Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.6% → 99.6%

Time: 30.5s

Alternatives: 21

Speedup: 1.0×

• 41.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (fma y (- (log z) t) (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(fma(y, (log(z) - t), (a * (log1p(-z) - b))));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(fma(y, Float64(log(z) - t), Float64(a * Float64(log1p(Float64(-z)) - b)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Step-by-step derivation

   1. fma-define 95.7%

      \[\leadsto x \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\log \left(1 - z\right) - b\right)\right)}} \]

   2. sub-neg 95.7%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)\right)} \]

   3. log1p-define 99.2%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)\right)} \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \]
4. Add Preprocessing

5. Final simplification 99.2%

   \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)} \]
6. Add Preprocessing

Alternative 2: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right) - y \cdot \left(t - \log z\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (- (* a (- (log (- 1.0 z)) b)) (* y (- t (log z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((a * (log((1.0 - z)) - b)) - (y * (t - log(z)))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((a * (log((1.0d0 - z)) - b)) - (y * (t - log(z)))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((a * (Math.log((1.0 - z)) - b)) - (y * (t - Math.log(z)))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((a * (math.log((1.0 - z)) - b)) - (y * (t - math.log(z)))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(a * Float64(log(Float64(1.0 - z)) - b)) - Float64(y * Float64(t - log(z))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((a * (log((1.0 - z)) - b)) - (y * (t - log(z)))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] - N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Final simplification 95.7%

   \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right) - y \cdot \left(t - \log z\right)} \]
4. Add Preprocessing

Alternative 3: 87.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-41} \lor \neg \left(y \leq 8.4 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e-41) (not (<= y 8.4e-19)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e-41) || !(y <= 8.4e-19)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((-a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.45d-41)) .or. (.not. (y <= 8.4d-19))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((-a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e-41) || !(y <= 8.4e-19)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e-41) or not (y <= 8.4e-19):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e-41) || !(y <= 8.4e-19))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e-41) || ~((y <= 8.4e-19)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e-41], N[Not[LessEqual[y, 8.4e-19]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999989e-41 or 8.3999999999999996e-19 < y

   1. Initial program 97.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.3%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   if -1.44999999999999989e-41 < y < 8.3999999999999996e-19

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 83.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 90.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 90.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-41} \lor \neg \left(y \leq 8.4 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-190}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* (- a) (+ z b))))) (t_2 (* x (exp (* y (- t))))))
   (if (<= t -2.45e+114)
     t_2
     (if (<= t -1.1e-285)
       t_1
       (if (<= t 2.9e-190) (* x (pow z y)) (if (<= t 5.8e+35) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((-a * (z + b)));
	double t_2 = x * exp((y * -t));
	double tmp;
	if (t <= -2.45e+114) {
		tmp = t_2;
	} else if (t <= -1.1e-285) {
		tmp = t_1;
	} else if (t <= 2.9e-190) {
		tmp = x * pow(z, y);
	} else if (t <= 5.8e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * exp((-a * (z + b)))
    t_2 = x * exp((y * -t))
    if (t <= (-2.45d+114)) then
        tmp = t_2
    else if (t <= (-1.1d-285)) then
        tmp = t_1
    else if (t <= 2.9d-190) then
        tmp = x * (z ** y)
    else if (t <= 5.8d+35) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((-a * (z + b)));
	double t_2 = x * Math.exp((y * -t));
	double tmp;
	if (t <= -2.45e+114) {
		tmp = t_2;
	} else if (t <= -1.1e-285) {
		tmp = t_1;
	} else if (t <= 2.9e-190) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 5.8e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((-a * (z + b)))
	t_2 = x * math.exp((y * -t))
	tmp = 0
	if t <= -2.45e+114:
		tmp = t_2
	elif t <= -1.1e-285:
		tmp = t_1
	elif t <= 2.9e-190:
		tmp = x * math.pow(z, y)
	elif t <= 5.8e+35:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (t <= -2.45e+114)
		tmp = t_2;
	elseif (t <= -1.1e-285)
		tmp = t_1;
	elseif (t <= 2.9e-190)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 5.8e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((-a * (z + b)));
	t_2 = x * exp((y * -t));
	tmp = 0.0;
	if (t <= -2.45e+114)
		tmp = t_2;
	elseif (t <= -1.1e-285)
		tmp = t_1;
	elseif (t <= 2.9e-190)
		tmp = x * (z ^ y);
	elseif (t <= 5.8e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e+114], t$95$2, If[LessEqual[t, -1.1e-285], t$95$1, If[LessEqual[t, 2.9e-190], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+35], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45e114 or 5.79999999999999989e35 < t

   1. Initial program 95.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.0%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 83.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 83.0%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 83.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   if -2.45e114 < t < -1.1e-285 or 2.9000000000000002e-190 < t < 5.79999999999999989e35

   1. Initial program 95.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 73.8%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 79.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 79.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 79.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 79.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 79.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 79.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 79.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 79.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   if -1.1e-285 < t < 2.9000000000000002e-190

