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

Percentage Accurate: 96.4% → 99.6%

Time: 23.4s

Alternatives: 16

Speedup: 1.0×

• 41.3% 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: 96.4% 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 96.6%

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

   1. fma-def 97.0%

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

   2. sub-neg 97.0%

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

   3. log1p-def 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 96.4% 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]

Derivation

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. Final simplification 96.6%

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

Alternative 3: 76.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {\left(e^{-y}\right)}^{t}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-38}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+265}:\\ \;\;\;\;x \cdot {\left(e^{y}\right)}^{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow (exp (- y)) t))))
   (if (<= y -1.6e+19)
     t_1
     (if (<= y 1.15e-38)
       (* x (exp (* (- a) (+ z b))))
       (if (<= y 1.8e+225)
         t_1
         (if (<= y 1.85e+265)
           (* x (pow (exp y) t))
           (* x (exp (* t (- y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(exp(-y), t);
	double tmp;
	if (y <= -1.6e+19) {
		tmp = t_1;
	} else if (y <= 1.15e-38) {
		tmp = x * exp((-a * (z + b)));
	} else if (y <= 1.8e+225) {
		tmp = t_1;
	} else if (y <= 1.85e+265) {
		tmp = x * pow(exp(y), t);
	} else {
		tmp = x * exp((t * -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) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-y) ** t)
    if (y <= (-1.6d+19)) then
        tmp = t_1
    else if (y <= 1.15d-38) then
        tmp = x * exp((-a * (z + b)))
    else if (y <= 1.8d+225) then
        tmp = t_1
    else if (y <= 1.85d+265) then
        tmp = x * (exp(y) ** t)
    else
        tmp = x * exp((t * -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 t_1 = x * Math.pow(Math.exp(-y), t);
	double tmp;
	if (y <= -1.6e+19) {
		tmp = t_1;
	} else if (y <= 1.15e-38) {
		tmp = x * Math.exp((-a * (z + b)));
	} else if (y <= 1.8e+225) {
		tmp = t_1;
	} else if (y <= 1.85e+265) {
		tmp = x * Math.pow(Math.exp(y), t);
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(math.exp(-y), t)
	tmp = 0
	if y <= -1.6e+19:
		tmp = t_1
	elif y <= 1.15e-38:
		tmp = x * math.exp((-a * (z + b)))
	elif y <= 1.8e+225:
		tmp = t_1
	elif y <= 1.85e+265:
		tmp = x * math.pow(math.exp(y), t)
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (exp(Float64(-y)) ^ t))
	tmp = 0.0
	if (y <= -1.6e+19)
		tmp = t_1;
	elseif (y <= 1.15e-38)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	elseif (y <= 1.8e+225)
		tmp = t_1;
	elseif (y <= 1.85e+265)
		tmp = Float64(x * (exp(y) ^ t));
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	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 (y <= -1.6e+19)
		tmp = t_1;
	elseif (y <= 1.15e-38)
		tmp = x * exp((-a * (z + b)));
	elseif (y <= 1.8e+225)
		tmp = t_1;
	elseif (y <= 1.85e+265)
		tmp = x * (exp(y) ^ t);
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[N[Exp[(-y)], $MachinePrecision], t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+19], t$95$1, If[LessEqual[y, 1.15e-38], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+225], t$95$1, If[LessEqual[y, 1.85e+265], N[(x * N[Power[N[Exp[y], $MachinePrecision], t], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e19 or 1.15000000000000001e-38 < y < 1.7999999999999999e225

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-lft-neg-out 59.9%

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

      3. *-commutative 59.9%

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

   5. Simplified 59.9%

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

      1. exp-prod 75.6%

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

      2. neg-mul-1 75.6%

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

      3. pow-unpow 75.6%

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

   7. Applied egg-rr 75.6%

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

      1. unpow-1 75.6%

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

      2. rec-exp 75.6%

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

   9. Simplified 75.6%

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

   if -1.6e19 < y < 1.15000000000000001e-38

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 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. neg-mul-1 79.4%

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

      3. log1p-def 84.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around 0 84.0%

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

      1. associate-*r* 84.0%

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

      2. associate-*r* 84.0%

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

      3. distribute-lft-out 84.0%

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

      4. neg-mul-1 84.0%

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

   8. Simplified 84.0%

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

   if 1.7999999999999999e225 < y < 1.85e265

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 16.6%

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

      1. mul-1-neg 16.6%

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

      2. distribute-lft-neg-out 16.6%

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

      3. *-commutative 16.6%

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

   5. Simplified 16.6%

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

      1. expm1-log1p-u 16.6%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{y \cdot \left(-t\right)}\right)\right)} \]

      2. expm1-udef 16.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(e^{y \cdot \left(-t\right)}\right)} - 1\right)} \]

      3. exp-prod 15.6%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{{\left(e^{y}\right)}^{\left(-t\right)}}\right)} - 1\right) \]

      4. add-sqr-sqrt 15.4%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}}\right)} - 1\right) \]

      5. sqrt-unprod 31.0%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{\left(\sqrt{\left(-t\right) \cdot \left(-t\right)}\right)}}\right)} - 1\right) \]

      6. sqr-neg 31.0%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\left(\sqrt{\color{blue}{t \cdot t}}\right)}\right)} - 1\right) \]

      7. sqrt-unprod 14.3%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}}\right)} - 1\right) \]

      8. add-sqr-sqrt 85.9%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{t}}\right)} - 1\right) \]

