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

Percentage Accurate: 98.4% → 98.4%

Time: 12.6s

Alternatives: 13

Speedup: 1.0×

• 46.4% 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 98.6%

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

3. Final simplification 98.6%

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

Alternative 2: 74.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{{a}^{t}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-23}:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -1.3e-10)
     t_1
     (if (<= y -9.4e-307)
       (/ (* (/ (pow a t) a) x) y)
       (if (<= y 2.9e-23) (* (/ (exp (- (- (log a)) 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 <= -1.3e-10) {
		tmp = t_1;
	} else if (y <= -9.4e-307) {
		tmp = ((pow(a, t) / a) * x) / y;
	} else if (y <= 2.9e-23) {
		tmp = (exp((-log(a) - 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 <= (-1.3d-10)) then
        tmp = t_1
    else if (y <= (-9.4d-307)) then
        tmp = (((a ** t) / a) * x) / y
    else if (y <= 2.9d-23) then
        tmp = (exp((-log(a) - 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 <= -1.3e-10) {
		tmp = t_1;
	} else if (y <= -9.4e-307) {
		tmp = ((Math.pow(a, t) / a) * x) / y;
	} else if (y <= 2.9e-23) {
		tmp = (Math.exp((-Math.log(a) - 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 <= -1.3e-10:
		tmp = t_1
	elif y <= -9.4e-307:
		tmp = ((math.pow(a, t) / a) * x) / y
	elif y <= 2.9e-23:
		tmp = (math.exp((-math.log(a) - 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 <= -1.3e-10)
		tmp = t_1;
	elseif (y <= -9.4e-307)
		tmp = Float64(Float64(Float64((a ^ t) / a) * x) / y);
	elseif (y <= 2.9e-23)
		tmp = Float64(Float64(exp(Float64(Float64(-log(a)) - 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 <= -1.3e-10)
		tmp = t_1;
	elseif (y <= -9.4e-307)
		tmp = (((a ^ t) / a) * x) / y;
	elseif (y <= 2.9e-23)
		tmp = (exp((-log(a) - 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, -1.3e-10], t$95$1, If[LessEqual[y, -9.4e-307], N[(N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.9e-23], N[(N[(N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.29999999999999991e-10 or 2.9000000000000002e-23 < y

   1. Initial program 99.9%

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

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.3%

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

   if -1.29999999999999991e-10 < y < -9.39999999999999935e-307

   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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 79.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 79.2%

       \[\leadsto \frac{x \cdot \frac{{a}^{t}}{a}}{y} \]

   if -9.39999999999999935e-307 < y < 2.9000000000000002e-23

   1. Initial program 96.9%

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

   3. Taylor expanded in 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 96.9

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.5

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

   10. Applied rewrites 78.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{{a}^{t}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-23}:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -520000:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+54}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log z \cdot y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -520000.0)
   (/ (* (/ (pow z y) a) x) y)
   (if (<= y 7e+54)
     (/ (* (exp (- (* (log a) (- t 1.0)) b)) x) y)
     (/ (* (exp (* (log z) y)) x) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -520000.0) {
		tmp = ((pow(z, y) / a) * x) / y;
	} else if (y <= 7e+54) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = (exp((log(z) * y)) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-520000.0d0)) then
        tmp = (((z ** y) / a) * x) / y
    else if (y <= 7d+54) then
        tmp = (exp(((log(a) * (t - 1.0d0)) - b)) * x) / y
    else
        tmp = (exp((log(z) * y)) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -520000.0) {
		tmp = ((Math.pow(z, y) / a) * x) / y;
	} else if (y <= 7e+54) {
		tmp = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = (Math.exp((Math.log(z) * y)) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -520000.0:
		tmp = ((math.pow(z, y) / a) * x) / y
	elif y <= 7e+54:
		tmp = (math.exp(((math.log(a) * (t - 1.0)) - b)) * x) / y
	else:
		tmp = (math.exp((math.log(z) * y)) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -520000.0)
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / y);
	elseif (y <= 7e+54)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * x) / y);
	else
		tmp = Float64(Float64(exp(Float64(log(z) * y)) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -520000.0)
		tmp = (((z ^ y) / a) * x) / y;
	elseif (y <= 7e+54)
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	else
		tmp = (exp((log(z) * y)) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -520000.0], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7e+54], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e5