   1. Initial program 96.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in t around 0 82.0%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+114}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-285}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-190}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+35}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-285}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* y (- t))))))
   (if (<= t -1.95e+116)
     t_1
     (if (<= t -1.5e-285)
       (* x (exp (* a (- b))))
       (if (<= t 5.5e-89) (* x (pow z y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * -t));
	double tmp;
	if (t <= -1.95e+116) {
		tmp = t_1;
	} else if (t <= -1.5e-285) {
		tmp = x * exp((a * -b));
	} else if (t <= 5.5e-89) {
		tmp = x * pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp((y * -t))
    if (t <= (-1.95d+116)) then
        tmp = t_1
    else if (t <= (-1.5d-285)) then
        tmp = x * exp((a * -b))
    else if (t <= 5.5d-89) then
        tmp = x * (z ** y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((y * -t));
	double tmp;
	if (t <= -1.95e+116) {
		tmp = t_1;
	} else if (t <= -1.5e-285) {
		tmp = x * Math.exp((a * -b));
	} else if (t <= 5.5e-89) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * -t))
	tmp = 0
	if t <= -1.95e+116:
		tmp = t_1
	elif t <= -1.5e-285:
		tmp = x * math.exp((a * -b))
	elif t <= 5.5e-89:
		tmp = x * math.pow(z, y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (t <= -1.95e+116)
		tmp = t_1;
	elseif (t <= -1.5e-285)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (t <= 5.5e-89)
		tmp = Float64(x * (z ^ y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((y * -t));
	tmp = 0.0;
	if (t <= -1.95e+116)
		tmp = t_1;
	elseif (t <= -1.5e-285)
		tmp = x * exp((a * -b));
	elseif (t <= 5.5e-89)
		tmp = x * (z ^ y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+116], t$95$1, If[LessEqual[t, -1.5e-285], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-89], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.95000000000000016e116 or 5.50000000000000012e-89 < t

   1. Initial program 94.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 79.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 79.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 79.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   if -1.95000000000000016e116 < t < -1.50000000000000002e-285

   1. Initial program 96.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 79.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 79.1%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 79.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   if -1.50000000000000002e-285 < t < 5.50000000000000012e-89

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in t around 0 73.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+116}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-285}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -55000000000000 \lor \neg \left(y \leq 8.4 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -55000000000000.0) (not (<= y 8.4e-19)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -55000000000000.0) || !(y <= 8.4e-19)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-55000000000000.0d0)) .or. (.not. (y <= 8.4d-19))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -55000000000000.0) || !(y <= 8.4e-19)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -55000000000000.0) or not (y <= 8.4e-19):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -55000000000000.0) || !(y <= 8.4e-19))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -55000000000000.0) || ~((y <= 8.4e-19)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -55000000000000.0], N[Not[LessEqual[y, 8.4e-19]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e13 or 8.3999999999999996e-19 < y

   1. Initial program 97.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in t around 0 66.7%

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

   if -5.5e13 < y < 8.3999999999999996e-19

   1. Initial program 94.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 79.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.9%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 79.9%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 79.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -55000000000000 \lor \neg \left(y \leq 8.4 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.1e+41) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.1e+41) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.1d+41)) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.1e+41) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.1e+41:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.1e+41)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.1e+41)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.1e+41], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.09999999999999978e41

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.7%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 79.7%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 79.7%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 79.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. unsub-neg 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in x around 0 42.4%

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

   if -5.09999999999999978e41 < t

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in t around 0 65.1%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \left(a + a \cdot \frac{b}{z}\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+158}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(\left(a \cdot 0.5\right) \cdot \left(x \cdot b\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+40)
   (* x (- 1.0 (* y t)))
   (if (<= t 2.7e-178)
     (* x (- 1.0 (* z (+ a (* a (/ b z))))))
     (if (<= t 8.2e-111)
       (* x (* y t))
       (if (<= t 7.6e+158)
         (+ x (* b (* a (- (* (* a 0.5) (* x b)) x))))
         (* t (* y (- x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+40) {
		tmp = x * (1.0 - (y * t));
	} else if (t <= 2.7e-178) {
		tmp = x * (1.0 - (z * (a + (a * (b / z)))));
	} else if (t <= 8.2e-111) {
		tmp = x * (y * t);
	} else if (t <= 7.6e+158) {
		tmp = x + (b * (a * (((a * 0.5) * (x * b)) - x)));
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.8d+40)) then
        tmp = x * (1.0d0 - (y * t))
    else if (t <= 2.7d-178) then
        tmp = x * (1.0d0 - (z * (a + (a * (b / z)))))
    else if (t <= 8.2d-111) then
        tmp = x * (y * t)
    else if (t <= 7.6d+158) then
        tmp = x + (b * (a * (((a * 0.5d0) * (x * b)) - x)))
    else
        tmp = t * (y * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+40) {
		tmp = x * (1.0 - (y * t));
	} else if (t <= 2.7e-178) {
		tmp = x * (1.0 - (z * (a + (a * (b / z)))));
	} else if (t <= 8.2e-111) {
		tmp = x * (y * t);
	} else if (t <= 7.6e+158) {
		tmp = x + (b * (a * (((a * 0.5) * (x * b)) - x)));
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.8e+40:
		tmp = x * (1.0 - (y * t))
	elif t <= 2.7e-178:
		tmp = x * (1.0 - (z * (a + (a * (b / z)))))
	elif t <= 8.2e-111:
		tmp = x * (y * t)
	elif t <= 7.6e+158:
		tmp = x + (b * (a * (((a * 0.5) * (x * b)) - x)))
	else:
		tmp = t * (y * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+40)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (t <= 2.7e-178)
		tmp = Float64(x * Float64(1.0 - Float64(z * Float64(a + Float64(a * Float64(b / z))))));
	elseif (t <= 8.2e-111)
		tmp = Float64(x * Float64(y * t));
	elseif (t <= 7.6e+158)
		tmp = Float64(x + Float64(b * Float64(a * Float64(Float64(Float64(a * 0.5) * Float64(x * b)) - x))));
	else
		tmp = Float64(t * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.8e+40)
		tmp = x * (1.0 - (y * t));
	elseif (t <= 2.7e-178)
		tmp = x * (1.0 - (z * (a + (a * (b / z)))));
	elseif (t <= 8.2e-111)
		tmp = x * (y * t);
	elseif (t <= 7.6e+158)
		tmp = x + (b * (a * (((a * 0.5) * (x * b)) - x)));
	else
		tmp = t * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+40], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-178], N[(x * N[(1.0 - N[(z * N[(a + N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-111], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+158], N[(x + N[(b * N[(a * N[(N[(N[(a * 0.5), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.8e40