   7. Applied egg-rr 85.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{t}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 85.9%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{t}\right)\right)} \]

      2. expm1-log1p 85.9%

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

   9. Simplified 85.9%

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

   if 1.85e265 < y

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot {\left(e^{-y}\right)}^{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-38}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+225}:\\ \;\;\;\;x \cdot {\left(e^{-y}\right)}^{t}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+265}:\\ \;\;\;\;x \cdot {\left(e^{y}\right)}^{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-57} \lor \neg \left(y \leq 9.6 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e-57) (not (<= y 9.6e-39)))
   (* 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 <= -3.6e-57) || !(y <= 9.6e-39)) {
		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 <= (-3.6d-57)) .or. (.not. (y <= 9.6d-39))) 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 <= -3.6e-57) || !(y <= 9.6e-39)) {
		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 <= -3.6e-57) or not (y <= 9.6e-39):
		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 <= -3.6e-57) || !(y <= 9.6e-39))
		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 <= -3.6e-57) || ~((y <= 9.6e-39)))
		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, -3.6e-57], N[Not[LessEqual[y, 9.6e-39]], $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 < -3.6000000000000002e-57 or 9.60000000000000063e-39 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 90.3%

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

   if -3.6000000000000002e-57 < y < 9.60000000000000063e-39

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. sub-neg 81.3%

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

      2. neg-mul-1 81.3%

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

      3. log1p-def 87.7%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in z around 0 87.7%

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

      1. associate-*r* 87.7%

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

      2. associate-*r* 87.7%

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

      3. distribute-lft-out 87.7%

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

      4. neg-mul-1 87.7%

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

   8. Simplified 87.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-57} \lor \neg \left(y \leq 9.6 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{if}\;t \leq -200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-183}:\\ \;\;\;\;x \cdot {\left(e^{y}\right)}^{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* t (- y))))))
   (if (<= t -200.0)
     t_1
     (if (<= t -1.35e-183)
       (* x (pow (exp y) t))
       (if (<= t 1.75e+28) (* x (exp (* (- a) (+ z b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((t * -y));
	double tmp;
	if (t <= -200.0) {
		tmp = t_1;
	} else if (t <= -1.35e-183) {
		tmp = x * pow(exp(y), t);
	} else if (t <= 1.75e+28) {
		tmp = x * exp((-a * (z + b)));
	} 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((t * -y))
    if (t <= (-200.0d0)) then
        tmp = t_1
    else if (t <= (-1.35d-183)) then
        tmp = x * (exp(y) ** t)
    else if (t <= 1.75d+28) then
        tmp = x * exp((-a * (z + b)))
    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((t * -y));
	double tmp;
	if (t <= -200.0) {
		tmp = t_1;
	} else if (t <= -1.35e-183) {
		tmp = x * Math.pow(Math.exp(y), t);
	} else if (t <= 1.75e+28) {
		tmp = x * Math.exp((-a * (z + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((t * -y))
	tmp = 0
	if t <= -200.0:
		tmp = t_1
	elif t <= -1.35e-183:
		tmp = x * math.pow(math.exp(y), t)
	elif t <= 1.75e+28:
		tmp = x * math.exp((-a * (z + b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(t * Float64(-y))))
	tmp = 0.0
	if (t <= -200.0)
		tmp = t_1;
	elseif (t <= -1.35e-183)
		tmp = Float64(x * (exp(y) ^ t));
	elseif (t <= 1.75e+28)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((t * -y));
	tmp = 0.0;
	if (t <= -200.0)
		tmp = t_1;
	elseif (t <= -1.35e-183)
		tmp = x * (exp(y) ^ t);
	elseif (t <= 1.75e+28)
		tmp = x * exp((-a * (z + b)));
	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[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -200.0], t$95$1, If[LessEqual[t, -1.35e-183], N[(x * N[Power[N[Exp[y], $MachinePrecision], t], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+28], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -200 or 1.75e28 < t

   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 77.9%

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

      1. mul-1-neg 77.9%

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

      2. distribute-lft-neg-out 77.9%

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

      3. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -200 < t < -1.35000000000000004e-183

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 24.0%

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

      1. mul-1-neg 24.0%

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

      2. distribute-lft-neg-out 24.0%

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

      3. *-commutative 24.0%

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

   5. Simplified 24.0%

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

      1. expm1-log1p-u 24.0%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{y \cdot \left(-t\right)}\right)\right)} \]

      2. expm1-udef 24.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(e^{y \cdot \left(-t\right)}\right)} - 1\right)} \]

      3. exp-prod 23.8%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{{\left(e^{y}\right)}^{\left(-t\right)}}\right)} - 1\right) \]

      4. add-sqr-sqrt 23.8%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}}\right)} - 1\right) \]

      5. sqrt-unprod 23.9%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{\left(\sqrt{\left(-t\right) \cdot \left(-t\right)}\right)}}\right)} - 1\right) \]

      6. sqr-neg 23.9%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\left(\sqrt{\color{blue}{t \cdot t}}\right)}\right)} - 1\right) \]

      7. sqrt-unprod 20.3%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}}\right)} - 1\right) \]

      8. add-sqr-sqrt 74.4%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{\color{blue}{t}}\right)} - 1\right) \]

   7. Applied egg-rr 74.4%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({\left(e^{y}\right)}^{t}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 74.4%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{t}\right)\right)} \]

