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

Percentage Accurate: 98.4% → 98.4%

Time: 11.2s

Alternatives: 17

Speedup: 1.0×

• 47.0% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 98.9%

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

Alternative 2: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b} \cdot x}{y}\\ \mathbf{if}\;y \leq -2700000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (fma (log z) y (- (log a))) b)) x) y)))
   (if (<= y -2700000000000.0)
     t_1
     (if (<= y 8e+83) (/ (* (exp (- (* (log a) (- t 1.0)) b)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp((fma(log(z), y, -log(a)) - b)) * x) / y;
	double tmp;
	if (y <= -2700000000000.0) {
		tmp = t_1;
	} else if (y <= 8e+83) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(fma(log(z), y, Float64(-log(a))) - b)) * x) / y)
	tmp = 0.0
	if (y <= -2700000000000.0)
		tmp = t_1;
	elseif (y <= 8e+83)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2700000000000.0], t$95$1, If[LessEqual[y, 8e+83], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e12 or 8.00000000000000025e83 < y

   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 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. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 94.5

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

   5. Applied rewrites 94.5%

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

   if -2.7e12 < y < 8.00000000000000025e83

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 97.3

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

   5. Applied rewrites 97.3%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2700000000000:\\ \;\;\;\;\frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ t_2 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{1}{e^{b} \cdot a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y))
        (t_2 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -9.5e+32)
     t_2
     (if (<= y -3.5e-144)
       t_1
       (if (<= y 2.6e-10)
         (/ (* (/ 1.0 (* (exp b) a)) x) y)
         (if (<= y 1.1e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double t_2 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_2;
	} else if (y <= -3.5e-144) {
		tmp = t_1;
	} else if (y <= 2.6e-10) {
		tmp = ((1.0 / (exp(b) * a)) * x) / y;
	} else if (y <= 1.1e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (exp(((log(a) * t) - b)) * x) / y
    t_2 = (((z ** y) / a) * x) / y
    if (y <= (-9.5d+32)) then
        tmp = t_2
    else if (y <= (-3.5d-144)) then
        tmp = t_1
    else if (y <= 2.6d-10) then
        tmp = ((1.0d0 / (exp(b) * a)) * x) / y
    else if (y <= 1.1d+84) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double t_2 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_2;
	} else if (y <= -3.5e-144) {
		tmp = t_1;
	} else if (y <= 2.6e-10) {
		tmp = ((1.0 / (Math.exp(b) * a)) * x) / y;
	} else if (y <= 1.1e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	t_2 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -9.5e+32:
		tmp = t_2
	elif y <= -3.5e-144:
		tmp = t_1
	elif y <= 2.6e-10:
		tmp = ((1.0 / (math.exp(b) * a)) * x) / y
	elif y <= 1.1e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	t_2 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -9.5e+32)
		tmp = t_2;
	elseif (y <= -3.5e-144)
		tmp = t_1;
	elseif (y <= 2.6e-10)
		tmp = Float64(Float64(Float64(1.0 / Float64(exp(b) * a)) * x) / y);
	elseif (y <= 1.1e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	t_2 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -9.5e+32)
		tmp = t_2;
	elseif (y <= -3.5e-144)
		tmp = t_1;
	elseif (y <= 2.6e-10)
		tmp = ((1.0 / (exp(b) * a)) * x) / y;
	elseif (y <= 1.1e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9.5e+32], t$95$2, If[LessEqual[y, -3.5e-144], t$95$1, If[LessEqual[y, 2.6e-10], N[(N[(N[(1.0 / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.1e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000006e32 or 1.0999999999999999e84 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.2%

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

   if -9.50000000000000006e32 < y < -3.4999999999999998e-144 or 2.59999999999999981e-10 < y < 1.0999999999999999e84