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.7%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 79.7%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 79.7%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 79.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. unsub-neg 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in x around 0 42.4%

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

   if -4.8e40 < t < 2.70000000000000009e-178

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.2%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 74.2%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 77.6%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 77.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 77.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 77.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 77.6%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 77.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 77.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 77.6%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 34.6%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 34.6%

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

       2. distribute-rgt-neg-in 34.6%

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

   11. Simplified 34.6%

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

   12. Taylor expanded in z around inf 44.8%

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

       1. distribute-lft-out 44.8%

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

       2. associate-/l* 48.8%

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

   14. Simplified 48.8%

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

   if 2.70000000000000009e-178 < t < 8.19999999999999936e-111

   1. Initial program 94.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 23.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 23.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 23.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 23.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.7%

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

      1. mul-1-neg 18.7%

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

      2. unsub-neg 18.7%

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

   8. Simplified 18.7%

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

   9. Taylor expanded in t around inf 40.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 40.5%

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

       2. distribute-rgt-neg-out 40.5%

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

       3. distribute-rgt-neg-in 40.5%

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

   11. Simplified 40.5%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
   12. Step-by-step derivation

       1. pow1 40.5%

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

       2. add-sqr-sqrt 27.3%

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

       3. sqrt-unprod 55.9%

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

       4. sqr-neg 55.9%

          \[\leadsto {\left(t \cdot \left(x \cdot \sqrt{\color{blue}{y \cdot y}}\right)\right)}^{1} \]

       5. sqrt-unprod 18.5%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right)}^{1} \]

       6. add-sqr-sqrt 40.2%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{y}\right)\right)}^{1} \]

   13. Applied egg-rr 40.2%

       \[\leadsto \color{blue}{{\left(t \cdot \left(x \cdot y\right)\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 40.2%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

       2. associate-*r* 40.2%

          \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot y} \]

       3. *-commutative 40.2%

          \[\leadsto \color{blue}{\left(x \cdot t\right)} \cdot y \]

       4. associate-*r* 45.3%

          \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   15. Simplified 45.3%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   if 8.19999999999999936e-111 < t < 7.5999999999999997e158

   1. Initial program 96.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 64.6%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 64.6%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 64.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in b around 0 40.5%

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(a \cdot x\right) + 0.5 \cdot \left({a}^{2} \cdot \left(b \cdot x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 40.5%

         \[\leadsto x + b \cdot \color{blue}{\left(0.5 \cdot \left({a}^{2} \cdot \left(b \cdot x\right)\right) + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 40.5%

         \[\leadsto x + b \cdot \left(0.5 \cdot \left({a}^{2} \cdot \left(b \cdot x\right)\right) + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 40.5%

         \[\leadsto x + b \cdot \color{blue}{\left(0.5 \cdot \left({a}^{2} \cdot \left(b \cdot x\right)\right) - a \cdot x\right)} \]

   8. Simplified 40.5%

      \[\leadsto \color{blue}{x + b \cdot \left(0.5 \cdot \left({a}^{2} \cdot \left(b \cdot x\right)\right) - a \cdot x\right)} \]

   9. Taylor expanded in a around 0 46.8%

      \[\leadsto x + b \cdot \color{blue}{\left(a \cdot \left(0.5 \cdot \left(a \cdot \left(b \cdot x\right)\right) - x\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 46.8%

          \[\leadsto x + b \cdot \left(a \cdot \left(\color{blue}{\left(0.5 \cdot a\right) \cdot \left(b \cdot x\right)} - x\right)\right) \]

   11. Simplified 46.8%

       \[\leadsto x + b \cdot \color{blue}{\left(a \cdot \left(\left(0.5 \cdot a\right) \cdot \left(b \cdot x\right) - x\right)\right)} \]

   if 7.5999999999999997e158 < t

   1. Initial program 97.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.5%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 82.5%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 82.5%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 82.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 23.5%

