Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.4% → 98.4%

Time: 10.4s

Alternatives: 12

Speedup: 1.0×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

Alternative 2: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+132}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+46}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))))
   (if (<= t_1 -2e+132)
     (/ (* x (exp (- (* (log a) t) b))) y)
     (if (<= t_1 2e+46)
       (/ (* x (exp (- (fma (log z) y (- (log a))) b))) y)
       (* (/ (pow a (- t 1.0)) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double tmp;
	if (t_1 <= -2e+132) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else if (t_1 <= 2e+46) {
		tmp = (x * exp((fma(log(z), y, -log(a)) - b))) / y;
	} else {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_1 <= -2e+132)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	elseif (t_1 <= 2e+46)
		tmp = Float64(Float64(x * exp(Float64(fma(log(z), y, Float64(-log(a))) - b))) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+132], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+46], N[(N[(x * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.99999999999999998e132

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a} - b}}{y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. lower-log.f64 100.0

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a} \cdot t - b}}{y} \]

   5. Applied rewrites 100.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   if -1.99999999999999998e132 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e46

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-log.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 2e46 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 89.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 89.7

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

   10. Applied rewrites 89.7%

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

Alternative 3: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+75} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(e^{b} \cdot y\right) \cdot a\right)}^{-1} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))))
   (if (or (<= t_1 -1e+75) (not (<= t_1 2e+46)))
     (* (/ (pow a (- t 1.0)) y) x)
     (* (pow (* (* (exp b) y) a) -1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double tmp;
	if ((t_1 <= -1e+75) || !(t_1 <= 2e+46)) {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	} else {
		tmp = pow(((exp(b) * y) * a), -1.0) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    if ((t_1 <= (-1d+75)) .or. (.not. (t_1 <= 2d+46))) then
        tmp = ((a ** (t - 1.0d0)) / y) * x
    else
        tmp = (((exp(b) * y) * a) ** (-1.0d0)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double tmp;
	if ((t_1 <= -1e+75) || !(t_1 <= 2e+46)) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	} else {
		tmp = Math.pow(((Math.exp(b) * y) * a), -1.0) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	tmp = 0
	if (t_1 <= -1e+75) or not (t_1 <= 2e+46):
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	else:
		tmp = math.pow(((math.exp(b) * y) * a), -1.0) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if ((t_1 <= -1e+75) || !(t_1 <= 2e+46))
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	else
		tmp = Float64((Float64(Float64(exp(b) * y) * a) ^ -1.0) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	tmp = 0.0;
	if ((t_1 <= -1e+75) || ~((t_1 <= 2e+46)))
		tmp = ((a ^ (t - 1.0)) / y) * x;
	else
		tmp = (((exp(b) * y) * a) ^ -1.0) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+75], N[Not[LessEqual[t$95$1, 2e+46]], $MachinePrecision]], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[Power[N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -9.99999999999999927e74 or 2e46 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 88.4

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

   10. Applied rewrites 88.4%

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

   if -9.99999999999999927e74 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e46

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 79.4

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

   5. Applied rewrites 79.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(-1 + t\right) \cdot \log a} - b}}{y} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 79.4%

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

   8. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. associate-/l/ N/A

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

      3. lower-/.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 74.6

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

   10. Applied rewrites 74.6%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 79.2%

       \[\leadsto \frac{1}{\color{blue}{\left(e^{b} \cdot y\right) \cdot a}} \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -1 \cdot 10^{+75} \lor \neg \left(\left(t - 1\right) \cdot \log a \leq 2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(e^{b} \cdot y\right) \cdot a\right)}^{-1} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+40} \lor \neg \left(b \leq 1.25\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y} \cdot {a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+40) (not (<= b 1.25)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* x (/ (* (pow z y) (pow a t)) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+40) || !(b <= 1.25)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * ((pow(z, y) * pow(a, t)) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.9d+40)) .or. (.not. (b <= 1.25d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * (((z ** y) * (a ** t)) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+40) || !(b <= 1.25)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * ((Math.pow(z, y) * Math.pow(a, t)) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+40) or not (b <= 1.25):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * ((math.pow(z, y) * math.pow(a, t)) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+40) || !(b <= 1.25))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) * (a ^ t)) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+40) || ~((b <= 1.25)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * (((z ^ y) * (a ^ t)) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+40], N[Not[LessEqual[b, 1.25]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.90000000000000002e40 or 1.25 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a} - b}}{y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. lower-log.f64 90.2