      2. expm1-log1p 74.4%

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

   9. Simplified 74.4%

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

   if -1.35000000000000004e-183 < t < 1.75e28

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 64.9%

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

      1. sub-neg 64.9%

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

      2. neg-mul-1 64.9%

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

      3. log1p-def 69.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around 0 69.3%

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

      1. associate-*r* 69.3%

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

      2. associate-*r* 69.3%

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

      3. distribute-lft-out 69.3%

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

      4. neg-mul-1 69.3%

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

   8. Simplified 69.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -200:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-183}:\\ \;\;\;\;x \cdot {\left(e^{y}\right)}^{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{if}\;b \leq -3 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{1}{a \cdot \left(x \cdot b\right)}}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- b))))))
   (if (<= b -3e-218)
     t_1
     (if (<= b 4.3e-302)
       (/ 1.0 (/ 1.0 (* a (* x b))))
       (if (<= b 4.2e-121) (* x (- 1.0 (* y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((a * -b));
	double tmp;
	if (b <= -3e-218) {
		tmp = t_1;
	} else if (b <= 4.3e-302) {
		tmp = 1.0 / (1.0 / (a * (x * b)));
	} else if (b <= 4.2e-121) {
		tmp = x * (1.0 - (y * t));
	} 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((a * -b))
    if (b <= (-3d-218)) then
        tmp = t_1
    else if (b <= 4.3d-302) then
        tmp = 1.0d0 / (1.0d0 / (a * (x * b)))
    else if (b <= 4.2d-121) then
        tmp = x * (1.0d0 - (y * t))
    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((a * -b));
	double tmp;
	if (b <= -3e-218) {
		tmp = t_1;
	} else if (b <= 4.3e-302) {
		tmp = 1.0 / (1.0 / (a * (x * b)));
	} else if (b <= 4.2e-121) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * -b))
	tmp = 0
	if b <= -3e-218:
		tmp = t_1
	elif b <= 4.3e-302:
		tmp = 1.0 / (1.0 / (a * (x * b)))
	elif b <= 4.2e-121:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(a * Float64(-b))))
	tmp = 0.0
	if (b <= -3e-218)
		tmp = t_1;
	elseif (b <= 4.3e-302)
		tmp = Float64(1.0 / Float64(1.0 / Float64(a * Float64(x * b))));
	elseif (b <= 4.2e-121)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((a * -b));
	tmp = 0.0;
	if (b <= -3e-218)
		tmp = t_1;
	elseif (b <= 4.3e-302)
		tmp = 1.0 / (1.0 / (a * (x * b)));
	elseif (b <= 4.2e-121)
		tmp = x * (1.0 - (y * t));
	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[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e-218], t$95$1, If[LessEqual[b, 4.3e-302], N[(1.0 / N[(1.0 / N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-121], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.9999999999999998e-218 or 4.1999999999999997e-121 < b

   1. Initial program 98.0%

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

   3. Taylor expanded in b around inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-rgt-neg-out 62.1%

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

   5. Simplified 62.1%

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

   if -2.9999999999999998e-218 < b < 4.3000000000000002e-302

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf 17.3%

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

      1. mul-1-neg 17.3%

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

      2. distribute-rgt-neg-out 17.3%

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

   5. Simplified 17.3%

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

   6. Taylor expanded in a around 0 17.4%

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

      1. mul-1-neg 17.4%

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

      2. unsub-neg 17.4%

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

   8. Simplified 17.4%

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

      1. distribute-rgt-out-- 17.4%

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

      2. *-un-lft-identity 17.4%

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

      3. associate-*r* 17.4%

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

      4. flip-- 42.7%

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

      5. clear-num 42.7%

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

      6. *-un-lft-identity 42.7%

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

      7. associate-*r* 42.7%

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

      8. distribute-rgt-out 42.7%

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

      9. difference-of-squares 42.7%

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

      10. add-sqr-sqrt 28.2%

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

      11. sqrt-unprod 33.1%

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

      12. sqr-neg 33.1%

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

      13. sqrt-unprod 14.5%

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

      14. add-sqr-sqrt 42.7%

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

      15. cancel-sign-sub-inv 42.7%

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

      16. pow2 42.7%

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

   10. Applied egg-rr 42.6%

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

   11. Taylor expanded in a around inf 47.4%

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

   if 4.3000000000000002e-302 < b < 4.1999999999999997e-121

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in y around 0 34.1%

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

      1. mul-1-neg 34.1%

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

      2. unsub-neg 34.1%

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

      3. *-commutative 34.1%

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

   8. Simplified 34.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-218}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{1}{a \cdot \left(x \cdot b\right)}}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+62} \lor \neg \left(t \leq 1.62 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.65e+62) (not (<= t 1.62e+28)))
   (* x (exp (* t (- y))))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.65e+62) || !(t <= 1.62e+28)) {
		tmp = x * exp((t * -y));
	} 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 ((t <= (-3.65d+62)) .or. (.not. (t <= 1.62d+28))) then
        tmp = x * exp((t * -y))
    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 ((t <= -3.65e+62) || !(t <= 1.62e+28)) {
		tmp = x * Math.exp((t * -y));
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.65e+62) or not (t <= 1.62e+28):
		tmp = x * math.exp((t * -y))
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.65e+62) || !(t <= 1.62e+28))
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	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 ((t <= -3.65e+62) || ~((t <= 1.62e+28)))
		tmp = x * exp((t * -y));
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.65e+62], N[Not[LessEqual[t, 1.62e+28]], $MachinePrecision]], N[(x * N[Exp[N[(t * (-y)), $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 t < -3.6499999999999998e62 or 1.62000000000000006e28 < t