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

      1. mul-1-neg 23.5%

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

      2. unsub-neg 23.5%

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

   8. Simplified 23.5%

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

   9. Taylor expanded in t around inf 32.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.0%

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

       2. distribute-rgt-neg-out 32.0%

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

       3. distribute-rgt-neg-in 32.0%

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

   11. Simplified 32.0%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \left(a + a \cdot \frac{b}{z}\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+158}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(\left(a \cdot 0.5\right) \cdot \left(x \cdot b\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.4% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* z (- (/ (- 1.0 (* a b)) z) a)))))
   (if (<= t -7.4e+39)
     (* x (- 1.0 (* y t)))
     (if (<= t 2.1e-180)
       t_1
       (if (<= t 4.6e-109)
         (* x (* y t))
         (if (<= t 7.2e+154) t_1 (* t (* y (- x)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (z * (((1.0 - (a * b)) / z) - a));
	double tmp;
	if (t <= -7.4e+39) {
		tmp = x * (1.0 - (y * t));
	} else if (t <= 2.1e-180) {
		tmp = t_1;
	} else if (t <= 4.6e-109) {
		tmp = x * (y * t);
	} else if (t <= 7.2e+154) {
		tmp = t_1;
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z * (((1.0d0 - (a * b)) / z) - a))
    if (t <= (-7.4d+39)) then
        tmp = x * (1.0d0 - (y * t))
    else if (t <= 2.1d-180) then
        tmp = t_1
    else if (t <= 4.6d-109) then
        tmp = x * (y * t)
    else if (t <= 7.2d+154) then
        tmp = t_1
    else
        tmp = t * (y * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (z * (((1.0 - (a * b)) / z) - a));
	double tmp;
	if (t <= -7.4e+39) {
		tmp = x * (1.0 - (y * t));
	} else if (t <= 2.1e-180) {
		tmp = t_1;
	} else if (t <= 4.6e-109) {
		tmp = x * (y * t);
	} else if (t <= 7.2e+154) {
		tmp = t_1;
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (z * (((1.0 - (a * b)) / z) - a))
	tmp = 0
	if t <= -7.4e+39:
		tmp = x * (1.0 - (y * t))
	elif t <= 2.1e-180:
		tmp = t_1
	elif t <= 4.6e-109:
		tmp = x * (y * t)
	elif t <= 7.2e+154:
		tmp = t_1
	else:
		tmp = t * (y * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(z * Float64(Float64(Float64(1.0 - Float64(a * b)) / z) - a)))
	tmp = 0.0
	if (t <= -7.4e+39)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (t <= 2.1e-180)
		tmp = t_1;
	elseif (t <= 4.6e-109)
		tmp = Float64(x * Float64(y * t));
	elseif (t <= 7.2e+154)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z * (((1.0 - (a * b)) / z) - a));
	tmp = 0.0;
	if (t <= -7.4e+39)
		tmp = x * (1.0 - (y * t));
	elseif (t <= 2.1e-180)
		tmp = t_1;
	elseif (t <= 4.6e-109)
		tmp = x * (y * t);
	elseif (t <= 7.2e+154)
		tmp = t_1;
	else
		tmp = t * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(z * N[(N[(N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+39], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-180], t$95$1, If[LessEqual[t, 4.6e-109], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+154], t$95$1, N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.40000000000000025e39

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.7%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 79.7%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 79.7%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 79.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. unsub-neg 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in x around 0 42.4%

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

   if -7.40000000000000025e39 < t < 2.0999999999999999e-180 or 4.6000000000000003e-109 < t < 7.2000000000000001e154

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 71.3%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 75.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 75.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 75.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 75.0%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 75.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 75.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 75.0%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 35.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 35.0%

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

       2. distribute-rgt-neg-in 35.0%

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

   11. Simplified 35.0%

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

   12. Taylor expanded in z around -inf 43.0%

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

       1. mul-1-neg 43.0%

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

       2. *-commutative 43.0%

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

       3. distribute-rgt-neg-in 43.0%

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

       4. mul-1-neg 43.0%

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

       5. unsub-neg 43.0%

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

       6. mul-1-neg 43.0%

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

       7. unsub-neg 43.0%

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

   14. Simplified 43.0%

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

   if 2.0999999999999999e-180 < t < 4.6000000000000003e-109

   1. Initial program 94.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 23.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 23.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 23.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 23.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.7%

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

      1. mul-1-neg 18.7%

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

      2. unsub-neg 18.7%

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

   8. Simplified 18.7%

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

   9. Taylor expanded in t around inf 40.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 40.5%

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

       2. distribute-rgt-neg-out 40.5%

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

       3. distribute-rgt-neg-in 40.5%

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

   11. Simplified 40.5%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
   12. Step-by-step derivation

       1. pow1 40.5%

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

       2. add-sqr-sqrt 27.3%

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

       3. sqrt-unprod 55.9%

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

       4. sqr-neg 55.9%

          \[\leadsto {\left(t \cdot \left(x \cdot \sqrt{\color{blue}{y \cdot y}}\right)\right)}^{1} \]

       5. sqrt-unprod 18.5%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right)}^{1} \]

       6. add-sqr-sqrt 40.2%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{y}\right)\right)}^{1} \]

   13. Applied egg-rr 40.2%

       \[\leadsto \color{blue}{{\left(t \cdot \left(x \cdot y\right)\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 40.2%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

       2. associate-*r* 40.2%

          \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot y} \]

       3. *-commutative 40.2%

          \[\leadsto \color{blue}{\left(x \cdot t\right)} \cdot y \]

       4. associate-*r* 45.3%

          \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   15. Simplified 45.3%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   if 7.2000000000000001e154 < t

   1. Initial program 97.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.0%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 83.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 83.0%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 83.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 23.0%

