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

Percentage Accurate: 88.0% → 98.8%

Time: 7.1s

Alternatives: 12

Speedup: 1.0×

• 20.0% 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: 88.0% 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: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.85 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.85) (not (<= z 1.0)))
   (- (* x (/ y z)) x)
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.85) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x + (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 ((z <= (-0.85d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.85) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.85) or not (z <= 1.0):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.85) || !(z <= 1.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.85) || ~((z <= 1.0)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.85], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.849999999999999978 or 1 < z

   1. Initial program 80.3%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 93.0%

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

      1. associate-/l* 95.0%

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

      2. associate-/r/ 98.7%

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

   6. Simplified 98.7%

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

   if -0.849999999999999978 < z < 1

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. *-rgt-identity 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.85 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]

Alternative 2: 65.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -4.9e+64)
     (- x)
     (if (<= z -6.6e-63)
       t_0
       (if (<= z 7.2e-211)
         (/ x z)
         (if (<= z 3.05e-176)
           t_0
           (if (<= z 5.1e-158) (/ x z) (if (<= z 3.6e+31) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -4.9e+64) {
		tmp = -x;
	} else if (z <= -6.6e-63) {
		tmp = t_0;
	} else if (z <= 7.2e-211) {
		tmp = x / z;
	} else if (z <= 3.05e-176) {
		tmp = t_0;
	} else if (z <= 5.1e-158) {
		tmp = x / z;
	} else if (z <= 3.6e+31) {
		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 <= (-4.9d+64)) then
        tmp = -x
    else if (z <= (-6.6d-63)) then
        tmp = t_0
    else if (z <= 7.2d-211) then
        tmp = x / z
    else if (z <= 3.05d-176) then
        tmp = t_0
    else if (z <= 5.1d-158) then
        tmp = x / z
    else if (z <= 3.6d+31) 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 <= -4.9e+64) {
		tmp = -x;
	} else if (z <= -6.6e-63) {
		tmp = t_0;
	} else if (z <= 7.2e-211) {
		tmp = x / z;
	} else if (z <= 3.05e-176) {
		tmp = t_0;
	} else if (z <= 5.1e-158) {
		tmp = x / z;
	} else if (z <= 3.6e+31) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -4.9e+64:
		tmp = -x
	elif z <= -6.6e-63:
		tmp = t_0
	elif z <= 7.2e-211:
		tmp = x / z
	elif z <= 3.05e-176:
		tmp = t_0
	elif z <= 5.1e-158:
		tmp = x / z
	elif z <= 3.6e+31:
		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 <= -4.9e+64)
		tmp = Float64(-x);
	elseif (z <= -6.6e-63)
		tmp = t_0;
	elseif (z <= 7.2e-211)
		tmp = Float64(x / z);
	elseif (z <= 3.05e-176)
		tmp = t_0;
	elseif (z <= 5.1e-158)
		tmp = Float64(x / z);
	elseif (z <= 3.6e+31)
		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 <= -4.9e+64)
		tmp = -x;
	elseif (z <= -6.6e-63)
		tmp = t_0;
	elseif (z <= 7.2e-211)
		tmp = x / z;
	elseif (z <= 3.05e-176)
		tmp = t_0;
	elseif (z <= 5.1e-158)
		tmp = x / z;
	elseif (z <= 3.6e+31)
		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, -4.9e+64], (-x), If[LessEqual[z, -6.6e-63], t$95$0, If[LessEqual[z, 7.2e-211], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.05e-176], t$95$0, If[LessEqual[z, 5.1e-158], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.6e+31], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9000000000000003e64 or 3.59999999999999996e31 < z

   1. Initial program 77.5%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around inf 82.3%

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

      1. neg-mul-1 82.3%

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

   6. Simplified 82.3%

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

   if -4.9000000000000003e64 < z < -6.59999999999999987e-63 or 7.1999999999999998e-211 < z < 3.0500000000000001e-176 or 5.1000000000000003e-158 < z < 3.59999999999999996e31

   1. Initial program 98.6%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 60.6%

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

      1. associate-/r/ 66.5%

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

   6. Applied egg-rr 66.5%

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

   if -6.59999999999999987e-63 < z < 7.1999999999999998e-211 or 3.0500000000000001e-176 < z < 5.1000000000000003e-158