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-lft-neg-out 80.1%

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

      3. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   if -3.6499999999999998e62 < t < 1.62000000000000006e28

   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 59.3%

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

      1. sub-neg 59.3%

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

      2. neg-mul-1 59.3%

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

      3. log1p-def 64.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in z around 0 64.8%

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

      1. associate-*r* 64.8%

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

      2. associate-*r* 64.8%

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

      3. distribute-lft-out 64.8%

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

      4. neg-mul-1 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+62} \lor \neg \left(t \leq 1.62 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+27} \lor \neg \left(t \leq 1.7 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4e+27) (not (<= t 1.7e+28)))
   (* x (exp (* t (- y))))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+27) || !(t <= 1.7e+28)) {
		tmp = x * exp((t * -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 ((t <= (-4d+27)) .or. (.not. (t <= 1.7d+28))) then
        tmp = x * exp((t * -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 ((t <= -4e+27) || !(t <= 1.7e+28)) {
		tmp = x * Math.exp((t * -y));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4e+27) or not (t <= 1.7e+28):
		tmp = x * math.exp((t * -y))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4e+27) || !(t <= 1.7e+28))
		tmp = Float64(x * exp(Float64(t * Float64(-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 ((t <= -4e+27) || ~((t <= 1.7e+28)))
		tmp = x * exp((t * -y));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4e+27], N[Not[LessEqual[t, 1.7e+28]], $MachinePrecision]], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000001e27 or 1.7e28 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in t around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

      3. *-commutative 78.9%

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

   5. Simplified 78.9%

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

   if -4.0000000000000001e27 < t < 1.7e28

   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 b around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-out 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+27} \lor \neg \left(t \leq 1.7 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - a \cdot b\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot e^{a \cdot b}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-258}:\\ \;\;\;\;x \cdot e^{y \cdot t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-288}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{1}{\frac{t_1}{x}}\\ \mathbf{elif}\;t \leq 3800000:\\ \;\;\;\;x \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (* a b))))
   (if (<= t -4.1e+27)
     (* x (exp (* a b)))
     (if (<= t -3.1e-258)
       (* x (exp (* y t)))
       (if (<= t 2.45e-288)
         (* (- b) (* x a))
         (if (<= t 4.2e-121)
           (/ 1.0 (/ t_1 x))
           (if (<= t 3800000.0) (* x t_1) (* x (- 1.0 (* y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - (a * b);
	double tmp;
	if (t <= -4.1e+27) {
		tmp = x * exp((a * b));
	} else if (t <= -3.1e-258) {
		tmp = x * exp((y * t));
	} else if (t <= 2.45e-288) {
		tmp = -b * (x * a);
	} else if (t <= 4.2e-121) {
		tmp = 1.0 / (t_1 / x);
	} else if (t <= 3800000.0) {
		tmp = x * t_1;
	} else {
		tmp = x * (1.0 - (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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - (a * b)
    if (t <= (-4.1d+27)) then
        tmp = x * exp((a * b))
    else if (t <= (-3.1d-258)) then
        tmp = x * exp((y * t))
    else if (t <= 2.45d-288) then
        tmp = -b * (x * a)
    else if (t <= 4.2d-121) then
        tmp = 1.0d0 / (t_1 / x)
    else if (t <= 3800000.0d0) then
        tmp = x * t_1
    else
        tmp = x * (1.0d0 - (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 t_1 = 1.0 - (a * b);
	double tmp;
	if (t <= -4.1e+27) {
		tmp = x * Math.exp((a * b));
	} else if (t <= -3.1e-258) {
		tmp = x * Math.exp((y * t));
	} else if (t <= 2.45e-288) {
		tmp = -b * (x * a);
	} else if (t <= 4.2e-121) {
		tmp = 1.0 / (t_1 / x);
	} else if (t <= 3800000.0) {
		tmp = x * t_1;
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 - (a * b)
	tmp = 0
	if t <= -4.1e+27:
		tmp = x * math.exp((a * b))
	elif t <= -3.1e-258:
		tmp = x * math.exp((y * t))
	elif t <= 2.45e-288:
		tmp = -b * (x * a)
	elif t <= 4.2e-121:
		tmp = 1.0 / (t_1 / x)
	elif t <= 3800000.0:
		tmp = x * t_1
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - Float64(a * b))
	tmp = 0.0
	if (t <= -4.1e+27)
		tmp = Float64(x * exp(Float64(a * b)));
	elseif (t <= -3.1e-258)
		tmp = Float64(x * exp(Float64(y * t)));
	elseif (t <= 2.45e-288)
		tmp = Float64(Float64(-b) * Float64(x * a));
	elseif (t <= 4.2e-121)
		tmp = Float64(1.0 / Float64(t_1 / x));
	elseif (t <= 3800000.0)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 - (a * b);
	tmp = 0.0;
	if (t <= -4.1e+27)
		tmp = x * exp((a * b));
	elseif (t <= -3.1e-258)
		tmp = x * exp((y * t));
	elseif (t <= 2.45e-288)
		tmp = -b * (x * a);
	elseif (t <= 4.2e-121)
		tmp = 1.0 / (t_1 / x);
	elseif (t <= 3800000.0)
		tmp = x * t_1;
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+27], N[(x * N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e-258], N[(x * N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-288], N[((-b) * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-121], N[(1.0 / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3800000.0], N[(x * t$95$1), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.1000000000000002e27