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 88.2

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

   5. Applied rewrites 88.2%

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

   if -3.4999999999999998e-144 < y < 2.59999999999999981e-10

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{1}{e^{b} \cdot a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-302}:\\ \;\;\;\;\left(\frac{{z}^{y}}{y} \cdot {a}^{\left(t - 1\right)}\right) \cdot x\\ \mathbf{elif}\;b \leq 8200:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= b -3.3e+38)
     t_1
     (if (<= b 6.8e-302)
       (* (* (/ (pow z y) y) (pow a (- t 1.0))) x)
       (if (<= b 8200.0) (/ (* (/ (pow z y) a) x) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -3.3e+38) {
		tmp = t_1;
	} else if (b <= 6.8e-302) {
		tmp = ((pow(z, y) / y) * pow(a, (t - 1.0))) * x;
	} else if (b <= 8200.0) {
		tmp = ((pow(z, y) / a) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(((log(a) * t) - b)) * x) / y
    if (b <= (-3.3d+38)) then
        tmp = t_1
    else if (b <= 6.8d-302) then
        tmp = (((z ** y) / y) * (a ** (t - 1.0d0))) * x
    else if (b <= 8200.0d0) then
        tmp = (((z ** y) / a) * x) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -3.3e+38) {
		tmp = t_1;
	} else if (b <= 6.8e-302) {
		tmp = ((Math.pow(z, y) / y) * Math.pow(a, (t - 1.0))) * x;
	} else if (b <= 8200.0) {
		tmp = ((Math.pow(z, y) / a) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if b <= -3.3e+38:
		tmp = t_1
	elif b <= 6.8e-302:
		tmp = ((math.pow(z, y) / y) * math.pow(a, (t - 1.0))) * x
	elif b <= 8200.0:
		tmp = ((math.pow(z, y) / a) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (b <= -3.3e+38)
		tmp = t_1;
	elseif (b <= 6.8e-302)
		tmp = Float64(Float64(Float64((z ^ y) / y) * (a ^ Float64(t - 1.0))) * x);
	elseif (b <= 8200.0)
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (b <= -3.3e+38)
		tmp = t_1;
	elseif (b <= 6.8e-302)
		tmp = (((z ^ y) / y) * (a ^ (t - 1.0))) * x;
	elseif (b <= 8200.0)
		tmp = (((z ^ y) / a) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3.3e+38], t$95$1, If[LessEqual[b, 6.8e-302], N[(N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 8200.0], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.2999999999999999e38 or 8200 < 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. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 90.3

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

   5. Applied rewrites 90.3%

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

   if -3.2999999999999999e38 < b < 6.8e-302

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 85.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.6%

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

   if 6.8e-302 < b < 8200

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 83.5

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

   5. Applied rewrites 83.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 84.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-302}:\\ \;\;\;\;\left(\frac{{z}^{y}}{y} \cdot {a}^{\left(t - 1\right)}\right) \cdot x\\ \mathbf{elif}\;b \leq 8200:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -9.5e+32)
     t_1
     (if (<= y 4.2e+141) (/ (* (exp (- (* (log a) (- t 1.0)) b)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_1;
	} else if (y <= 4.2e+141) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z ** y) / a) * x) / y
    if (y <= (-9.5d+32)) then
        tmp = t_1
    else if (y <= 4.2d+141) then
        tmp = (exp(((log(a) * (t - 1.0d0)) - b)) * x) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_1;
	} else if (y <= 4.2e+141) {
		tmp = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -9.5e+32:
		tmp = t_1
	elif y <= 4.2e+141:
		tmp = (math.exp(((math.log(a) * (t - 1.0)) - b)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -9.5e+32)
		tmp = t_1;
	elseif (y <= 4.2e+141)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -9.5e+32)
		tmp = t_1;
	elseif (y <= 4.2e+141)
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9.5e+32], t$95$1, If[LessEqual[y, 4.2e+141], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000006e32 or 4.1999999999999997e141 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 93.2%

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

   if -9.50000000000000006e32 < y < 4.1999999999999997e141

   1. Initial program 98.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 95.3

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

   5. Applied rewrites 95.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -9.5e+32)
     t_1
     (if (<= y 1.1e+84) (* (/ (exp (- (* (log a) (- t 1.0)) b)) y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_1;
	} else if (y <= 1.1e+84) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z ** y) / a) * x) / y
    if (y <= (-9.5d+32)) then
        tmp = t_1
    else if (y <= 1.1d+84) then
        tmp = (exp(((log(a) * (t - 1.0d0)) - b)) / y) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_1;
	} else if (y <= 1.1e+84) {
		tmp = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -9.5e+32:
		tmp = t_1
	elif y <= 1.1e+84:
		tmp = (math.exp(((math.log(a) * (t - 1.0)) - b)) / y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -9.5e+32)
		tmp = t_1;
	elseif (y <= 1.1e+84)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) / y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -9.5e+32)
		tmp = t_1;
	elseif (y <= 1.1e+84)
		tmp = (exp(((log(a) * (t - 1.0)) - b)) / y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9.5e+32], t$95$1, If[LessEqual[y, 1.1e+84], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000006e32 or 1.0999999999999999e84 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.2%

