1.12e-63)
         (/ x z)
         (if (<= z -1.6e-217)
           t_0
           (if (<= z 1.25e-199)
             (/ x z)
             (if (<= z 4.2e-160)
               t_0
               (if (<= z 8.5e-53)
                 (/ x z)
                 (if (<= z 2.75e+94) t_1 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -4.2e+69) {
		tmp = -x;
	} else if (z <= -1.42e-5) {
		tmp = t_1;
	} else if (z <= -1.12e-63) {
		tmp = x / z;
	} else if (z <= -1.6e-217) {
		tmp = t_0;
	} else if (z <= 1.25e-199) {
		tmp = x / z;
	} else if (z <= 4.2e-160) {
		tmp = t_0;
	} else if (z <= 8.5e-53) {
		tmp = x / z;
	} else if (z <= 2.75e+94) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y * (x / z)
    t_1 = x * (y / z)
    if (z <= (-4.2d+69)) then
        tmp = -x
    else if (z <= (-1.42d-5)) then
        tmp = t_1
    else if (z <= (-1.12d-63)) then
        tmp = x / z
    else if (z <= (-1.6d-217)) then
        tmp = t_0
    else if (z <= 1.25d-199) then
        tmp = x / z
    else if (z <= 4.2d-160) then
        tmp = t_0
    else if (z <= 8.5d-53) then
        tmp = x / z
    else if (z <= 2.75d+94) then
        tmp = t_1
    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 t_1 = x * (y / z);
	double tmp;
	if (z <= -4.2e+69) {
		tmp = -x;
	} else if (z <= -1.42e-5) {
		tmp = t_1;
	} else if (z <= -1.12e-63) {
		tmp = x / z;
	} else if (z <= -1.6e-217) {
		tmp = t_0;
	} else if (z <= 1.25e-199) {
		tmp = x / z;
	} else if (z <= 4.2e-160) {
		tmp = t_0;
	} else if (z <= 8.5e-53) {
		tmp = x / z;
	} else if (z <= 2.75e+94) {
		tmp = t_1;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	t_1 = x * (y / z)
	tmp = 0
	if z <= -4.2e+69:
		tmp = -x
	elif z <= -1.42e-5:
		tmp = t_1
	elif z <= -1.12e-63:
		tmp = x / z
	elif z <= -1.6e-217:
		tmp = t_0
	elif z <= 1.25e-199:
		tmp = x / z
	elif z <= 4.2e-160:
		tmp = t_0
	elif z <= 8.5e-53:
		tmp = x / z
	elif z <= 2.75e+94:
		tmp = t_1
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -4.2e+69)
		tmp = Float64(-x);
	elseif (z <= -1.42e-5)
		tmp = t_1;
	elseif (z <= -1.12e-63)
		tmp = Float64(x / z);
	elseif (z <= -1.6e-217)
		tmp = t_0;
	elseif (z <= 1.25e-199)
		tmp = Float64(x / z);
	elseif (z <= 4.2e-160)
		tmp = t_0;
	elseif (z <= 8.5e-53)
		tmp = Float64(x / z);
	elseif (z <= 2.75e+94)
		tmp = t_1;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -4.2e+69)
		tmp = -x;
	elseif (z <= -1.42e-5)
		tmp = t_1;
	elseif (z <= -1.12e-63)
		tmp = x / z;
	elseif (z <= -1.6e-217)
		tmp = t_0;
	elseif (z <= 1.25e-199)
		tmp = x / z;
	elseif (z <= 4.2e-160)
		tmp = t_0;
	elseif (z <= 8.5e-53)
		tmp = x / z;
	elseif (z <= 2.75e+94)
		tmp = t_1;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+69], (-x), If[LessEqual[z, -1.42e-5], t$95$1, If[LessEqual[z, -1.12e-63], N[(x / z), $MachinePrecision], If[LessEqual[z, -1.6e-217], t$95$0, If[LessEqual[z, 1.25e-199], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.2e-160], t$95$0, If[LessEqual[z, 8.5e-53], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.75e+94], t$95$1, (-x)]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2000000000000003e69 or 2.7499999999999999e94 < z

   1. Initial program 70.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.3%

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

      1. neg-mul-1 80.3%

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

   6. Simplified 80.3%

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

   if -4.2000000000000003e69 < z < -1.42e-5 or 8.50000000000000044e-53 < z < 2.7499999999999999e94

   1. Initial program 88.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.3%

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

      1. associate-/l* 67.8%

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

      2. associate-/r/ 70.3%

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

   6. Simplified 70.3%

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

   if -1.42e-5 < z < -1.12000000000000002e-63 or -1.6000000000000001e-217 < z < 1.2499999999999999e-199 or 4.2000000000000001e-160 < z < 8.50000000000000044e-53

   1. Initial program 99.9%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 73.2%

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

   5. Taylor expanded in z around 0 72.1%

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

   if -1.12000000000000002e-63 < z < -1.6000000000000001e-217 or 1.2499999999999999e-199 < z < 4.2000000000000001e-160