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

      1. mul-1-neg 23.0%

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

      2. unsub-neg 23.0%

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

   8. Simplified 23.0%

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

   9. Taylor expanded in t around inf 31.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 31.2%

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

       2. distribute-rgt-neg-out 31.2%

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

       3. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 33.6% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - z \cdot \left(a + a \cdot \frac{b}{z}\right)\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* z (+ a (* a (/ b z))))))))
   (if (<= t -1.8e+43)
     (* x (- 1.0 (* y t)))
     (if (<= t 2.45e-179)
       t_1
       (if (<= t 8.2e-111)
         (* x (* y t))
         (if (<= t 7.5e+154) t_1 (* t (* y (- x)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (z * (a + (a * (b / z)))));
	double tmp;
	if (t <= -1.8e+43) {
		tmp = x * (1.0 - (y * t));
	} else if (t <= 2.45e-179) {
		tmp = t_1;
	} else if (t <= 8.2e-111) {
		tmp = x * (y * t);
	} else if (t <= 7.5e+154) {
		tmp = t_1;
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z * (a + (a * (b / z)))))
    if (t <= (-1.8d+43)) then
        tmp = x * (1.0d0 - (y * t))
    else if (t <= 2.45d-179) then
        tmp = t_1
    else if (t <= 8.2d-111) then
        tmp = x * (y * t)
    else if (t <= 7.5d+154) then
        tmp = t_1
    else
        tmp = t * (y * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (z * (a + (a * (b / z)))));
	double tmp;
	if (t <= -1.8e+43) {
		tmp = x * (1.0 - (y * t));
	} else if (t <= 2.45e-179) {
		tmp = t_1;
	} else if (t <= 8.2e-111) {
		tmp = x * (y * t);
	} else if (t <= 7.5e+154) {
		tmp = t_1;
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (z * (a + (a * (b / z)))))
	tmp = 0
	if t <= -1.8e+43:
		tmp = x * (1.0 - (y * t))
	elif t <= 2.45e-179:
		tmp = t_1
	elif t <= 8.2e-111:
		tmp = x * (y * t)
	elif t <= 7.5e+154:
		tmp = t_1
	else:
		tmp = t * (y * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 - Float64(z * Float64(a + Float64(a * Float64(b / z))))))
	tmp = 0.0
	if (t <= -1.8e+43)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (t <= 2.45e-179)
		tmp = t_1;
	elseif (t <= 8.2e-111)
		tmp = Float64(x * Float64(y * t));
	elseif (t <= 7.5e+154)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 - (z * (a + (a * (b / z)))));
	tmp = 0.0;
	if (t <= -1.8e+43)
		tmp = x * (1.0 - (y * t));
	elseif (t <= 2.45e-179)
		tmp = t_1;
	elseif (t <= 8.2e-111)
		tmp = x * (y * t);
	elseif (t <= 7.5e+154)
		tmp = t_1;
	else
		tmp = t * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z * N[(a + N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+43], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-179], t$95$1, If[LessEqual[t, 8.2e-111], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+154], t$95$1, N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.80000000000000005e43

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.7%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 79.7%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 79.7%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 79.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. unsub-neg 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in x around 0 42.4%

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

   if -1.80000000000000005e43 < t < 2.45e-179 or 8.19999999999999936e-111 < t < 7.5000000000000004e154

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 71.3%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 75.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 75.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 75.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 75.0%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 75.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 75.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 75.0%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 35.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 35.0%

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

       2. distribute-rgt-neg-in 35.0%

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

   11. Simplified 35.0%

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

   12. Taylor expanded in z around inf 43.1%

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

       1. distribute-lft-out 43.1%

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

       2. associate-/l* 47.0%

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

   14. Simplified 47.0%

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

   if 2.45e-179 < t < 8.19999999999999936e-111

   1. Initial program 94.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 23.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 23.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 23.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 23.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.7%

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

      1. mul-1-neg 18.7%

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

      2. unsub-neg 18.7%

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

   8. Simplified 18.7%

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

   9. Taylor expanded in t around inf 40.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 40.5%

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

       2. distribute-rgt-neg-out 40.5%

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

       3. distribute-rgt-neg-in 40.5%

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

   11. Simplified 40.5%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
   12. Step-by-step derivation

       1. pow1 40.5%

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

       2. add-sqr-sqrt 27.3%

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

       3. sqrt-unprod 55.9%

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

       4. sqr-neg 55.9%

          \[\leadsto {\left(t \cdot \left(x \cdot \sqrt{\color{blue}{y \cdot y}}\right)\right)}^{1} \]

       5. sqrt-unprod 18.5%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right)}^{1} \]

       6. add-sqr-sqrt 40.2%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{y}\right)\right)}^{1} \]

   13. Applied egg-rr 40.2%

       \[\leadsto \color{blue}{{\left(t \cdot \left(x \cdot y\right)\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 40.2%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

       2. associate-*r* 40.2%

          \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot y} \]

       3. *-commutative 40.2%

          \[\leadsto \color{blue}{\left(x \cdot t\right)} \cdot y \]

       4. associate-*r* 45.3%

          \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   15. Simplified 45.3%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   if 7.5000000000000004e154 < t

   1. Initial program 97.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.0%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 83.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 83.0%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 83.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 23.0%

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

      1. mul-1-neg 23.0%

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

      2. unsub-neg 23.0%

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

   8. Simplified 23.0%

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

   9. Taylor expanded in t around inf 31.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 31.2%

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

       2. distribute-rgt-neg-out 31.2%

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

       3. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \left(a + a \cdot \frac{b}{z}\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \left(a + a \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.3% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.0135:\\ \;\;\;\;x \cdot \left(b \cdot \left(\frac{1 - z \cdot a}{b} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.3e-42)
   (* t (- (/ x t) (* x y)))
   (if (<= y 0.0135)
     (* x (* b (- (/ (- 1.0 (* z a)) b) a)))
     (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.3e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.0135) {
		tmp = x * (b * (((1.0 - (z * a)) / b) - a));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.3d-42)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 0.0135d0) then
        tmp = x * (b * (((1.0d0 - (z * a)) / b) - a))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.3e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.0135) {
		tmp = x * (b * (((1.0 - (z * a)) / b) - a));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.3e-42:
		tmp = t * ((x / t) - (x * y))
	elif y <= 0.0135:
		tmp = x * (b * (((1.0 - (z * a)) / b) - a))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.3e-42)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 0.0135)
		tmp = Float64(x * Float64(b * Float64(Float64(Float64(1.0 - Float64(z * a)) / b) - a)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.3e-42)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 0.0135)
		tmp = x * (b * (((1.0 - (z * a)) / b) - a));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.3e-42], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0135], N[(x * N[(b * N[(N[(N[(1.0 - N[(z * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3000000000000001e-42