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a} \cdot t - b}}{y} \]

   5. Applied rewrites 90.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   if -1.90000000000000002e40 < b < 1.25

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 93.2

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

   5. Applied rewrites 93.2%

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

   7. Applied rewrites 93.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+40} \lor \neg \left(b \leq 1.25\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y} \cdot {a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{if}\;b \leq -1950000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot \mathsf{fma}\left(-b, x, x\right)}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) t) b))) y)))
   (if (<= b -1950000.0)
     t_1
     (if (<= b -1.75e-307)
       (/ (* (/ (pow z y) a) (fma (- b) x x)) y)
       (if (<= b 3.6e-35) (/ (* x (/ (pow a t) a)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * t) - b))) / y;
	double tmp;
	if (b <= -1950000.0) {
		tmp = t_1;
	} else if (b <= -1.75e-307) {
		tmp = ((pow(z, y) / a) * fma(-b, x, x)) / y;
	} else if (b <= 3.6e-35) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y)
	tmp = 0.0
	if (b <= -1950000.0)
		tmp = t_1;
	elseif (b <= -1.75e-307)
		tmp = Float64(Float64(Float64((z ^ y) / a) * fma(Float64(-b), x, x)) / y);
	elseif (b <= 3.6e-35)
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1950000.0], t$95$1, If[LessEqual[b, -1.75e-307], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[((-b) * x + x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.6e-35], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.95e6 or 3.60000000000000019e-35 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a} - b}}{y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. lower-log.f64 88.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a} \cdot t - b}}{y} \]

   5. Applied rewrites 88.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   if -1.95e6 < b < -1.7500000000000001e-307

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-rgt-out N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 96.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{\frac{{z}^{y}}{a} \cdot \mathsf{fma}\left(\color{blue}{-b}, x, x\right)}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.3%

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

   if -1.7500000000000001e-307 < b < 3.60000000000000019e-35

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 91.0

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

   5. Applied rewrites 91.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.0%

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

   10. Applied rewrites 86.2%

       \[\leadsto \frac{x \cdot \frac{{a}^{t}}{a}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 86.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+40} \lor \neg \left(b \leq 1.25\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+40) (not (<= b 1.25)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (* (/ (* (pow z y) (pow a (- t 1.0))) y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+40) || !(b <= 1.25)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = ((pow(z, y) * pow(a, (t - 1.0))) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.9d+40)) .or. (.not. (b <= 1.25d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (((z ** y) * (a ** (t - 1.0d0))) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+40) || !(b <= 1.25)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = ((Math.pow(z, y) * Math.pow(a, (t - 1.0))) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+40) or not (b <= 1.25):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = ((math.pow(z, y) * math.pow(a, (t - 1.0))) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+40) || !(b <= 1.25))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(Float64((z ^ y) * (a ^ Float64(t - 1.0))) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+40) || ~((b <= 1.25)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (((z ^ y) * (a ^ (t - 1.0))) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+40], N[Not[LessEqual[b, 1.25]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.90000000000000002e40 or 1.25 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a} - b}}{y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. lower-log.f64 90.2

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a} \cdot t - b}}{y} \]