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

   if -9.50000000000000006e32 < y < 1.0999999999999999e84

   1. Initial program 98.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 96.8

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

   5. Applied rewrites 96.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 95.2

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

   7. Applied rewrites 95.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\log a \cdot \left(t - 1\right) - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -9.5e+32)
     t_1
     (if (<= y 1.1e+84) (* (/ x y) (exp (- (* (log a) (- t 1.0)) b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_1;
	} else if (y <= 1.1e+84) {
		tmp = (x / y) * exp(((log(a) * (t - 1.0)) - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z ** y) / a) * x) / y
    if (y <= (-9.5d+32)) then
        tmp = t_1
    else if (y <= 1.1d+84) then
        tmp = (x / y) * exp(((log(a) * (t - 1.0d0)) - b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -9.5e+32) {
		tmp = t_1;
	} else if (y <= 1.1e+84) {
		tmp = (x / y) * Math.exp(((Math.log(a) * (t - 1.0)) - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -9.5e+32:
		tmp = t_1
	elif y <= 1.1e+84:
		tmp = (x / y) * math.exp(((math.log(a) * (t - 1.0)) - b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -9.5e+32)
		tmp = t_1;
	elseif (y <= 1.1e+84)
		tmp = Float64(Float64(x / y) * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -9.5e+32)
		tmp = t_1;
	elseif (y <= 1.1e+84)
		tmp = (x / y) * exp(((log(a) * (t - 1.0)) - b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9.5e+32], t$95$1, If[LessEqual[y, 1.1e+84], N[(N[(x / y), $MachinePrecision] * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000006e32 or 1.0999999999999999e84 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.2%

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

   if -9.50000000000000006e32 < y < 1.0999999999999999e84

   1. Initial program 98.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 96.8

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

   5. Applied rewrites 96.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 88.4

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

   7. Applied rewrites 88.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\log a \cdot \left(t - 1\right) - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8000:\\ \;\;\;\;\frac{\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= b -2.2e+14)
     t_1
     (if (<= b 8000.0) (/ (* (* (pow a (- t 1.0)) (pow z y)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -2.2e+14) {
		tmp = t_1;
	} else if (b <= 8000.0) {
		tmp = ((pow(a, (t - 1.0)) * pow(z, y)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(((log(a) * t) - b)) * x) / y
    if (b <= (-2.2d+14)) then
        tmp = t_1
    else if (b <= 8000.0d0) then
        tmp = (((a ** (t - 1.0d0)) * (z ** y)) * x) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -2.2e+14) {
		tmp = t_1;
	} else if (b <= 8000.0) {
		tmp = ((Math.pow(a, (t - 1.0)) * Math.pow(z, y)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if b <= -2.2e+14:
		tmp = t_1
	elif b <= 8000.0:
		tmp = ((math.pow(a, (t - 1.0)) * math.pow(z, y)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (b <= -2.2e+14)
		tmp = t_1;
	elseif (b <= 8000.0)
		tmp = Float64(Float64(Float64((a ^ Float64(t - 1.0)) * (z ^ y)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (b <= -2.2e+14)
		tmp = t_1;
	elseif (b <= 8000.0)
		tmp = (((a ^ (t - 1.0)) * (z ^ y)) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.2e+14], t$95$1, If[LessEqual[b, 8000.0], N[(N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2e14 or 8e3 < 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. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 90.6

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

   5. Applied rewrites 90.6%

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

   if -2.2e14 < b < 8e3

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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-prod N/A

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

      5. lower-pow.f64 N/A

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

      6. rem-exp-log N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 83.0

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

   5. Applied rewrites 83.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;b \leq 8000:\\ \;\;\;\;\frac{\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -4.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b} \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -4.1)
     t_1
     (if (<= y 1.05e+84) (* (/ (pow a (- t 1.0)) (* (exp b) y)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -4.1) {
		tmp = t_1;
	} else if (y <= 1.05e+84) {
		tmp = (pow(a, (t - 1.0)) / (exp(b) * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z ** y) / a) * x) / y
    if (y <= (-4.1d0)) then
        tmp = t_1
    else if (y <= 1.05d+84) then
        tmp = ((a ** (t - 1.0d0)) / (exp(b) * y)) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -4.1) {
		tmp = t_1;
	} else if (y <= 1.05e+84) {
		tmp = (Math.pow(a, (t - 1.0)) / (Math.exp(b) * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -4.1:
		tmp = t_1
	elif y <= 1.05e+84:
		tmp = (math.pow(a, (t - 1.0)) / (math.exp(b) * y)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -4.1)
		tmp = t_1;
	elseif (y <= 1.05e+84)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / Float64(exp(b) * y)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -4.1)
		tmp = t_1;
	elseif (y <= 1.05e+84)
		tmp = ((a ^ (t - 1.0)) / (exp(b) * y)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.1], t$95$1, If[LessEqual[y, 1.05e+84], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999996 or 1.05000000000000009e84 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 73.7