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 84.2%

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

   if -5.2e5 < y < 7.0000000000000002e54

   1. Initial program 97.7%

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

   3. Taylor expanded in 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 96.7

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

   5. Applied rewrites 96.7%

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

   if 7.0000000000000002e54 < 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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 92.0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -520000:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+54}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log z \cdot y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -520000:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+54}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log z \cdot y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -520000.0)
   (/ (* (/ (pow z y) a) x) y)
   (if (<= y 7e+54)
     (* (/ (exp (- (* (log a) (- t 1.0)) b)) y) x)
     (/ (* (exp (* (log z) y)) x) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -520000.0) {
		tmp = ((pow(z, y) / a) * x) / y;
	} else if (y <= 7e+54) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) / y) * x;
	} else {
		tmp = (exp((log(z) * y)) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-520000.0d0)) then
        tmp = (((z ** y) / a) * x) / y
    else if (y <= 7d+54) then
        tmp = (exp(((log(a) * (t - 1.0d0)) - b)) / y) * x
    else
        tmp = (exp((log(z) * y)) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -520000.0) {
		tmp = ((Math.pow(z, y) / a) * x) / y;
	} else if (y <= 7e+54) {
		tmp = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) / y) * x;
	} else {
		tmp = (Math.exp((Math.log(z) * y)) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -520000.0:
		tmp = ((math.pow(z, y) / a) * x) / y
	elif y <= 7e+54:
		tmp = (math.exp(((math.log(a) * (t - 1.0)) - b)) / y) * x
	else:
		tmp = (math.exp((math.log(z) * y)) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -520000.0)
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / y);
	elseif (y <= 7e+54)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) / y) * x);
	else
		tmp = Float64(Float64(exp(Float64(log(z) * y)) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -520000.0)
		tmp = (((z ^ y) / a) * x) / y;
	elseif (y <= 7e+54)
		tmp = (exp(((log(a) * (t - 1.0)) - b)) / y) * x;
	else
		tmp = (exp((log(z) * y)) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -520000.0], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7e+54], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e5

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 84.2%

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

   if -5.2e5 < y < 7.0000000000000002e54

   1. Initial program 97.7%

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

   3. Taylor expanded in 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 96.7

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

   5. Applied rewrites 96.7%

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

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

   7. Applied rewrites 95.8%

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

   if 7.0000000000000002e54 < 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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 92.0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -520000:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+54}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log z \cdot y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+54}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b} \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log z \cdot y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -30.0)
   (/ (* (/ (pow z y) a) x) y)
   (if (<= y 6e+54)
     (* (/ (pow a (- t 1.0)) (* (exp b) y)) x)
     (/ (* (exp (* (log z) y)) x) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -30.0) {
		tmp = ((pow(z, y) / a) * x) / y;
	} else if (y <= 6e+54) {
		tmp = (pow(a, (t - 1.0)) / (exp(b) * y)) * x;
	} else {
		tmp = (exp((log(z) * y)) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-30.0d0)) then
        tmp = (((z ** y) / a) * x) / y
    else if (y <= 6d+54) then
        tmp = ((a ** (t - 1.0d0)) / (exp(b) * y)) * x
    else
        tmp = (exp((log(z) * y)) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -30.0) {
		tmp = ((Math.pow(z, y) / a) * x) / y;
	} else if (y <= 6e+54) {
		tmp = (Math.pow(a, (t - 1.0)) / (Math.exp(b) * y)) * x;
	} else {
		tmp = (Math.exp((Math.log(z) * y)) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -30.0:
		tmp = ((math.pow(z, y) / a) * x) / y
	elif y <= 6e+54:
		tmp = (math.pow(a, (t - 1.0)) / (math.exp(b) * y)) * x
	else:
		tmp = (math.exp((math.log(z) * y)) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -30.0)
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / y);
	elseif (y <= 6e+54)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / Float64(exp(b) * y)) * x);
	else
		tmp = Float64(Float64(exp(Float64(log(z) * y)) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -30.0)
		tmp = (((z ^ y) / a) * x) / y;
	elseif (y <= 6e+54)
		tmp = ((a ^ (t - 1.0)) / (exp(b) * y)) * x;
	else
		tmp = (exp((log(z) * y)) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -30.0], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6e+54], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -30