   1. Initial program 99.9%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. associate-/r/ 75.4%

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

   6. Applied egg-rr 75.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+69}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.7e+188)
   (- x)
   (if (<= z 4.2e+205) (* (+ (- y z) 1.0) (/ x z)) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.7e+188) {
		tmp = -x;
	} else if (z <= 4.2e+205) {
		tmp = ((y - z) + 1.0) * (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 <= (-2.7d+188)) then
        tmp = -x
    else if (z <= 4.2d+205) then
        tmp = ((y - z) + 1.0d0) * (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 <= -2.7e+188) {
		tmp = -x;
	} else if (z <= 4.2e+205) {
		tmp = ((y - z) + 1.0) * (x / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.7e+188:
		tmp = -x
	elif z <= 4.2e+205:
		tmp = ((y - z) + 1.0) * (x / z)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.7e+188)
		tmp = Float64(-x);
	elseif (z <= 4.2e+205)
		tmp = Float64(Float64(Float64(y - z) + 1.0) * Float64(x / z));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.7e+188)
		tmp = -x;
	elseif (z <= 4.2e+205)
		tmp = ((y - z) + 1.0) * (x / z);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.7e+188], (-x), If[LessEqual[z, 4.2e+205], N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e188 or 4.2000000000000001e205 < z

   1. Initial program 63.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 95.8%

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

      1. neg-mul-1 95.8%

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

   6. Simplified 95.8%

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

   if -2.7e188 < z < 4.2000000000000001e205

   1. Initial program 92.3%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

      1. associate-/r/ 95.1%

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

   5. Applied egg-rr 95.1%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -195000000 \lor \neg \left(y \leq 3.2 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -195000000.0) (not (<= y 3.2e+65)))
   (* y (/ x z))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -195000000.0) || !(y <= 3.2e+65)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-195000000.0d0)) .or. (.not. (y <= 3.2d+65))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -195000000.0) || !(y <= 3.2e+65)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -195000000.0) or not (y <= 3.2e+65):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -195000000.0) || !(y <= 3.2e+65))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -195000000.0) || ~((y <= 3.2e+65)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -195000000.0], N[Not[LessEqual[y, 3.2e+65]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e8 or 3.20000000000000007e65 < y

   1. Initial program 84.8%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 74.5%

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

      1. associate-/r/ 77.0%

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

   6. Applied egg-rr 77.0%

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

   if -1.95e8 < y < 3.20000000000000007e65

   1. Initial program 88.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.2%

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

   5. Taylor expanded in z around 0 96.2%

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

      1. neg-mul-1 96.2%

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

      2. +-commutative 96.2%

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

      3. unsub-neg 96.2%

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

   7. Simplified 96.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -195000000 \lor \neg \left(y \leq 3.2 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 6: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -650000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -650000.0)
   (/ (* x y) z)
   (if (<= y 5.5e+65) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -650000.0) {
		tmp = (x * y) / z;
	} else if (y <= 5.5e+65) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (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 (y <= (-650000.0d0)) then
        tmp = (x * y) / z
    else if (y <= 5.5d+65) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -650000.0) {
		tmp = (x * y) / z;
	} else if (y <= 5.5e+65) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -650000.0:
		tmp = (x * y) / z
	elif y <= 5.5e+65:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -650000.0)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 5.5e+65)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -650000.0)
		tmp = (x * y) / z;
	elseif (y <= 5.5e+65)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -650000.0], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 5.5e+65], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e5

   1. Initial program 87.7%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 68.5%

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

   if -6.5e5 < y < 5.4999999999999996e65

   1. Initial program 88.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.2%

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

   5. Taylor expanded in z around 0 96.2%

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

      1. neg-mul-1 96.2%

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

      2. +-commutative 96.2%

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

      3. unsub-neg 96.2%

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

   7. Simplified 96.2%

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

   if 5.4999999999999996e65 < y

   1. Initial program 82.4%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. associate-/r/ 86.9%

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

   6. Applied egg-rr 86.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -650000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 7: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28000:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -28000.0)
   (/ (+ x (* x y)) z)
   (if (<= y 7.2e+65) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -28000.0) {
		tmp = (x + (x * y)) / z;
	} else if (y <= 7.2e+65) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (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 (y <= (-28000.0d0)) then
        tmp = (x + (x * y)) / z
    else if (y <= 7.2d+65) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -28000.0) {
		tmp = (x + (x * y)) / z;
	} else if (y <= 7.2e+65) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -28000.0:
		tmp = (x + (x * y)) / z
	elif y <= 7.2e+65:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -28000.0)
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	elseif (y <= 7.2e+65)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -28000.0)
		tmp = (x + (x * y)) / z;
	elseif (y <= 7.2e+65)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -28000.0], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.2e+65], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -28000

   1. Initial program 87.7%

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

      1. distribute-lft-in 87.7%

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

      2. fma-def 87.7%

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

      3. *-rgt-identity 87.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, y - z, \color{blue}{x}\right)}{z} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]

   4. Taylor expanded in z around 0 69.4%

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

   if -28000 < y < 7.19999999999999957e65

   1. Initial program 88.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.2%

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

   5. Taylor expanded in z around 0 96.2%

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

      1. neg-mul-1 96.2%

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

      2. +-commutative 96.2%

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

      3. unsub-neg 96.2%

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

   7. Simplified 96.2%

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

   if 7.19999999999999957e65 < y

   1. Initial program 82.4%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. associate-/r/ 86.9%

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

   6. Applied egg-rr 86.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28000:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 64.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 72.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.5%

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

      1. neg-mul-1 71.5%

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

   6. Simplified 71.5%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 56.3%

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

   5. Taylor expanded in z around 0 54.7%

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

4. Final simplification 62.7%

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

Alternative 9: 38.5% 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* 96.7%

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

3. Simplified 96.7%

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

4. Taylor expanded in z around inf 35.8%

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

   1. neg-mul-1 35.8%

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

6. Simplified 35.8%

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

7. Final simplification 35.8%

   \[\leadsto -x \]

Developer target: 99.4% 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 2023257 
(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))