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

   5. Applied rewrites 73.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 88.4%

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

   if -4.0999999999999996 < y < 1.05000000000000009e84

   1. Initial program 98.1%

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

   3. Taylor expanded in 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 80.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.5%

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

   10. Applied rewrites 83.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b} \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.016:\\ \;\;\;\;\frac{1}{\left(e^{b} \cdot y\right) \cdot a} \cdot x\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 235000:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.016)
   (* (/ 1.0 (* (* (exp b) y) a)) x)
   (if (<= b -2.6e-232)
     (/ (* (pow a (- t 1.0)) x) y)
     (if (<= b 235000.0)
       (* (/ x a) (/ (pow z y) y))
       (* (/ (exp (- b)) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.016) {
		tmp = (1.0 / ((exp(b) * y) * a)) * x;
	} else if (b <= -2.6e-232) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 235000.0) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = (exp(-b) / 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 <= (-0.016d0)) then
        tmp = (1.0d0 / ((exp(b) * y) * a)) * x
    else if (b <= (-2.6d-232)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if (b <= 235000.0d0) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = (exp(-b) / 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 <= -0.016) {
		tmp = (1.0 / ((Math.exp(b) * y) * a)) * x;
	} else if (b <= -2.6e-232) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 235000.0) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = (Math.exp(-b) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.016:
		tmp = (1.0 / ((math.exp(b) * y) * a)) * x
	elif b <= -2.6e-232:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif b <= 235000.0:
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = (math.exp(-b) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.016)
		tmp = Float64(Float64(1.0 / Float64(Float64(exp(b) * y) * a)) * x);
	elseif (b <= -2.6e-232)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (b <= 235000.0)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.016)
		tmp = (1.0 / ((exp(b) * y) * a)) * x;
	elseif (b <= -2.6e-232)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif (b <= 235000.0)
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = (exp(-b) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.016], N[(N[(1.0 / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -2.6e-232], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 235000.0], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.016

   1. Initial program 98.5%

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

   3. Taylor expanded in 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 66.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 72.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 89.0%

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

   if -0.016 < b < -2.59999999999999996e-232

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.6%

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

   if -2.59999999999999996e-232 < b < 235000

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.3%

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

   if 235000 < 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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 80.0

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

   5. Applied rewrites 80.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.0

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

   7. Applied rewrites 80.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.016:\\ \;\;\;\;\frac{1}{\left(e^{b} \cdot y\right) \cdot a} \cdot x\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 235000:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{1}{e^{b} \cdot a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -3.1e+32)
     t_1
     (if (<= y 8e+83) (/ (* (/ 1.0 (* (exp b) a)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -3.1e+32) {
		tmp = t_1;
	} else if (y <= 8e+83) {
		tmp = ((1.0 / (exp(b) * a)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z ** y) / a) * x) / y
    if (y <= (-3.1d+32)) then
        tmp = t_1
    else if (y <= 8d+83) then
        tmp = ((1.0d0 / (exp(b) * a)) * x) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -3.1e+32) {
		tmp = t_1;
	} else if (y <= 8e+83) {
		tmp = ((1.0 / (Math.exp(b) * a)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -3.1e+32:
		tmp = t_1
	elif y <= 8e+83:
		tmp = ((1.0 / (math.exp(b) * a)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -3.1e+32)
		tmp = t_1;
	elseif (y <= 8e+83)
		tmp = Float64(Float64(Float64(1.0 / Float64(exp(b) * a)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -3.1e+32)
		tmp = t_1;
	elseif (y <= 8e+83)
		tmp = ((1.0 / (exp(b) * a)) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.1e+32], t$95$1, If[LessEqual[y, 8e+83], N[(N[(N[(1.0 / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999993e32 or 8.00000000000000025e83 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.2%