   1. Initial program 95.3%

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

   3. Taylor expanded in b around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. distribute-rgt-neg-out 40.3%

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

   5. Simplified 40.3%

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

      1. expm1-log1p-u 40.3%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{a \cdot \left(-b\right)}\right)\right)} \]

      2. expm1-udef 40.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(e^{a \cdot \left(-b\right)}\right)} - 1\right)} \]

      3. *-commutative 40.3%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(e^{\color{blue}{\left(-b\right) \cdot a}}\right)} - 1\right) \]

      4. exp-prod 38.7%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{{\left(e^{-b}\right)}^{a}}\right)} - 1\right) \]

      5. add-sqr-sqrt 14.5%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)}^{a}\right)} - 1\right) \]

      6. sqrt-unprod 24.0%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)}^{a}\right)} - 1\right) \]

      7. sqr-neg 24.0%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\sqrt{\color{blue}{b \cdot b}}}\right)}^{a}\right)} - 1\right) \]

      8. sqrt-unprod 9.4%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)}^{a}\right)} - 1\right) \]

      9. add-sqr-sqrt 15.8%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{b}}\right)}^{a}\right)} - 1\right) \]

   7. Applied egg-rr 15.8%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({\left(e^{b}\right)}^{a}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 15.8%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{b}\right)}^{a}\right)\right)} \]

      2. expm1-log1p 15.8%

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

      3. exp-prod 20.6%

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

      4. *-commutative 20.6%

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

      5. exp-prod 20.6%

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

   9. Simplified 20.6%

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

   10. Taylor expanded in a around inf 20.6%

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

   if -4.1000000000000002e27 < t < -3.09999999999999999e-258

   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 28.1%

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

      1. mul-1-neg 28.1%

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

      2. distribute-lft-neg-out 28.1%

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

      3. *-commutative 28.1%

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

   5. Simplified 28.1%

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

      1. exp-prod 29.6%

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

      2. neg-mul-1 29.6%

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

      3. pow-unpow 29.6%

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

   7. Applied egg-rr 29.6%

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

      1. unpow-1 29.6%

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

      2. rec-exp 29.6%

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

   9. Simplified 29.6%

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

       1. add-sqr-sqrt 11.6%

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

       2. sqrt-unprod 39.7%

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

       3. sqr-neg 39.7%

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

       4. sqrt-unprod 28.1%

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

       5. add-sqr-sqrt 66.9%

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

       6. exp-prod 51.9%

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

   11. Applied egg-rr 51.9%

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

   if -3.09999999999999999e-258 < t < 2.45000000000000013e-288

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-rgt-neg-out 38.8%

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

   5. Simplified 38.8%

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

   6. Taylor expanded in a around 0 12.4%

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

      1. mul-1-neg 12.4%

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

      2. unsub-neg 12.4%

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

   8. Simplified 12.4%

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

   9. Taylor expanded in a around inf 38.2%

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

       1. mul-1-neg 38.2%

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

       2. *-commutative 38.2%

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

       3. associate-*r* 46.9%

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

       4. distribute-lft-neg-in 46.9%

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

       5. *-commutative 46.9%

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

   11. Simplified 46.9%

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

   if 2.45000000000000013e-288 < t < 4.1999999999999997e-121

   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 b around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-out 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in a around 0 30.2%

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

      1. mul-1-neg 30.2%

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

      2. unsub-neg 30.2%

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

   8. Simplified 30.2%

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

      1. distribute-rgt-out-- 30.2%

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

      2. *-un-lft-identity 30.2%

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

      3. associate-*r* 30.3%

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

      4. flip-- 29.7%

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

      5. clear-num 29.6%

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

      6. *-un-lft-identity 29.6%

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

      7. associate-*r* 29.5%

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

      8. distribute-rgt-out 29.5%

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

      9. difference-of-squares 29.5%

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

      10. add-sqr-sqrt 12.2%

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

      11. sqrt-unprod 26.6%

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

      12. sqr-neg 26.6%

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

      13. sqrt-unprod 14.4%

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

      14. add-sqr-sqrt 21.1%

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

      15. cancel-sign-sub-inv 21.1%

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

      16. pow2 21.1%

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

   10. Applied egg-rr 21.1%

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

   11. Taylor expanded in a around 0 38.3%

       \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{a \cdot b}{x} + \frac{1}{x}}} \]
   12. Step-by-step derivation

       1. +-commutative 38.3%

          \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{a \cdot b}{x}}} \]

       2. mul-1-neg 38.3%

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

       3. unsub-neg 38.3%

          \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} - \frac{a \cdot b}{x}}} \]

       4. div-sub 38.3%

          \[\leadsto \frac{1}{\color{blue}{\frac{1 - a \cdot b}{x}}} \]

   13. Simplified 38.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1 - a \cdot b}{x}}} \]

   if 4.1999999999999997e-121 < t < 3.8e6

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. distribute-rgt-neg-out 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in a around 0 40.1%