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in t around inf 29.0%

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

   if -4.3000000000000001e-42 < y < 0.0134999999999999998

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 83.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 90.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 90.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 47.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 47.5%

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

       2. distribute-rgt-neg-in 47.5%

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

   11. Simplified 47.5%

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

   12. Taylor expanded in b around -inf 50.1%

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

       1. mul-1-neg 50.1%

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

       2. distribute-rgt-neg-in 50.1%

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

       3. mul-1-neg 50.1%

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

       4. unsub-neg 50.1%

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

       5. mul-1-neg 50.1%

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

       6. unsub-neg 50.1%

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

   14. Simplified 50.1%

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

   if 0.0134999999999999998 < y

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

   8. Simplified 22.0%

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

   9. Taylor expanded in t around inf 26.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

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

       2. associate-*r* 31.2%

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

       3. neg-mul-1 31.2%

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

       4. distribute-rgt-neg-in 31.2%

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

       5. *-commutative 31.2%

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

       6. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.0135:\\ \;\;\;\;x \cdot \left(b \cdot \left(\frac{1 - z \cdot a}{b} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.9% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.16e-42)
   (* t (- (/ x t) (* x y)))
   (if (<= y 1.15e-5) (- x (* a (* x (+ z b)))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.16e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.15e-5) {
		tmp = x - (a * (x * (z + b)));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.16d-42)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 1.15d-5) then
        tmp = x - (a * (x * (z + b)))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.16e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.15e-5) {
		tmp = x - (a * (x * (z + b)));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.16e-42:
		tmp = t * ((x / t) - (x * y))
	elif y <= 1.15e-5:
		tmp = x - (a * (x * (z + b)))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.16e-42)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 1.15e-5)
		tmp = Float64(x - Float64(a * Float64(x * Float64(z + b))));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.16e-42)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 1.15e-5)
		tmp = x - (a * (x * (z + b)));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.16e-42], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-5], N[(x - N[(a * N[(x * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1600000000000001e-42

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in t around inf 29.0%

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

   if -1.1600000000000001e-42 < y < 1.15e-5

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 83.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 90.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 90.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 47.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 47.2%

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

       2. unsub-neg 47.2%

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

       3. *-commutative 47.2%

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

   11. Simplified 47.2%

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

   if 1.15e-5 < y

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

   8. Simplified 22.0%

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

   9. Taylor expanded in t around inf 26.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

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

       2. associate-*r* 31.2%

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

       3. neg-mul-1 31.2%

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

       4. distribute-rgt-neg-in 31.2%

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

       5. *-commutative 31.2%

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

       6. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.8% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.28:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e-42)
   (* t (- (/ x t) (* x y)))
   (if (<= y 0.28) (* x (- 1.0 (* a (+ z b)))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.28) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.8d-42)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 0.28d0) then
        tmp = x * (1.0d0 - (a * (z + b)))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.28) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.8e-42:
		tmp = t * ((x / t) - (x * y))
	elif y <= 0.28:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e-42)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 0.28)
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.8e-42)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 0.28)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e-42], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.28], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000005e-42

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in t around inf 29.0%

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

   if -4.80000000000000005e-42 < y < 0.28000000000000003

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 83.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 90.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 90.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 47.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 47.5%

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

       2. distribute-rgt-neg-in 47.5%

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

   11. Simplified 47.5%

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

   if 0.28000000000000003 < y

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

   8. Simplified 22.0%

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

   9. Taylor expanded in t around inf 26.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

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

       2. associate-*r* 31.2%

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

       3. neg-mul-1 31.2%

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

       4. distribute-rgt-neg-in 31.2%

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

       5. *-commutative 31.2%

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

       6. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.28:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.1e+22)
   (* t (* y (- x)))
   (if (<= y 1.25e-7) (* x (- 1.0 (* a b))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.1e+22) {
		tmp = t * (y * -x);
	} else if (y <= 1.25e-7) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.1d+22)) then
        tmp = t * (y * -x)
    else if (y <= 1.25d-7) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.1e+22) {
		tmp = t * (y * -x);
	} else if (y <= 1.25e-7) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.1e+22:
		tmp = t * (y * -x)
	elif y <= 1.25e-7:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.1e+22)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 1.25e-7)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.1e+22)
		tmp = t * (y * -x);
	elseif (y <= 1.25e-7)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.1e+22], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-7], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e22

   1. Initial program 98.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.2%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.2%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 61.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 61.2%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 61.2%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 27.4%

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

      1. mul-1-neg 27.4%

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

      2. unsub-neg 27.4%

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

   8. Simplified 27.4%

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

   9. Taylor expanded in t around inf 30.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 30.3%

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

       2. distribute-rgt-neg-out 30.3%

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

       3. distribute-rgt-neg-in 30.3%

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

   11. Simplified 30.3%

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

   if -1.1e22 < y < 1.24999999999999994e-7

   1. Initial program 94.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 86.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 86.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 86.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 86.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 86.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 86.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 86.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 86.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 43.8%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 43.8%

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

       2. distribute-rgt-neg-in 43.8%

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

   11. Simplified 43.8%

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

   12. Taylor expanded in z around 0 42.7%

       \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left(a \cdot b\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 42.7%

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

       2. unsub-neg 42.7%

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

   14. Simplified 42.7%

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

   if 1.24999999999999994e-7 < y

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

   8. Simplified 22.0%

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

   9. Taylor expanded in t around inf 26.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

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

       2. associate-*r* 31.2%

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

       3. neg-mul-1 31.2%

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

       4. distribute-rgt-neg-in 31.2%

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

       5. *-commutative 31.2%

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

       6. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.044:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e-42)
   (* t (- (/ x t) (* x y)))
   (if (<= y 0.044) (* x (- 1.0 (* a b))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.044) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.8d-42)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 0.044d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e-42) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.044) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.8e-42:
		tmp = t * ((x / t) - (x * y))
	elif y <= 0.044:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e-42)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 0.044)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.8e-42)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 0.044)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e-42], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.044], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000005e-42

