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

Percentage Accurate: 88.2% → 99.9%

Time: 13.3s

Alternatives: 13

Speedup: 0.6×

• 21.7% 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: 88.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * ((y - z) + 1.0d0)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \left(1 - z\right)\\ t_1 := \frac{x}{\frac{z}{t\_0}}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-35}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (- 1.0 z))) (t_1 (/ x (/ z t_0))))
   (if (<= z -5e-14) t_1 (if (<= z 3e-35) (* t_0 (/ x z)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y + (1.0 - z);
	double t_1 = x / (z / t_0);
	double tmp;
	if (z <= -5e-14) {
		tmp = t_1;
	} else if (z <= 3e-35) {
		tmp = t_0 * (x / z);
	} else {
		tmp = t_1;
	}
	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 + (1.0d0 - z)
    t_1 = x / (z / t_0)
    if (z <= (-5d-14)) then
        tmp = t_1
    else if (z <= 3d-35) then
        tmp = t_0 * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (1.0 - z);
	double t_1 = x / (z / t_0);
	double tmp;
	if (z <= -5e-14) {
		tmp = t_1;
	} else if (z <= 3e-35) {
		tmp = t_0 * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (1.0 - z)
	t_1 = x / (z / t_0)
	tmp = 0
	if z <= -5e-14:
		tmp = t_1
	elif z <= 3e-35:
		tmp = t_0 * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(1.0 - z))
	t_1 = Float64(x / Float64(z / t_0))
	tmp = 0.0
	if (z <= -5e-14)
		tmp = t_1;
	elseif (z <= 3e-35)
		tmp = Float64(t_0 * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (1.0 - z);
	t_1 = x / (z / t_0);
	tmp = 0.0;
	if (z <= -5e-14)
		tmp = t_1;
	elseif (z <= 3e-35)
		tmp = t_0 * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-14], t$95$1, If[LessEqual[z, 3e-35], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-14 or 2.99999999999999989e-35 < z

   1. Initial program 78.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if -5.0000000000000002e-14 < z < 2.99999999999999989e-35

   1. Initial program 99.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 65.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+38}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6000000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)))
   (if (<= z -7.2e+38)
     (- x)
     (if (<= z -1.15e-59)
       (* x (/ y z))
       (if (<= z 6.2e-262)
         (/ x z)
         (if (<= z 4.3e-202)
           t_0
           (if (<= z 2.3e-71)
             (/ x z)
             (if (<= z 6000000000000.0) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (z <= -7.2e+38) {
		tmp = -x;
	} else if (z <= -1.15e-59) {
		tmp = x * (y / z);
	} else if (z <= 6.2e-262) {
		tmp = x / z;
	} else if (z <= 4.3e-202) {
		tmp = t_0;
	} else if (z <= 2.3e-71) {
		tmp = x / z;
	} else if (z <= 6000000000000.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / z) * y
    if (z <= (-7.2d+38)) then
        tmp = -x
    else if (z <= (-1.15d-59)) then
        tmp = x * (y / z)
    else if (z <= 6.2d-262) then
        tmp = x / z
    else if (z <= 4.3d-202) then
        tmp = t_0
    else if (z <= 2.3d-71) then
        tmp = x / z
    else if (z <= 6000000000000.0d0) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (z <= -7.2e+38) {
		tmp = -x;
	} else if (z <= -1.15e-59) {
		tmp = x * (y / z);
	} else if (z <= 6.2e-262) {
		tmp = x / z;
	} else if (z <= 4.3e-202) {
		tmp = t_0;
	} else if (z <= 2.3e-71) {
		tmp = x / z;
	} else if (z <= 6000000000000.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	tmp = 0
	if z <= -7.2e+38:
		tmp = -x
	elif z <= -1.15e-59:
		tmp = x * (y / z)
	elif z <= 6.2e-262:
		tmp = x / z
	elif z <= 4.3e-202:
		tmp = t_0
	elif z <= 2.3e-71:
		tmp = x / z
	elif z <= 6000000000000.0:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * y)
	tmp = 0.0
	if (z <= -7.2e+38)
		tmp = Float64(-x);
	elseif (z <= -1.15e-59)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 6.2e-262)
		tmp = Float64(x / z);
	elseif (z <= 4.3e-202)
		tmp = t_0;
	elseif (z <= 2.3e-71)
		tmp = Float64(x / z);
	elseif (z <= 6000000000000.0)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * y;
	tmp = 0.0;
	if (z <= -7.2e+38)
		tmp = -x;
	elseif (z <= -1.15e-59)
		tmp = x * (y / z);
	elseif (z <= 6.2e-262)
		tmp = x / z;
	elseif (z <= 4.3e-202)
		tmp = t_0;
	elseif (z <= 2.3e-71)
		tmp = x / z;
	elseif (z <= 6000000000000.0)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -7.2e+38], (-x), If[LessEqual[z, -1.15e-59], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-262], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.3e-202], t$95$0, If[LessEqual[z, 2.3e-71], N[(x / z), $MachinePrecision], If[LessEqual[z, 6000000000000.0], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.19999999999999938e38 or 6e12 < z