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

      1. mul-1-neg 40.1%

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

      2. unsub-neg 40.1%

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

   8. Simplified 40.1%

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

   if 3.8e6 < t

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-lft-neg-out 83.5%

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

      3. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. unsub-neg 40.2%

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

      3. *-commutative 40.2%

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

   8. Simplified 40.2%

      \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot e^{a \cdot b}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-258}:\\ \;\;\;\;x \cdot e^{y \cdot t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-288}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{1}{\frac{1 - a \cdot b}{x}}\\ \mathbf{elif}\;t \leq 3800000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot e^{a \cdot b}\\ \mathbf{elif}\;t \leq 3900000:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.7e-188)
   (* x (exp (* a b)))
   (if (<= t 3900000.0) (- x (* (+ z b) (* x a))) (* x (- 1.0 (* y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.7e-188) {
		tmp = x * exp((a * b));
	} else if (t <= 3900000.0) {
		tmp = x - ((z + b) * (x * a));
	} else {
		tmp = x * (1.0 - (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 (t <= (-3.7d-188)) then
        tmp = x * exp((a * b))
    else if (t <= 3900000.0d0) then
        tmp = x - ((z + b) * (x * a))
    else
        tmp = x * (1.0d0 - (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 (t <= -3.7e-188) {
		tmp = x * Math.exp((a * b));
	} else if (t <= 3900000.0) {
		tmp = x - ((z + b) * (x * a));
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.7e-188:
		tmp = x * math.exp((a * b))
	elif t <= 3900000.0:
		tmp = x - ((z + b) * (x * a))
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.7e-188)
		tmp = Float64(x * exp(Float64(a * b)));
	elseif (t <= 3900000.0)
		tmp = Float64(x - Float64(Float64(z + b) * Float64(x * a)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.7e-188)
		tmp = x * exp((a * b));
	elseif (t <= 3900000.0)
		tmp = x - ((z + b) * (x * a));
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.7e-188], N[(x * N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3900000.0], N[(x - N[(N[(z + b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999972e-188

   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 b around inf 45.2%

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

      1. mul-1-neg 45.2%

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

      2. distribute-rgt-neg-out 45.2%

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

   5. Simplified 45.2%

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

      1. expm1-log1p-u 45.2%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{a \cdot \left(-b\right)}\right)\right)} \]

      2. expm1-udef 45.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(e^{a \cdot \left(-b\right)}\right)} - 1\right)} \]

      3. *-commutative 45.2%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(e^{\color{blue}{\left(-b\right) \cdot a}}\right)} - 1\right) \]

      4. exp-prod 37.2%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{{\left(e^{-b}\right)}^{a}}\right)} - 1\right) \]

      5. add-sqr-sqrt 17.2%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)}^{a}\right)} - 1\right) \]

      6. sqrt-unprod 26.0%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)}^{a}\right)} - 1\right) \]

      7. sqr-neg 26.0%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\sqrt{\color{blue}{b \cdot b}}}\right)}^{a}\right)} - 1\right) \]

      8. sqrt-unprod 8.7%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)}^{a}\right)} - 1\right) \]

      9. add-sqr-sqrt 18.5%

         \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left({\left(e^{\color{blue}{b}}\right)}^{a}\right)} - 1\right) \]

   7. Applied egg-rr 18.5%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({\left(e^{b}\right)}^{a}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 18.5%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{b}\right)}^{a}\right)\right)} \]

      2. expm1-log1p 18.5%

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

      3. exp-prod 27.7%

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

      4. *-commutative 27.7%

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

      5. exp-prod 24.1%

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

   9. Simplified 24.1%

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

   10. Taylor expanded in a around inf 27.7%

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

   if -3.69999999999999972e-188 < t < 3.9e6

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 62.6%

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

      1. sub-neg 62.6%

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

      2. neg-mul-1 62.6%

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

      3. log1p-def 66.2%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in z around 0 66.2%

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

      1. associate-*r* 66.2%

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

      2. associate-*r* 66.2%

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

      3. distribute-lft-out 66.2%

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

      4. neg-mul-1 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in a around 0 30.0%

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

       1. mul-1-neg 30.0%

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

       2. unsub-neg 30.0%

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

       3. *-commutative 30.0%

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

       4. *-commutative 30.0%

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

       5. associate-*l* 31.2%

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

       6. *-commutative 31.2%

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

   11. Simplified 31.2%

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

   if 3.9e6 < t

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-lft-neg-out 83.5%

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

      3. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. unsub-neg 40.2%

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

      3. *-commutative 40.2%

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

   8. Simplified 40.2%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot e^{a \cdot b}\\ \mathbf{elif}\;t \leq 3900000:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.1% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 155000000000:\\ \;\;\;\;\frac{1}{\frac{1 - a \cdot b}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.2e-83)
   (* x (- 1.0 (* y t)))
   (if (<= y 155000000000.0) (/ 1.0 (/ (- 1.0 (* a b)) x)) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e-83) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 155000000000.0) {
		tmp = 1.0 / ((1.0 - (a * b)) / x);
	} else {
		tmp = a * (x * -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 <= (-8.2d-83)) then
        tmp = x * (1.0d0 - (y * t))
    else if (y <= 155000000000.0d0) then
        tmp = 1.0d0 / ((1.0d0 - (a * b)) / x)
    else
        tmp = a * (x * -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 <= -8.2e-83) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 155000000000.0) {
		tmp = 1.0 / ((1.0 - (a * b)) / x);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.2e-83:
		tmp = x * (1.0 - (y * t))
	elif y <= 155000000000.0:
		tmp = 1.0 / ((1.0 - (a * b)) / x)
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.2e-83)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (y <= 155000000000.0)
		tmp = Float64(1.0 / Float64(Float64(1.0 - Float64(a * b)) / x));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.2e-83)
		tmp = x * (1.0 - (y * t));
	elseif (y <= 155000000000.0)
		tmp = 1.0 / ((1.0 - (a * b)) / x);
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.2e-83], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 155000000000.0], N[(1.0 / N[(N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999999e-83