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in t around inf 29.0%

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

   if -4.80000000000000005e-42 < y < 0.043999999999999997

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 83.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 90.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 90.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot b} + -1 \cdot \left(a \cdot z\right)} \]

      2. associate-*r* 90.8%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \color{blue}{\left(-1 \cdot a\right) \cdot z}} \]

      3. distribute-lft-out 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(b + z\right)}} \]

      4. mul-1-neg 90.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(b + z\right)} \]

   8. Simplified 90.8%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(b + z\right)}} \]

   9. Taylor expanded in a around 0 47.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot \left(b + z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 47.5%

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

       2. distribute-rgt-neg-in 47.5%

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

   11. Simplified 47.5%

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

   12. Taylor expanded in z around 0 46.2%

       \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left(a \cdot b\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 46.2%

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

       2. unsub-neg 46.2%

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

   14. Simplified 46.2%

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

   if 0.043999999999999997 < y

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

   8. Simplified 22.0%

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

   9. Taylor expanded in t around inf 26.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

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

       2. associate-*r* 31.2%

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

       3. neg-mul-1 31.2%

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

       4. distribute-rgt-neg-in 31.2%

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

       5. *-commutative 31.2%

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

       6. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.044:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.0% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-42} \lor \neg \left(y \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e-42) (not (<= y 5.5e-5))) (* t (* y (- x))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e-42) || !(y <= 5.5e-5)) {
		tmp = t * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.4d-42)) .or. (.not. (y <= 5.5d-5))) then
        tmp = t * (y * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e-42) || !(y <= 5.5e-5)) {
		tmp = t * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.4e-42) or not (y <= 5.5e-5):
		tmp = t * (y * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.4e-42) || !(y <= 5.5e-5))
		tmp = Float64(t * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.4e-42) || ~((y <= 5.5e-5)))
		tmp = t * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.4e-42], N[Not[LessEqual[y, 5.5e-5]], $MachinePrecision]], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.39999999999999998e-42 or 5.5000000000000002e-5 < y

   1. Initial program 97.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 58.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 58.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 58.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in t around inf 27.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.2%

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

       2. distribute-rgt-neg-out 27.2%

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

       3. distribute-rgt-neg-in 27.2%

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

   11. Simplified 27.2%

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

   if -5.39999999999999998e-42 < y < 5.5000000000000002e-5

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 53.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in y around 0 37.3%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-42} \lor \neg \left(y \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.9% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.4e-42)
   (* t (* y (- x)))
   (if (<= y 0.00032) x (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.4e-42) {
		tmp = t * (y * -x);
	} else if (y <= 0.00032) {
		tmp = x;
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.4d-42)) then
        tmp = t * (y * -x)
    else if (y <= 0.00032d0) then
        tmp = x
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.4e-42) {
		tmp = t * (y * -x);
	} else if (y <= 0.00032) {
		tmp = x;
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.4e-42:
		tmp = t * (y * -x)
	elif y <= 0.00032:
		tmp = x
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.4e-42)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 0.00032)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.4e-42)
		tmp = t * (y * -x);
	elseif (y <= 0.00032)
		tmp = x;
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.4e-42], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00032], x, N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.39999999999999998e-42

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in t around inf 27.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.8%

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

       2. distribute-rgt-neg-out 27.8%

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

       3. distribute-rgt-neg-in 27.8%

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

   11. Simplified 27.8%

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

   if -5.39999999999999998e-42 < y < 3.20000000000000026e-4

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 53.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in y around 0 37.3%

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

   if 3.20000000000000026e-4 < y

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

   8. Simplified 22.0%

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

   9. Taylor expanded in t around inf 26.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

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

       2. associate-*r* 31.2%

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

       3. neg-mul-1 31.2%

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

       4. distribute-rgt-neg-in 31.2%

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

       5. *-commutative 31.2%

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

       6. distribute-rgt-neg-in 31.2%

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

   11. Simplified 31.2%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.3% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+133} \lor \neg \left(b \leq 4.6 \cdot 10^{+184}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3e+133) (not (<= b 4.6e+184))) (* t (* x y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+133) || !(b <= 4.6e+184)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3d+133)) .or. (.not. (b <= 4.6d+184))) then
        tmp = t * (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+133) || !(b <= 4.6e+184)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3e+133) or not (b <= 4.6e+184):
		tmp = t * (x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3e+133) || !(b <= 4.6e+184))
		tmp = Float64(t * Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3e+133) || ~((b <= 4.6e+184)))
		tmp = t * (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3e+133], N[Not[LessEqual[b, 4.6e+184]], $MachinePrecision]], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -3.00000000000000007e133 or 4.6e184 < b

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 36.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 36.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 36.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 36.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 36.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 13.4%

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

      1. mul-1-neg 13.4%

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

      2. unsub-neg 13.4%

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

   8. Simplified 13.4%

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

   9. Taylor expanded in t around inf 26.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 26.9%

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

       2. distribute-rgt-neg-out 26.9%

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

       3. distribute-rgt-neg-in 26.9%

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

   11. Simplified 26.9%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
   12. Step-by-step derivation

       1. pow1 26.9%

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

       2. add-sqr-sqrt 16.3%

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

       3. sqrt-unprod 33.1%

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

       4. sqr-neg 33.1%

          \[\leadsto {\left(t \cdot \left(x \cdot \sqrt{\color{blue}{y \cdot y}}\right)\right)}^{1} \]