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

   if -3.09999999999999993e32 < y < 8.00000000000000025e83

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 76.8

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 79.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{1}{e^{b} \cdot a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.016:\\ \;\;\;\;\frac{1}{\left(e^{b} \cdot y\right) \cdot a} \cdot x\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 235000:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.016)
   (* (/ 1.0 (* (* (exp b) y) a)) x)
   (if (<= b -2.6e-232)
     (/ (* (pow a (- t 1.0)) x) y)
     (if (<= b 235000.0)
       (/ (* (pow z y) x) (* a y))
       (* (/ (exp (- b)) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.016) {
		tmp = (1.0 / ((exp(b) * y) * a)) * x;
	} else if (b <= -2.6e-232) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 235000.0) {
		tmp = (pow(z, y) * x) / (a * y);
	} else {
		tmp = (exp(-b) / 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 <= (-0.016d0)) then
        tmp = (1.0d0 / ((exp(b) * y) * a)) * x
    else if (b <= (-2.6d-232)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if (b <= 235000.0d0) then
        tmp = ((z ** y) * x) / (a * y)
    else
        tmp = (exp(-b) / 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 <= -0.016) {
		tmp = (1.0 / ((Math.exp(b) * y) * a)) * x;
	} else if (b <= -2.6e-232) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 235000.0) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else {
		tmp = (Math.exp(-b) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.016:
		tmp = (1.0 / ((math.exp(b) * y) * a)) * x
	elif b <= -2.6e-232:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif b <= 235000.0:
		tmp = (math.pow(z, y) * x) / (a * y)
	else:
		tmp = (math.exp(-b) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.016)
		tmp = Float64(Float64(1.0 / Float64(Float64(exp(b) * y) * a)) * x);
	elseif (b <= -2.6e-232)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (b <= 235000.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	else
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.016)
		tmp = (1.0 / ((exp(b) * y) * a)) * x;
	elseif (b <= -2.6e-232)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif (b <= 235000.0)
		tmp = ((z ^ y) * x) / (a * y);
	else
		tmp = (exp(-b) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.016], N[(N[(1.0 / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -2.6e-232], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 235000.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.016

   1. Initial program 98.5%

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

   3. Taylor expanded in 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 66.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 72.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 89.0%

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

   if -0.016 < b < -2.59999999999999996e-232

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.6%

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

   if -2.59999999999999996e-232 < b < 235000

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.3%

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

   10. Applied rewrites 75.2%

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

   if 235000 < 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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 80.0

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

   5. Applied rewrites 80.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.0

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

   7. Applied rewrites 80.0%

      \[\leadsto \color{blue}{\frac{e^{-b}}{y} \cdot x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 73.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -225000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 235000:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -225000000.0)
     t_1
     (if (<= b -2.6e-232)
       (/ (* (pow a (- t 1.0)) x) y)
       (if (<= b 235000.0) (/ (* (pow z y) x) (* a y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -225000000.0) {
		tmp = t_1;
	} else if (b <= -2.6e-232) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 235000.0) {
		tmp = (pow(z, y) * x) / (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-225000000.0d0)) then
        tmp = t_1
    else if (b <= (-2.6d-232)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if (b <= 235000.0d0) then
        tmp = ((z ** y) * x) / (a * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -225000000.0) {
		tmp = t_1;
	} else if (b <= -2.6e-232) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 235000.0) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -225000000.0:
		tmp = t_1
	elif b <= -2.6e-232:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif b <= 235000.0:
		tmp = (math.pow(z, y) * x) / (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -225000000.0)
		tmp = t_1;
	elseif (b <= -2.6e-232)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (b <= 235000.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -225000000.0)
		tmp = t_1;
	elseif (b <= -2.6e-232)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif (b <= 235000.0)
		tmp = ((z ^ y) * x) / (a * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -225000000.0], t$95$1, If[LessEqual[b, -2.6e-232], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 235000.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.25e8 or 235000 < 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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.5