   1. Initial program 100.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. Taylor expanded in z around 0 94.1%

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

   5. Taylor expanded in y around 0 71.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+97}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-184}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -2.1e+97)
     (- x)
     (if (<= z -3.2e-29)
       (* x (/ y z))
       (if (<= z 7.5e-214)
         (/ x z)
         (if (<= z 4.8e-184)
           t_0
           (if (<= z 9.6e-162) (/ x z) (if (<= z 1.2e+31) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2.1e+97) {
		tmp = -x;
	} else if (z <= -3.2e-29) {
		tmp = x * (y / z);
	} else if (z <= 7.5e-214) {
		tmp = x / z;
	} else if (z <= 4.8e-184) {
		tmp = t_0;
	} else if (z <= 9.6e-162) {
		tmp = x / z;
	} else if (z <= 1.2e+31) {
		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 <= (-2.1d+97)) then
        tmp = -x
    else if (z <= (-3.2d-29)) then
        tmp = x * (y / z)
    else if (z <= 7.5d-214) then
        tmp = x / z
    else if (z <= 4.8d-184) then
        tmp = t_0
    else if (z <= 9.6d-162) then
        tmp = x / z
    else if (z <= 1.2d+31) 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 <= -2.1e+97) {
		tmp = -x;
	} else if (z <= -3.2e-29) {
		tmp = x * (y / z);
	} else if (z <= 7.5e-214) {
		tmp = x / z;
	} else if (z <= 4.8e-184) {
		tmp = t_0;
	} else if (z <= 9.6e-162) {
		tmp = x / z;
	} else if (z <= 1.2e+31) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -2.1e+97:
		tmp = -x
	elif z <= -3.2e-29:
		tmp = x * (y / z)
	elif z <= 7.5e-214:
		tmp = x / z
	elif z <= 4.8e-184:
		tmp = t_0
	elif z <= 9.6e-162:
		tmp = x / z
	elif z <= 1.2e+31:
		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 <= -2.1e+97)
		tmp = Float64(-x);
	elseif (z <= -3.2e-29)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 7.5e-214)
		tmp = Float64(x / z);
	elseif (z <= 4.8e-184)
		tmp = t_0;
	elseif (z <= 9.6e-162)
		tmp = Float64(x / z);
	elseif (z <= 1.2e+31)
		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 <= -2.1e+97)
		tmp = -x;
	elseif (z <= -3.2e-29)
		tmp = x * (y / z);
	elseif (z <= 7.5e-214)
		tmp = x / z;
	elseif (z <= 4.8e-184)
		tmp = t_0;
	elseif (z <= 9.6e-162)
		tmp = x / z;
	elseif (z <= 1.2e+31)
		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, -2.1e+97], (-x), If[LessEqual[z, -3.2e-29], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-214], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.8e-184], t$95$0, If[LessEqual[z, 9.6e-162], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.2e+31], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000012e97 or 1.19999999999999991e31 < z

   1. Initial program 76.5%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. neg-mul-1 84.2%

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

   6. Simplified 84.2%

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

   if -2.10000000000000012e97 < z < -3.2e-29

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. div-inv 61.4%

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

      2. clear-num 61.5%

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

      3. *-commutative 61.5%

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

   6. Applied egg-rr 61.5%

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

   if -3.2e-29 < z < 7.49999999999999966e-214 or 4.80000000000000049e-184 < z < 9.6000000000000007e-162

   1. Initial program 100.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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 z around 0 94.5%

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

   5. Taylor expanded in y around 0 71.9%

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

   if 7.49999999999999966e-214 < z < 4.80000000000000049e-184 or 9.6000000000000007e-162 < z < 1.19999999999999991e31

   1. Initial program 98.1%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around inf 62.4%

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

      1. associate-/r/ 67.6%

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

   6. Applied egg-rr 67.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+97}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+23} \lor \neg \left(y \leq 3.8 \cdot 10^{+68}\right) \land y \leq 9.2 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+46)
   (* y (/ x z))
   (if (or (<= y 1.5e+23) (and (not (<= y 3.8e+68)) (<= y 9.2e+142)))
     (- (/ x z) x)
     (* x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+46) {
		tmp = y * (x / z);
	} else if ((y <= 1.5e+23) || (!(y <= 3.8e+68) && (y <= 9.2e+142))) {
		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 <= (-1.8d+46)) then
        tmp = y * (x / z)
    else if ((y <= 1.5d+23) .or. (.not. (y <= 3.8d+68)) .and. (y <= 9.2d+142)) 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 <= -1.8e+46) {
		tmp = y * (x / z);
	} else if ((y <= 1.5e+23) || (!(y <= 3.8e+68) && (y <= 9.2e+142))) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.8e+46:
		tmp = y * (x / z)
	elif (y <= 1.5e+23) or (not (y <= 3.8e+68) and (y <= 9.2e+142)):
		tmp = (x / z) - x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+46)
		tmp = Float64(y * Float64(x / z));
	elseif ((y <= 1.5e+23) || (!(y <= 3.8e+68) && (y <= 9.2e+142)))
		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 <= -1.8e+46)
		tmp = y * (x / z);
	elseif ((y <= 1.5e+23) || (~((y <= 3.8e+68)) && (y <= 9.2e+142)))
		tmp = (x / z) - x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e+46], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.5e+23], And[N[Not[LessEqual[y, 3.8e+68]], $MachinePrecision], LessEqual[y, 9.2e+142]]], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e46