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. distribute-lft-neg-out 63.3%

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

      3. *-commutative 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in y around 0 26.4%

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

      1. mul-1-neg 26.4%

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

      2. unsub-neg 26.4%

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

      3. *-commutative 26.4%

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

   8. Simplified 26.4%

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

   if -8.1999999999999999e-83 < y < 1.55e11

   1. Initial program 93.5%

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

   3. Taylor expanded in 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%

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

   6. Taylor expanded in a around 0 34.9%

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

      1. mul-1-neg 34.9%

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

      2. unsub-neg 34.9%

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

   8. Simplified 34.9%

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

      1. distribute-rgt-out-- 34.9%

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

      2. *-un-lft-identity 34.9%

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

      3. associate-*r* 31.4%

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

      4. flip-- 28.8%

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

      5. clear-num 28.7%

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

      6. *-un-lft-identity 28.7%

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

      7. associate-*r* 27.7%

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

      8. distribute-rgt-out 27.7%

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

      9. difference-of-squares 28.7%

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

      10. add-sqr-sqrt 15.4%

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

      11. sqrt-unprod 26.4%

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

      12. sqr-neg 26.4%

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

      13. sqrt-unprod 12.2%

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

      14. add-sqr-sqrt 25.4%

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

      15. cancel-sign-sub-inv 25.4%

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

      16. pow2 25.4%

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

   10. Applied egg-rr 21.6%

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

   11. Taylor expanded in a around 0 40.5%

       \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{a \cdot b}{x} + \frac{1}{x}}} \]
   12. Step-by-step derivation

       1. +-commutative 40.5%

          \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{a \cdot b}{x}}} \]

       2. mul-1-neg 40.5%

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

       3. unsub-neg 40.5%

          \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} - \frac{a \cdot b}{x}}} \]

       4. div-sub 40.5%

          \[\leadsto \frac{1}{\color{blue}{\frac{1 - a \cdot b}{x}}} \]

   13. Simplified 40.5%

       \[\leadsto \frac{1}{\color{blue}{\frac{1 - a \cdot b}{x}}} \]

   if 1.55e11 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. distribute-rgt-neg-out 29.0%

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

   5. Simplified 29.0%

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

   6. Taylor expanded in a around 0 13.0%

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

      1. mul-1-neg 13.0%

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

      2. unsub-neg 13.0%

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

   8. Simplified 13.0%

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

   9. Taylor expanded in a around inf 27.5%

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

       1. mul-1-neg 27.5%

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

       2. distribute-rgt-neg-in 27.5%

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

       3. distribute-rgt-neg-in 27.5%

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

   11. Simplified 27.5%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 155000000000:\\ \;\;\;\;\frac{1}{\frac{1 - a \cdot b}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+172} \lor \neg \left(a \leq 2.8 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.6e+172) (not (<= a 2.8e+138)))
   (* a (* x (- b)))
   (* x (- 1.0 (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.6e+172) || !(a <= 2.8e+138)) {
		tmp = a * (x * -b);
	} else {
		tmp = x * (1.0 - (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 ((a <= (-3.6d+172)) .or. (.not. (a <= 2.8d+138))) then
        tmp = a * (x * -b)
    else
        tmp = x * (1.0d0 - (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 ((a <= -3.6e+172) || !(a <= 2.8e+138)) {
		tmp = a * (x * -b);
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.6e+172) or not (a <= 2.8e+138):
		tmp = a * (x * -b)
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.6e+172) || !(a <= 2.8e+138))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.6e+172) || ~((a <= 2.8e+138)))
		tmp = a * (x * -b);
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.6e+172], N[Not[LessEqual[a, 2.8e+138]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.59999999999999975e172 or 2.8000000000000001e138 < a

   1. Initial program 94.4%

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

   3. Taylor expanded in b around inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. distribute-rgt-neg-out 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in a around 0 29.1%

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

      1. mul-1-neg 29.1%

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

      2. unsub-neg 29.1%

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

   8. Simplified 29.1%

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

   9. Taylor expanded in a around inf 33.3%

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

       1. mul-1-neg 33.3%

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

       2. distribute-rgt-neg-in 33.3%

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

       3. distribute-rgt-neg-in 33.3%

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

   11. Simplified 33.3%

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

   if -3.59999999999999975e172 < a < 2.8000000000000001e138

   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 59.5%

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

      1. mul-1-neg 59.5%

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

      2. distribute-lft-neg-out 59.5%

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

      3. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around 0 30.7%

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

      1. mul-1-neg 30.7%

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

      2. unsub-neg 30.7%

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

      3. *-commutative 30.7%

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

   8. Simplified 30.7%

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

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+172} \lor \neg \left(a \leq 2.8 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.32:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+19)
   (* (- b) (* x a))
   (if (<= y 0.32) (* x (- 1.0 (* a b))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+19) {
		tmp = -b * (x * a);
	} else if (y <= 0.32) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -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 <= (-1.6d+19)) then
        tmp = -b * (x * a)
    else if (y <= 0.32d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * (x * -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 <= -1.6e+19) {
		tmp = -b * (x * a);
	} else if (y <= 0.32) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e+19:
		tmp = -b * (x * a)
	elif y <= 0.32:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e+19)
		tmp = Float64(Float64(-b) * Float64(x * a));
	elseif (y <= 0.32)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e+19)
		tmp = -b * (x * a);
	elseif (y <= 0.32)
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+19], N[((-b) * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.32], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e19