   5. Applied rewrites 90.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   if -1.90000000000000002e40 < b < 1.25

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 93.2

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

   5. Applied rewrites 93.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.3

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

   7. Applied rewrites 93.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+40} \lor \neg \left(b \leq 1.25\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+40} \lor \neg \left(b \leq 1.25\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot x\right) \cdot \frac{{z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+40) (not (<= b 1.25)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (* (* (pow a (- t 1.0)) x) (/ (pow z y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+40) || !(b <= 1.25)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (pow(a, (t - 1.0)) * x) * (pow(z, y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.9d+40)) .or. (.not. (b <= 1.25d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = ((a ** (t - 1.0d0)) * x) * ((z ** y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+40) || !(b <= 1.25)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) * x) * (Math.pow(z, y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+40) or not (b <= 1.25):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (math.pow(a, (t - 1.0)) * x) * (math.pow(z, y) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+40) || !(b <= 1.25))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) * Float64((z ^ y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+40) || ~((b <= 1.25)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = ((a ^ (t - 1.0)) * x) * ((z ^ y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+40], N[Not[LessEqual[b, 1.25]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.90000000000000002e40 or 1.25 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a} - b}}{y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. lower-log.f64 90.2

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a} \cdot t - b}}{y} \]

   5. Applied rewrites 90.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   if -1.90000000000000002e40 < b < 1.25

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 92.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+40} \lor \neg \left(b \leq 1.25\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot x\right) \cdot \frac{{z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -310000000000 \lor \neg \left(b \leq 6.5 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -310000000000.0) (not (<= b 6.5e+44)))
   (* (/ (exp (- b)) y) x)
   (* (/ (pow a (- t 1.0)) y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -310000000000.0) || !(b <= 6.5e+44)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-310000000000.0d0)) .or. (.not. (b <= 6.5d+44))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = ((a ** (t - 1.0d0)) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -310000000000.0) || !(b <= 6.5e+44)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -310000000000.0) or not (b <= 6.5e+44):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -310000000000.0) || !(b <= 6.5e+44))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -310000000000.0) || ~((b <= 6.5e+44)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = ((a ^ (t - 1.0)) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -310000000000.0], N[Not[LessEqual[b, 6.5e+44]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1e11 or 6.50000000000000018e44 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 89.1

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

   5. Applied rewrites 89.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(-1 + t\right) \cdot \log a} - b}}{y} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 89.1%

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

   8. Taylor expanded in b around inf

      \[\leadsto \frac{e^{\color{blue}{-1 \cdot b}}}{y} \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{e^{\color{blue}{\mathsf{neg}\left(b\right)}}}{y} \cdot x \]

      2. lower-neg.f64 80.5

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

   10. Applied rewrites 80.5%

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

   if -3.1e11 < b < 6.50000000000000018e44

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 92.7

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

   5. Applied rewrites 92.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.3

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

   10. Applied rewrites 78.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -310000000000 \lor \neg \left(b \leq 6.5 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -900 \lor \neg \left(b \leq 6.5 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t - 1\right)} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -900.0) (not (<= b 6.5e+44)))
   (* (/ (exp (- b)) y) x)
   (* (pow a (- t 1.0)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -900.0) || !(b <= 6.5e+44)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = pow(a, (t - 1.0)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-900.0d0)) .or. (.not. (b <= 6.5d+44))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (a ** (t - 1.0d0)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -900.0) || !(b <= 6.5e+44)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = Math.pow(a, (t - 1.0)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -900.0) or not (b <= 6.5e+44):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = math.pow(a, (t - 1.0)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -900.0) || !(b <= 6.5e+44))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64((a ^ Float64(t - 1.0)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -900.0) || ~((b <= 6.5e+44)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (a ^ (t - 1.0)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -900.0], N[Not[LessEqual[b, 6.5e+44]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -900 or 6.50000000000000018e44 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 89.3

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

   5. Applied rewrites 89.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(-1 + t\right) \cdot \log a} - b}}{y} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 89.3%

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

   8. Taylor expanded in b around inf

      \[\leadsto \frac{e^{\color{blue}{-1 \cdot b}}}{y} \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{e^{\color{blue}{\mathsf{neg}\left(b\right)}}}{y} \cdot x \]