   1. Initial program 74.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -7.19999999999999938e38 < z < -1.1499999999999999e-59

   1. Initial program 99.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.1499999999999999e-59 < z < 6.1999999999999997e-262 or 4.29999999999999993e-202 < z < 2.2999999999999998e-71

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 6.1999999999999997e-262 < z < 4.29999999999999993e-202 or 2.2999999999999998e-71 < z < 6e12

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+38}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -9.6e+38)
     (- x)
     (if (<= z -4.2e-59)
       t_0
       (if (<= z 2.1e-71) (/ x z) (if (<= z 3.8e+16) t_0 (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -9.6e+38) {
		tmp = -x;
	} else if (z <= -4.2e-59) {
		tmp = t_0;
	} else if (z <= 2.1e-71) {
		tmp = x / z;
	} else if (z <= 3.8e+16) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y / z)
    if (z <= (-9.6d+38)) then
        tmp = -x
    else if (z <= (-4.2d-59)) then
        tmp = t_0
    else if (z <= 2.1d-71) then
        tmp = x / z
    else if (z <= 3.8d+16) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -9.6e+38) {
		tmp = -x;
	} else if (z <= -4.2e-59) {
		tmp = t_0;
	} else if (z <= 2.1e-71) {
		tmp = x / z;
	} else if (z <= 3.8e+16) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -9.6e+38:
		tmp = -x
	elif z <= -4.2e-59:
		tmp = t_0
	elif z <= 2.1e-71:
		tmp = x / z
	elif z <= 3.8e+16:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -9.6e+38)
		tmp = Float64(-x);
	elseif (z <= -4.2e-59)
		tmp = t_0;
	elseif (z <= 2.1e-71)
		tmp = Float64(x / z);
	elseif (z <= 3.8e+16)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -9.6e+38)
		tmp = -x;
	elseif (z <= -4.2e-59)
		tmp = t_0;
	elseif (z <= 2.1e-71)
		tmp = x / z;
	elseif (z <= 3.8e+16)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+38], (-x), If[LessEqual[z, -4.2e-59], t$95$0, If[LessEqual[z, 2.1e-71], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.8e+16], t$95$0, (-x)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.60000000000000069e38 or 3.8e16 < z

   1. Initial program 74.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -9.60000000000000069e38 < z < -4.19999999999999993e-59 or 2.1000000000000001e-71 < z < 3.8e16

   1. Initial program 99.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.19999999999999993e-59 < z < 2.1000000000000001e-71

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \mathbf{elif}\;z \leq 6500000000:\\ \;\;\;\;\left(y + \left(1 - z\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e-12)
   (* x (+ -1.0 (/ (+ y 1.0) z)))
   (if (<= z 6500000000.0)
     (* (+ y (- 1.0 z)) (/ x z))
     (* x (+ -1.0 (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e-12) {
		tmp = x * (-1.0 + ((y + 1.0) / z));
	} else if (z <= 6500000000.0) {
		tmp = (y + (1.0 - z)) * (x / z);
	} else {
		tmp = x * (-1.0 + (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.6d-12)) then
        tmp = x * ((-1.0d0) + ((y + 1.0d0) / z))
    else if (z <= 6500000000.0d0) then
        tmp = (y + (1.0d0 - z)) * (x / z)
    else
        tmp = x * ((-1.0d0) + (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e-12) {
		tmp = x * (-1.0 + ((y + 1.0) / z));
	} else if (z <= 6500000000.0) {
		tmp = (y + (1.0 - z)) * (x / z);
	} else {
		tmp = x * (-1.0 + (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.6e-12:
		tmp = x * (-1.0 + ((y + 1.0) / z))
	elif z <= 6500000000.0:
		tmp = (y + (1.0 - z)) * (x / z)
	else:
		tmp = x * (-1.0 + (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e-12)
		tmp = Float64(x * Float64(-1.0 + Float64(Float64(y + 1.0) / z)));
	elseif (z <= 6500000000.0)
		tmp = Float64(Float64(y + Float64(1.0 - z)) * Float64(x / z));
	else
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e-12)
		tmp = x * (-1.0 + ((y + 1.0) / z));
	elseif (z <= 6500000000.0)
		tmp = (y + (1.0 - z)) * (x / z);
	else
		tmp = x * (-1.0 + (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e-12], N[(x * N[(-1.0 + N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6500000000.0], N[(N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-12