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 28.4%

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

      1. mul-1-neg 28.4%

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

      2. distribute-rgt-neg-out 28.4%

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

   5. Simplified 28.4%

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

   6. Taylor expanded in a around 0 11.6%

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

      1. mul-1-neg 11.6%

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

      2. unsub-neg 11.6%

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

   8. Simplified 11.6%

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

   9. Taylor expanded in a around inf 14.0%

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

       1. mul-1-neg 14.0%

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

       2. *-commutative 14.0%

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

       3. associate-*r* 17.9%

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

       4. distribute-lft-neg-in 17.9%

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

       5. *-commutative 17.9%

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

   11. Simplified 17.9%

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

   if -1.6e19 < y < 0.320000000000000007

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-rgt-neg-out 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. unsub-neg 35.8%

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

   8. Simplified 35.8%

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

   if 0.320000000000000007 < y

   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 b around inf 29.3%

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

      1. mul-1-neg 29.3%

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

      2. distribute-rgt-neg-out 29.3%

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

   5. Simplified 29.3%

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

   6. Taylor expanded in a around 0 12.5%

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

      1. mul-1-neg 12.5%

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

      2. unsub-neg 12.5%

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

   8. Simplified 12.5%

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

   9. Taylor expanded in a around inf 26.3%

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

       1. mul-1-neg 26.3%

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

       2. distribute-rgt-neg-in 26.3%

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

       3. distribute-rgt-neg-in 26.3%

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

   11. Simplified 26.3%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.32:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.1% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+172} \lor \neg \left(a \leq 1.5 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.75e+172) (not (<= a 1.5e+107))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.75e+172) || !(a <= 1.5e+107)) {
		tmp = a * (x * -b);
	} 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 ((a <= (-1.75d+172)) .or. (.not. (a <= 1.5d+107))) then
        tmp = a * (x * -b)
    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 ((a <= -1.75e+172) || !(a <= 1.5e+107)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.75e+172) or not (a <= 1.5e+107):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.75e+172) || !(a <= 1.5e+107))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.75e+172) || ~((a <= 1.5e+107)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.75e+172], N[Not[LessEqual[a, 1.5e+107]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.74999999999999989e172 or 1.50000000000000012e107 < a

   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 b around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-out 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in a around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. unsub-neg 28.1%

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

   8. Simplified 28.1%

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

   9. Taylor expanded in a around inf 31.9%

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

       1. mul-1-neg 31.9%

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

       2. distribute-rgt-neg-in 31.9%

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

       3. distribute-rgt-neg-in 31.9%

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

   11. Simplified 31.9%

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

   if -1.74999999999999989e172 < a < 1.50000000000000012e107

   1. Initial program 97.8%

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

   3. Taylor expanded in b around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-rgt-neg-out 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in a around 0 20.9%

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

4. Final simplification 24.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+172} \lor \neg \left(a \leq 1.5 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.8% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 155000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+19)
   (* (- b) (* x a))
   (if (<= y 155000000000.0) x (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+19) {
		tmp = -b * (x * a);
	} else if (y <= 155000000000.0) {
		tmp = x;
	} else {
		tmp = a * (x * -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 <= (-1.6d+19)) then
        tmp = -b * (x * a)
    else if (y <= 155000000000.0d0) then
        tmp = x
    else
        tmp = a * (x * -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 <= -1.6e+19) {
		tmp = -b * (x * a);
	} else if (y <= 155000000000.0) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e+19:
		tmp = -b * (x * a)
	elif y <= 155000000000.0:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e+19)
		tmp = Float64(Float64(-b) * Float64(x * a));
	elseif (y <= 155000000000.0)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e+19)
		tmp = -b * (x * a);
	elseif (y <= 155000000000.0)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+19], N[((-b) * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 155000000000.0], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e19

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 28.4%

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

      1. mul-1-neg 28.4%

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

      2. distribute-rgt-neg-out 28.4%

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

   5. Simplified 28.4%

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

   6. Taylor expanded in a around 0 11.6%

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

      1. mul-1-neg 11.6%

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

      2. unsub-neg 11.6%

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

   8. Simplified 11.6%

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

   9. Taylor expanded in a around inf 14.0%

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

       1. mul-1-neg 14.0%

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

       2. *-commutative 14.0%

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

       3. associate-*r* 17.9%

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

       4. distribute-lft-neg-in 17.9%

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

       5. *-commutative 17.9%

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

   11. Simplified 17.9%

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

   if -1.6e19 < y < 1.55e11

   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 b around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-rgt-neg-out 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around 0 27.9%

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

   if 1.55e11 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. distribute-rgt-neg-out 29.0%

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

   5. Simplified 29.0%

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

   6. Taylor expanded in a around 0 13.0%

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

      1. mul-1-neg 13.0%

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

      2. unsub-neg 13.0%

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

   8. Simplified 13.0%

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

   9. Taylor expanded in a around inf 27.5%

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

       1. mul-1-neg 27.5%

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

       2. distribute-rgt-neg-in 27.5%

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

       3. distribute-rgt-neg-in 27.5%

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

   11. Simplified 27.5%

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

4. Final simplification 25.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 155000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 19.9% 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 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 b around inf 52.3%

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

   1. mul-1-neg 52.3%

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

   2. distribute-rgt-neg-out 52.3%

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

5. Simplified 52.3%

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

6. Taylor expanded in a around 0 15.7%

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

7. Final simplification 15.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024017 
(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))))))