       5. sqrt-unprod 8.6%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right)}^{1} \]

       6. add-sqr-sqrt 23.0%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{y}\right)\right)}^{1} \]

   13. Applied egg-rr 23.0%

       \[\leadsto \color{blue}{{\left(t \cdot \left(x \cdot y\right)\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 23.0%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

   15. Simplified 23.0%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

   if -3.00000000000000007e133 < b < 4.6e184

   1. Initial program 95.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in y around 0 21.8%

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

4. Final simplification 22.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+133} \lor \neg \left(b \leq 4.6 \cdot 10^{+184}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.3% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+127) (* t (* x y)) (if (<= b 1.35e+181) x (* x (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+127) {
		tmp = t * (x * y);
	} else if (b <= 1.35e+181) {
		tmp = x;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.8d+127)) then
        tmp = t * (x * y)
    else if (b <= 1.35d+181) then
        tmp = x
    else
        tmp = x * (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+127) {
		tmp = t * (x * y);
	} else if (b <= 1.35e+181) {
		tmp = x;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+127:
		tmp = t * (x * y)
	elif b <= 1.35e+181:
		tmp = x
	else:
		tmp = x * (y * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+127)
		tmp = Float64(t * Float64(x * y));
	elseif (b <= 1.35e+181)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+127)
		tmp = t * (x * y);
	elseif (b <= 1.35e+181)
		tmp = x;
	else
		tmp = x * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+127], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+181], x, N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.79999999999999955e127

   1. Initial program 97.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 41.5%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 41.5%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 41.5%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 41.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 12.4%

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

      1. mul-1-neg 12.4%

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

      2. unsub-neg 12.4%

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

   8. Simplified 12.4%

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

   9. Taylor expanded in t around inf 26.7%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 26.7%

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

       2. distribute-rgt-neg-out 26.7%

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

       3. distribute-rgt-neg-in 26.7%

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

   11. Simplified 26.7%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
   12. Step-by-step derivation

       1. pow1 26.7%

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

       2. add-sqr-sqrt 19.3%

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

       3. sqrt-unprod 34.9%

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

       4. sqr-neg 34.9%

          \[\leadsto {\left(t \cdot \left(x \cdot \sqrt{\color{blue}{y \cdot y}}\right)\right)}^{1} \]

       5. sqrt-unprod 4.0%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right)}^{1} \]

       6. add-sqr-sqrt 23.0%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{y}\right)\right)}^{1} \]

   13. Applied egg-rr 23.0%

       \[\leadsto \color{blue}{{\left(t \cdot \left(x \cdot y\right)\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 23.0%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

   15. Simplified 23.0%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

   if -6.79999999999999955e127 < b < 1.35000000000000004e181

   1. Initial program 95.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

   4. Taylor expanded in y around 0 21.8%

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

   if 1.35000000000000004e181 < b

   1. Initial program 96.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 30.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 30.8%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 30.8%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 30.8%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 30.8%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 14.6%

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

      1. mul-1-neg 14.6%

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

      2. unsub-neg 14.6%

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

   8. Simplified 14.6%

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

   9. Taylor expanded in t around inf 27.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.1%

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

       2. distribute-rgt-neg-out 27.1%

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

       3. distribute-rgt-neg-in 27.1%

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

   11. Simplified 27.1%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]
   12. Step-by-step derivation

       1. pow1 27.1%

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

       2. add-sqr-sqrt 12.4%

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

       3. sqrt-unprod 30.7%

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

       4. sqr-neg 30.7%

          \[\leadsto {\left(t \cdot \left(x \cdot \sqrt{\color{blue}{y \cdot y}}\right)\right)}^{1} \]

       5. sqrt-unprod 14.7%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)\right)}^{1} \]

       6. add-sqr-sqrt 23.0%

          \[\leadsto {\left(t \cdot \left(x \cdot \color{blue}{y}\right)\right)}^{1} \]

   13. Applied egg-rr 23.0%

       \[\leadsto \color{blue}{{\left(t \cdot \left(x \cdot y\right)\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 23.0%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]

       2. associate-*r* 26.9%

          \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot y} \]

       3. *-commutative 26.9%

          \[\leadsto \color{blue}{\left(x \cdot t\right)} \cdot y \]

       4. associate-*r* 23.1%

          \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]

   15. Simplified 23.1%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 22.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* y (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return y * (x / y);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = y * (x / y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return y * (x / y);
}

Python

def code(x, y, z, t, a, b):
	return y * (x / y)

Julia

function code(x, y, z, t, a, b)
	return Float64(y * Float64(x / y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = y * (x / y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in t around inf 56.7%

   \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
4. Step-by-step derivation

   1. mul-1-neg 56.7%

      \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

   2. distribute-lft-neg-out 56.7%

      \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

   3. *-commutative 56.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

5. Simplified 56.7%

   \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

6. Taylor expanded in y around 0 29.8%

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

   1. mul-1-neg 29.8%

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

   2. unsub-neg 29.8%

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

8. Simplified 29.8%

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

9. Taylor expanded in y around inf 28.7%

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

    1. *-commutative 28.7%

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

11. Simplified 28.7%

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

12. Taylor expanded in y around 0 22.2%

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

13. Final simplification 22.2%

    \[\leadsto y \cdot \frac{x}{y} \]
14. Add Preprocessing

Alternative 21: 19.6% accurate, 315.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.7%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 73.1%

   \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(\log z - t\right)}} \]

4. Taylor expanded in y around 0 18.2%

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

5. Final simplification 18.2%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))