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 84.5%

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

   if -30 < y < 5.9999999999999998e54

   1. Initial program 97.7%

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

   3. Taylor expanded in 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 96.6

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

   5. Applied rewrites 96.6%

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

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

   7. Applied rewrites 95.8%

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

   8. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l/ N/A

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

      3. lower-/.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 86.8

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

   10. Applied rewrites 86.8%

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

   if 5.9999999999999998e54 < 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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 92.0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+54}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b} \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log z \cdot y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-171}:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{1}{\sqrt{a}} \cdot \frac{{a}^{t}}{\sqrt{a}}\right) \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.1e+128)
   (* (/ (pow a (- t 1.0)) y) x)
   (if (<= t 6.8e-171)
     (/ (* (exp (- (- (log a)) b)) x) y)
     (if (<= t 5.1e+33)
       (/ (* (/ (pow z y) a) x) y)
       (/ (* (* (/ 1.0 (sqrt a)) (/ (pow a t) (sqrt a))) x) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+128) {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	} else if (t <= 6.8e-171) {
		tmp = (exp((-log(a) - b)) * x) / y;
	} else if (t <= 5.1e+33) {
		tmp = ((pow(z, y) / a) * x) / y;
	} else {
		tmp = (((1.0 / sqrt(a)) * (pow(a, t) / sqrt(a))) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.1d+128)) then
        tmp = ((a ** (t - 1.0d0)) / y) * x
    else if (t <= 6.8d-171) then
        tmp = (exp((-log(a) - b)) * x) / y
    else if (t <= 5.1d+33) then
        tmp = (((z ** y) / a) * x) / y
    else
        tmp = (((1.0d0 / sqrt(a)) * ((a ** t) / sqrt(a))) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+128) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	} else if (t <= 6.8e-171) {
		tmp = (Math.exp((-Math.log(a) - b)) * x) / y;
	} else if (t <= 5.1e+33) {
		tmp = ((Math.pow(z, y) / a) * x) / y;
	} else {
		tmp = (((1.0 / Math.sqrt(a)) * (Math.pow(a, t) / Math.sqrt(a))) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.1e+128:
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	elif t <= 6.8e-171:
		tmp = (math.exp((-math.log(a) - b)) * x) / y
	elif t <= 5.1e+33:
		tmp = ((math.pow(z, y) / a) * x) / y
	else:
		tmp = (((1.0 / math.sqrt(a)) * (math.pow(a, t) / math.sqrt(a))) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.1e+128)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	elseif (t <= 6.8e-171)
		tmp = Float64(Float64(exp(Float64(Float64(-log(a)) - b)) * x) / y);
	elseif (t <= 5.1e+33)
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / y);
	else
		tmp = Float64(Float64(Float64(Float64(1.0 / sqrt(a)) * Float64((a ^ t) / sqrt(a))) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.1e+128)
		tmp = ((a ^ (t - 1.0)) / y) * x;
	elseif (t <= 6.8e-171)
		tmp = (exp((-log(a) - b)) * x) / y;
	elseif (t <= 5.1e+33)
		tmp = (((z ^ y) / a) * x) / y;
	else
		tmp = (((1.0 / sqrt(a)) * ((a ^ t) / sqrt(a))) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.1e+128], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 6.8e-171], N[(N[(N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 5.1e+33], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[(1.0 / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.10000000000000004e128

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 82.7

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

   5. Applied rewrites 82.7%

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

   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 89.3%

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

   if -3.10000000000000004e128 < t < 6.7999999999999997e-171

   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 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 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.4%

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

   if 6.7999999999999997e-171 < t < 5.0999999999999999e33

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.4%

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

   if 5.0999999999999999e33 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 90.5%

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

   10. Applied rewrites 90.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-171}:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{1}{\sqrt{a}} \cdot \frac{{a}^{t}}{\sqrt{a}}\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (/ (pow z y) a) x) y)))
   (if (<= y -1.3e-10)
     t_1
     (if (<= y 5.2e-6) (* (/ (pow a (- t 1.0)) 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 <= -1.3e-10) {
		tmp = t_1;
	} else if (y <= 5.2e-6) {
		tmp = (pow(a, (t - 1.0)) / 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 <= (-1.3d-10)) then
        tmp = t_1
    else if (y <= 5.2d-6) then
        tmp = ((a ** (t - 1.0d0)) / 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 <= -1.3e-10) {
		tmp = t_1;
	} else if (y <= 5.2e-6) {
		tmp = (Math.pow(a, (t - 1.0)) / 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 <= -1.3e-10:
		tmp = t_1
	elif y <= 5.2e-6:
		tmp = (math.pow(a, (t - 1.0)) / 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 <= -1.3e-10)
		tmp = t_1;
	elseif (y <= 5.2e-6)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / 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 <= -1.3e-10)
		tmp = t_1;
	elseif (y <= 5.2e-6)
		tmp = ((a ^ (t - 1.0)) / 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, -1.3e-10], t$95$1, If[LessEqual[y, 5.2e-6], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999991e-10 or 5.20000000000000019e-6 < y