      2. lower-neg.f64 79.4

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

   10. Applied rewrites 79.4%

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

   if -900 < b < 6.50000000000000018e44

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 92.5

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 73.9

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

   10. Applied rewrites 73.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -900 \lor \neg \left(b \leq 6.5 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t - 1\right)} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.3:\\ \;\;\;\;\frac{{a}^{-1} \cdot \mathsf{fma}\left(-b, x, x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{-1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.3)
   (/ (* (pow a -1.0) (fma (- b) x x)) y)
   (/ (* x (pow a -1.0)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.3) {
		tmp = (pow(a, -1.0) * fma(-b, x, x)) / y;
	} else {
		tmp = (x * pow(a, -1.0)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.3)
		tmp = Float64(Float64((a ^ -1.0) * fma(Float64(-b), x, x)) / y);
	else
		tmp = Float64(Float64(x * (a ^ -1.0)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.3], N[(N[(N[Power[a, -1.0], $MachinePrecision] * N[((-b) * x + x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.30000000000000004

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-rgt-out N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right)} \cdot \mathsf{fma}\left(\color{blue}{-b}, x, x\right)}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

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

   9. Taylor expanded in t around 0

      \[\leadsto \frac{\frac{1}{a} \cdot \mathsf{fma}\left(-b, x, x\right)}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 45.7%

       \[\leadsto \frac{\frac{1}{a} \cdot \mathsf{fma}\left(-b, x, x\right)}{y} \]

   if 1.30000000000000004 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 47.0

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

   5. Applied rewrites 47.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

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

   9. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 28.3%

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.3:\\ \;\;\;\;\frac{{a}^{-1} \cdot \mathsf{fma}\left(-b, x, x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{-1}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -450 \lor \neg \left(b \leq 27000000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{-1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -450.0) (not (<= b 27000000.0)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (pow a -1.0)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -450.0) || !(b <= 27000000.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * pow(a, -1.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-450.0d0)) .or. (.not. (b <= 27000000.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * (a ** (-1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -450.0) || !(b <= 27000000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * Math.pow(a, -1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -450.0) or not (b <= 27000000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * math.pow(a, -1.0)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -450.0) || !(b <= 27000000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * (a ^ -1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -450.0) || ~((b <= 27000000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * (a ^ -1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -450.0], N[Not[LessEqual[b, 27000000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -450 or 2.7e7 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 89.5

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

   5. Applied rewrites 89.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(-1 + t\right) \cdot \log a} - b}}{y} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 89.5%

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

   8. Taylor expanded in b around inf

      \[\leadsto \frac{e^{\color{blue}{-1 \cdot b}}}{y} \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{e^{\color{blue}{\mathsf{neg}\left(b\right)}}}{y} \cdot x \]

      2. lower-neg.f64 78.2

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

   10. Applied rewrites 78.2%

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

   if -450 < b < 2.7e7

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 93.5

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

   5. Applied rewrites 93.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 79.0%

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

   9. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 44.0%

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -450 \lor \neg \left(b \leq 27000000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{-1}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot {a}^{-1}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (* x (pow a -1.0)) y))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in b around 0

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

   1. +-commutative N/A

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

   2. exp-sum N/A

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

   3. lower-*.f64 N/A

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

   4. exp-to-pow N/A

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

   5. lower-pow.f64 N/A

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

   6. lower--.f64 N/A

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

   7. *-commutative N/A

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

   8. exp-to-pow N/A

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

   9. lower-pow.f64 71.4

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

5. Applied rewrites 71.4%

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

6. Taylor expanded in y around 0

   \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y} \]
7. Step-by-step derivation

8. Applied rewrites 61.7%

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

9. Taylor expanded in t around 0

   \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
10. Step-by-step derivation

11. Applied rewrites 35.0%

    \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]

12. Final simplification 35.0%

    \[\leadsto \frac{x \cdot {a}^{-1}}{y} \]
13. Add Preprocessing

Developer Target 1: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024337 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))