   1. Initial program 88.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. associate-/r/ 74.7%

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

   6. Applied egg-rr 74.7%

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

   if -1.7999999999999999e46 < y < 1.5e23 or 3.8000000000000001e68 < y < 9.20000000000000009e142

   1. Initial program 87.8%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around 0 93.6%

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

   if 1.5e23 < y < 3.8000000000000001e68 or 9.20000000000000009e142 < y

   1. Initial program 96.1%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 88.0%

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

      1. div-inv 88.1%

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

      2. clear-num 88.2%

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

      3. *-commutative 88.2%

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

   6. Applied egg-rr 88.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+23} \lor \neg \left(y \leq 3.8 \cdot 10^{+68}\right) \land y \leq 9.2 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 5: 83.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} - x\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ x z) x)))
   (if (<= y -3.2e+43)
     (* y (/ x z))
     (if (<= y 1.2e+23)
       t_0
       (if (<= y 2e+68)
         (* x (/ y z))
         (if (<= y 4.2e+127) t_0 (/ x (/ z y))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) - x;
	double tmp;
	if (y <= -3.2e+43) {
		tmp = y * (x / z);
	} else if (y <= 1.2e+23) {
		tmp = t_0;
	} else if (y <= 2e+68) {
		tmp = x * (y / z);
	} else if (y <= 4.2e+127) {
		tmp = t_0;
	} 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) :: tmp
    t_0 = (x / z) - x
    if (y <= (-3.2d+43)) then
        tmp = y * (x / z)
    else if (y <= 1.2d+23) then
        tmp = t_0
    else if (y <= 2d+68) then
        tmp = x * (y / z)
    else if (y <= 4.2d+127) then
        tmp = t_0
    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) - x;
	double tmp;
	if (y <= -3.2e+43) {
		tmp = y * (x / z);
	} else if (y <= 1.2e+23) {
		tmp = t_0;
	} else if (y <= 2e+68) {
		tmp = x * (y / z);
	} else if (y <= 4.2e+127) {
		tmp = t_0;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) - x
	tmp = 0
	if y <= -3.2e+43:
		tmp = y * (x / z)
	elif y <= 1.2e+23:
		tmp = t_0
	elif y <= 2e+68:
		tmp = x * (y / z)
	elif y <= 4.2e+127:
		tmp = t_0
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) - x)
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.2e+23)
		tmp = t_0;
	elseif (y <= 2e+68)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 4.2e+127)
		tmp = t_0;
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) - x;
	tmp = 0.0;
	if (y <= -3.2e+43)
		tmp = y * (x / z);
	elseif (y <= 1.2e+23)
		tmp = t_0;
	elseif (y <= 2e+68)
		tmp = x * (y / z);
	elseif (y <= 4.2e+127)
		tmp = t_0;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -3.2e+43], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+23], t$95$0, If[LessEqual[y, 2e+68], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+127], t$95$0, N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.20000000000000014e43

   1. Initial program 88.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. associate-/r/ 74.7%

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

   6. Applied egg-rr 74.7%

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

   if -3.20000000000000014e43 < y < 1.2e23 or 1.99999999999999991e68 < y < 4.19999999999999983e127