   1. Initial program 79.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   if -3.6e-12 < z < 6.5e9

   1. Initial program 99.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 6.5e9 < z

   1. Initial program 76.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -1.0 (/ (+ y 1.0) z)))))
   (if (<= z -1.16e-15) t_0 (if (<= z 3e-47) (* (/ x z) (+ y 1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + ((y + 1.0) / z));
	double tmp;
	if (z <= -1.16e-15) {
		tmp = t_0;
	} else if (z <= 3e-47) {
		tmp = (x / z) * (y + 1.0);
	} 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 = x * ((-1.0d0) + ((y + 1.0d0) / z))
    if (z <= (-1.16d-15)) then
        tmp = t_0
    else if (z <= 3d-47) then
        tmp = (x / z) * (y + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + ((y + 1.0) / z));
	double tmp;
	if (z <= -1.16e-15) {
		tmp = t_0;
	} else if (z <= 3e-47) {
		tmp = (x / z) * (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-1.0 + ((y + 1.0) / z))
	tmp = 0
	if z <= -1.16e-15:
		tmp = t_0
	elif z <= 3e-47:
		tmp = (x / z) * (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-1.0 + Float64(Float64(y + 1.0) / z)))
	tmp = 0.0
	if (z <= -1.16e-15)
		tmp = t_0;
	elseif (z <= 3e-47)
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-1.0 + ((y + 1.0) / z));
	tmp = 0.0;
	if (z <= -1.16e-15)
		tmp = t_0;
	elseif (z <= 3e-47)
		tmp = (x / z) * (y + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-1.0 + N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e-15], t$95$0, If[LessEqual[z, 3e-47], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1599999999999999e-15 or 3.00000000000000017e-47 < z

   1. Initial program 79.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   if -1.1599999999999999e-15 < z < 3.00000000000000017e-47

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 10^{-20}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -1.0 (/ y z)))))
   (if (<= z -1.0) t_0 (if (<= z 1e-20) (* (/ x z) (+ y 1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + (y / z));
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1e-20) {
		tmp = (x / z) * (y + 1.0);
	} 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 = x * ((-1.0d0) + (y / z))
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1d-20) then
        tmp = (x / z) * (y + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + (y / z));
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1e-20) {
		tmp = (x / z) * (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-1.0 + (y / z))
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 1e-20:
		tmp = (x / z) * (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-1.0 + Float64(y / z)))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1e-20)
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-1.0 + (y / z));
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1e-20)
		tmp = (x / z) * (y + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1e-20], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 9.99999999999999945e-21 < z

   1. Initial program 77.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1 < z < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 10^{-20}:\\ \;\;\;\;x \cdot \frac{1 + y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -1.0 (/ y z)))))
   (if (<= z -1.0) t_0 (if (<= z 1e-20) (* x (/ (+ 1.0 y) z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + (y / z));
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1e-20) {
		tmp = x * ((1.0 + y) / 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 = x * ((-1.0d0) + (y / z))
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1d-20) then
        tmp = x * ((1.0d0 + y) / 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 = x * (-1.0 + (y / z));
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1e-20) {
		tmp = x * ((1.0 + y) / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-1.0 + (y / z))
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 1e-20:
		tmp = x * ((1.0 + y) / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-1.0 + Float64(y / z)))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1e-20)
		tmp = Float64(x * Float64(Float64(1.0 + y) / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-1.0 + (y / z));
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1e-20)
		tmp = x * ((1.0 + y) / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1e-20], N[(x * N[(N[(1.0 + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 9.99999999999999945e-21 < z