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

   5. Applied rewrites 85.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.5

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

   7. Applied rewrites 85.5%

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

   if -2.25e8 < b < -2.59999999999999996e-232

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.0

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.9%

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

   if -2.59999999999999996e-232 < b < 235000

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.3%

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

   10. Applied rewrites 75.2%

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

Alternative 14: 73.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\frac{1}{\left(e^{b} \cdot y\right) \cdot a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -3.1e+32)
     t_1
     (if (<= y 8e+83) (* (/ 1.0 (* (* (exp b) y) a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -3.1e+32) {
		tmp = t_1;
	} else if (y <= 8e+83) {
		tmp = (1.0 / ((exp(b) * y) * a)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z ** y) / a) * x) / y
    if (y <= (-3.1d+32)) then
        tmp = t_1
    else if (y <= 8d+83) then
        tmp = (1.0d0 / ((exp(b) * y) * a)) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((Math.pow(z, y) / a) * x) / y;
	double tmp;
	if (y <= -3.1e+32) {
		tmp = t_1;
	} else if (y <= 8e+83) {
		tmp = (1.0 / ((Math.exp(b) * y) * a)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((math.pow(z, y) / a) * x) / y
	tmp = 0
	if y <= -3.1e+32:
		tmp = t_1
	elif y <= 8e+83:
		tmp = (1.0 / ((math.exp(b) * y) * a)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64((z ^ y) / a) * x) / y)
	tmp = 0.0
	if (y <= -3.1e+32)
		tmp = t_1;
	elseif (y <= 8e+83)
		tmp = Float64(Float64(1.0 / Float64(Float64(exp(b) * y) * a)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z ^ y) / a) * x) / y;
	tmp = 0.0;
	if (y <= -3.1e+32)
		tmp = t_1;
	elseif (y <= 8e+83)
		tmp = (1.0 / ((exp(b) * y) * a)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.1e+32], t$95$1, If[LessEqual[y, 8e+83], N[(N[(1.0 / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999993e32 or 8.00000000000000025e83 < y

   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 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.2%

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

   if -3.09999999999999993e32 < y < 8.00000000000000025e83

   1. Initial program 98.2%

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

   3. Taylor expanded in 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 77.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 79.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 77.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\frac{1}{\left(e^{b} \cdot y\right) \cdot a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -225000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 250000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -225000000.0)
     t_1
     (if (<= b 250000.0) (/ (* (pow a (- t 1.0)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -225000000.0) {
		tmp = t_1;
	} else if (b <= 250000.0) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-225000000.0d0)) then
        tmp = t_1
    else if (b <= 250000.0d0) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -225000000.0) {
		tmp = t_1;
	} else if (b <= 250000.0) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -225000000.0:
		tmp = t_1
	elif b <= 250000.0:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -225000000.0)
		tmp = t_1;
	elseif (b <= 250000.0)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -225000000.0)
		tmp = t_1;
	elseif (b <= 250000.0)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -225000000.0], t$95$1, If[LessEqual[b, 250000.0], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.25e8 or 2.5e5 < 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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.5

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

   5. Applied rewrites 85.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.5

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

   7. Applied rewrites 85.5%

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

   if -2.25e8 < b < 2.5e5

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.3%

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

Alternative 16: 58.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8000:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -190000000.0) t_1 (if (<= b 8000.0) (/ (/ x a) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -190000000.0) {
		tmp = t_1;
	} else if (b <= 8000.0) {
		tmp = (x / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-190000000.0d0)) then
        tmp = t_1
    else if (b <= 8000.0d0) then
        tmp = (x / a) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -190000000.0) {
		tmp = t_1;
	} else if (b <= 8000.0) {
		tmp = (x / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -190000000.0:
		tmp = t_1
	elif b <= 8000.0:
		tmp = (x / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -190000000.0)
		tmp = t_1;
	elseif (b <= 8000.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -190000000.0)
		tmp = t_1;
	elseif (b <= 8000.0)
		tmp = (x / a) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -190000000.0], t$95$1, If[LessEqual[b, 8000.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9e8 or 8e3 < 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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.5

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

   5. Applied rewrites 85.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.5

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

   7. Applied rewrites 85.5%

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

   if -1.9e8 < b < 8e3

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 44.8%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 31.1% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / 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) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

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

Wolfram

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

Derivation

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

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. +-commutative N/A

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

   5. exp-sum N/A

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

   6. lower-*.f64 N/A

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

   7. exp-prod N/A

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

   8. lower-pow.f64 N/A

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

   9. rem-exp-log N/A

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

   10. lower--.f64 N/A

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

   11. *-commutative N/A

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

   12. exp-to-pow N/A

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

   13. lower-pow.f64 N/A

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

   14. lower-/.f64 62.7

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

5. Applied rewrites 62.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 58.7%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 32.9%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
12. Add Preprocessing

Developer Target 1: 72.5% 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 2024298 
(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))