   1. Initial program 88.0%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 95.2%

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

   if 1.2e23 < y < 1.99999999999999991e68

   1. Initial program 99.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 86.8%

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

      1. div-inv 87.0%

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

      2. clear-num 87.3%

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

      3. *-commutative 87.3%

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

   6. Applied egg-rr 87.3%

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

   if 4.19999999999999983e127 < y

   1. Initial program 92.8%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 83.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 6: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} - x\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ x z) x)))
   (if (<= y -2.3e+42)
     (* y (/ x z))
     (if (<= y 1.28e+23)
       t_0
       (if (<= y 5.4e+68)
         (* x (/ y z))
         (if (<= y 2.8e+127) t_0 (/ (* x y) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) - x;
	double tmp;
	if (y <= -2.3e+42) {
		tmp = y * (x / z);
	} else if (y <= 1.28e+23) {
		tmp = t_0;
	} else if (y <= 5.4e+68) {
		tmp = x * (y / z);
	} else if (y <= 2.8e+127) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x / z) - x
    if (y <= (-2.3d+42)) then
        tmp = y * (x / z)
    else if (y <= 1.28d+23) then
        tmp = t_0
    else if (y <= 5.4d+68) then
        tmp = x * (y / z)
    else if (y <= 2.8d+127) then
        tmp = t_0
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) - x;
	double tmp;
	if (y <= -2.3e+42) {
		tmp = y * (x / z);
	} else if (y <= 1.28e+23) {
		tmp = t_0;
	} else if (y <= 5.4e+68) {
		tmp = x * (y / z);
	} else if (y <= 2.8e+127) {
		tmp = t_0;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) - x
	tmp = 0
	if y <= -2.3e+42:
		tmp = y * (x / z)
	elif y <= 1.28e+23:
		tmp = t_0
	elif y <= 5.4e+68:
		tmp = x * (y / z)
	elif y <= 2.8e+127:
		tmp = t_0
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) - x)
	tmp = 0.0
	if (y <= -2.3e+42)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.28e+23)
		tmp = t_0;
	elseif (y <= 5.4e+68)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.8e+127)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) - x;
	tmp = 0.0;
	if (y <= -2.3e+42)
		tmp = y * (x / z);
	elseif (y <= 1.28e+23)
		tmp = t_0;
	elseif (y <= 5.4e+68)
		tmp = x * (y / z);
	elseif (y <= 2.8e+127)
		tmp = t_0;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -2.3e+42], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e+23], t$95$0, If[LessEqual[y, 5.4e+68], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+127], t$95$0, N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3e42

   1. Initial program 88.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. associate-/r/ 74.7%

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

   6. Applied egg-rr 74.7%

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

   if -2.3e42 < y < 1.28e23 or 5.39999999999999982e68 < y < 2.8000000000000002e127

   1. Initial program 88.0%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 95.2%

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

   if 1.28e23 < y < 5.39999999999999982e68

   1. Initial program 99.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 86.8%

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

      1. div-inv 87.0%

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

      2. clear-num 87.3%

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

      3. *-commutative 87.3%

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

   6. Applied egg-rr 87.3%

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

   if 2.8000000000000002e127 < y

   1. Initial program 92.8%

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

   2. Taylor expanded in y around inf 85.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 7: 94.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 90.6%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 92.8%

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

      1. associate-/l* 95.0%

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

      2. associate-/r/ 93.7%

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

   6. Simplified 93.7%

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

   if -1 < y < 1

   1. Initial program 88.6%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

4. Final simplification 96.8%

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

Alternative 8: 95.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = (x / (z / y)) - x
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 90.6%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 92.8%

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

      1. associate-/l* 95.0%

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

      2. associate-/r/ 93.7%

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

   6. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. clear-num 93.6%

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

      3. div-inv 94.5%

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

   8. Applied egg-rr 94.5%

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

   if -1 < y < 1

   1. Initial program 88.6%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

4. Final simplification 97.1%

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

Alternative 9: 97.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = (y / (z / x)) - x
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 90.6%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 92.8%

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

      1. associate-/l* 95.0%

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

   6. Simplified 95.0%

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

   if -1 < y < 1

   1. Initial program 88.6%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

4. Final simplification 97.3%

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

Alternative 10: 96.1% 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 89.5%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 11: 65.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 122000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 122000.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 122000.0) {
		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 <= 122000.0d0) 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 <= 122000.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 122000.0:
		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 <= 122000.0)
		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 <= 122000.0)
		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, 122000.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 122000 < z

   1. Initial program 80.0%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around inf 76.4%

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

      1. neg-mul-1 76.4%

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

   6. Simplified 76.4%

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

   if -1 < z < 122000

   1. Initial program 99.9%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 93.8%

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

   5. Taylor expanded in y around 0 55.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 122000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 12: 38.8% 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 89.5%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around inf 41.2%

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

   1. neg-mul-1 41.2%

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

6. Simplified 41.2%

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

7. Final simplification 41.2%

   \[\leadsto -x \]

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 2023185 
(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))