   1. Initial program 77.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1 < z < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{if}\;y \leq -2020:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -1.0 (/ y z)))))
   (if (<= y -2020.0) t_0 (if (<= y 9.8e-13) (- (/ x z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + (y / z));
	double tmp;
	if (y <= -2020.0) {
		tmp = t_0;
	} else if (y <= 9.8e-13) {
		tmp = (x / z) - x;
	} 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 = x * ((-1.0d0) + (y / z))
    if (y <= (-2020.0d0)) then
        tmp = t_0
    else if (y <= 9.8d-13) then
        tmp = (x / z) - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-1.0 + (y / z));
	double tmp;
	if (y <= -2020.0) {
		tmp = t_0;
	} else if (y <= 9.8e-13) {
		tmp = (x / z) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-1.0 + (y / z))
	tmp = 0
	if y <= -2020.0:
		tmp = t_0
	elif y <= 9.8e-13:
		tmp = (x / z) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-1.0 + Float64(y / z)))
	tmp = 0.0
	if (y <= -2020.0)
		tmp = t_0;
	elseif (y <= 9.8e-13)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-1.0 + (y / z));
	tmp = 0.0;
	if (y <= -2020.0)
		tmp = t_0;
	elseif (y <= 9.8e-13)
		tmp = (x / z) - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2020.0], t$95$0, If[LessEqual[y, 9.8e-13], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2020 or 9.80000000000000065e-13 < y

   1. Initial program 88.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2020 < y < 9.80000000000000065e-13

   1. Initial program 89.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e+47)
   (/ (* x y) z)
   (if (<= y 1.9e+29) (- (/ x z) x) (* (/ x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+47) {
		tmp = (x * y) / z;
	} else if (y <= 1.9e+29) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.15d+47)) then
        tmp = (x * y) / z
    else if (y <= 1.9d+29) then
        tmp = (x / z) - x
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+47) {
		tmp = (x * y) / z;
	} else if (y <= 1.9e+29) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e+47:
		tmp = (x * y) / z
	elif y <= 1.9e+29:
		tmp = (x / z) - x
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e+47)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 1.9e+29)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.15e+47)
		tmp = (x * y) / z;
	elseif (y <= 1.9e+29)
		tmp = (x / z) - x;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e+47], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.9e+29], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1499999999999999e47

   1. Initial program 91.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.1499999999999999e47 < y < 1.89999999999999985e29

   1. Initial program 88.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1.89999999999999985e29 < y

   1. Initial program 87.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -1620000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)))
   (if (<= y -1620000.0) t_0 (if (<= y 1.05e+29) (- (/ x z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -1620000.0) {
		tmp = t_0;
	} else if (y <= 1.05e+29) {
		tmp = (x / z) - x;
	} 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 = (x / z) * y
    if (y <= (-1620000.0d0)) then
        tmp = t_0
    else if (y <= 1.05d+29) then
        tmp = (x / z) - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -1620000.0) {
		tmp = t_0;
	} else if (y <= 1.05e+29) {
		tmp = (x / z) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	tmp = 0
	if y <= -1620000.0:
		tmp = t_0
	elif y <= 1.05e+29:
		tmp = (x / z) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * y)
	tmp = 0.0
	if (y <= -1620000.0)
		tmp = t_0;
	elseif (y <= 1.05e+29)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * y;
	tmp = 0.0;
	if (y <= -1620000.0)
		tmp = t_0;
	elseif (y <= 1.05e+29)
		tmp = (x / z) - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1620000.0], t$95$0, If[LessEqual[y, 1.05e+29], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.62e6 or 1.0500000000000001e29 < y

   1. Initial program 88.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.62e6 < y < 1.0500000000000001e29

   1. Initial program 88.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-114}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + \left(1 - z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2e-114) (/ (* x (+ (- y z) 1.0)) z) (/ x (/ z (+ y (- 1.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-114) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = x / (z / (y + (1.0 - 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 (x <= 2d-114) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = x / (z / (y + (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-114) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = x / (z / (y + (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e-114:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = x / (z / (y + (1.0 - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e-114)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(x / Float64(z / Float64(y + Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2e-114)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = x / (z / (y + (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e-114], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000001e-114

   1. Initial program 92.0%

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

   if 2.0000000000000001e-114 < x

   1. Initial program 82.6%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 200000000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 200000000000.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 200000000000.0) {
		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 <= 200000000000.0d0) 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 <= 200000000000.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 200000000000.0:
		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 <= 200000000000.0)
		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 <= 200000000000.0)
		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, 200000000000.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2e11 < z

   1. Initial program 76.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1 < z < 2e11

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 38.0% accurate, 4.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in z around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

9. Applied egg-rr 0

   \[\leadsto expr\]
10. Add Preprocessing

Developer target: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (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))