   1. Initial program 99.9%

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

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.9%

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

   if -1.29999999999999991e-10 < y < 5.20000000000000019e-6

   1. Initial program 97.5%

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

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 75.4

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

   5. Applied rewrites 75.4%

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

   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 75.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4500:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -3.2e+23)
     t_1
     (if (<= b 4500.0) (/ (* (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 <= -3.2e+23) {
		tmp = t_1;
	} else if (b <= 4500.0) {
		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 <= (-3.2d+23)) then
        tmp = t_1
    else if (b <= 4500.0d0) 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 <= -3.2e+23) {
		tmp = t_1;
	} else if (b <= 4500.0) {
		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 <= -3.2e+23:
		tmp = t_1
	elif b <= 4500.0:
		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 <= -3.2e+23)
		tmp = t_1;
	elseif (b <= 4500.0)
		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 <= -3.2e+23)
		tmp = t_1;
	elseif (b <= 4500.0)
		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, -3.2e+23], t$95$1, If[LessEqual[b, 4500.0], 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 < -3.2e23 or 4500 < 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 79.7

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

   5. Applied rewrites 79.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 79.7

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

   7. Applied rewrites 79.7%

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

   if -3.2e23 < b < 4500

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 77.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 4500:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4500:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -3.2e+23)
     t_1
     (if (<= b 4500.0) (* (/ (pow a (- t 1.0)) y) x) 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 <= -3.2e+23) {
		tmp = t_1;
	} else if (b <= 4500.0) {
		tmp = (pow(a, (t - 1.0)) / 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 = (exp(-b) / y) * x
    if (b <= (-3.2d+23)) then
        tmp = t_1
    else if (b <= 4500.0d0) then
        tmp = ((a ** (t - 1.0d0)) / 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.exp(-b) / y) * x;
	double tmp;
	if (b <= -3.2e+23) {
		tmp = t_1;
	} else if (b <= 4500.0) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	} 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 <= -3.2e+23:
		tmp = t_1
	elif b <= 4500.0:
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	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 <= -3.2e+23)
		tmp = t_1;
	elseif (b <= 4500.0)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	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 <= -3.2e+23)
		tmp = t_1;
	elseif (b <= 4500.0)
		tmp = ((a ^ (t - 1.0)) / 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[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -3.2e+23], t$95$1, If[LessEqual[b, 4500.0], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.2e23 or 4500 < 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 79.7

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

   5. Applied rewrites 79.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 79.7

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

   7. Applied rewrites 79.7%

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

   if -3.2e23 < b < 4500

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 89.7

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

   5. Applied rewrites 89.7%

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

   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 76.6%

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

Alternative 10: 59.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -135:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -135.0) t_1 (if (<= b 2.05e-8) (/ (* (/ 1.0 a) 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 <= -135.0) {
		tmp = t_1;
	} else if (b <= 2.05e-8) {
		tmp = ((1.0 / 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(-b) / y) * x
    if (b <= (-135.0d0)) then
        tmp = t_1
    else if (b <= 2.05d-8) then
        tmp = ((1.0d0 / 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(-b) / y) * x;
	double tmp;
	if (b <= -135.0) {
		tmp = t_1;
	} else if (b <= 2.05e-8) {
		tmp = ((1.0 / a) * 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 <= -135.0:
		tmp = t_1
	elif b <= 2.05e-8:
		tmp = ((1.0 / a) * 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 <= -135.0)
		tmp = t_1;
	elseif (b <= 2.05e-8)
		tmp = Float64(Float64(Float64(1.0 / 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(-b) / y) * x;
	tmp = 0.0;
	if (b <= -135.0)
		tmp = t_1;
	elseif (b <= 2.05e-8)
		tmp = ((1.0 / 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[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -135.0], t$95$1, If[LessEqual[b, 2.05e-8], N[(N[(N[(1.0 / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -135 or 2.05000000000000016e-8 < 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 77.1

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

   5. Applied rewrites 77.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 77.1

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

   7. Applied rewrites 77.1%

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

   if -135 < b < 2.05000000000000016e-8

   1. Initial program 97.1%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 43.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -135:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.0% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e-177) (/ (* (/ 1.0 a) x) y) (* (/ (/ 1.0 a) y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-177) {
		tmp = ((1.0 / a) * x) / y;
	} else {
		tmp = ((1.0 / a) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d-177)) then
        tmp = ((1.0d0 / a) * x) / y
    else
        tmp = ((1.0d0 / a) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-177) {
		tmp = ((1.0 / a) * x) / y;
	} else {
		tmp = ((1.0 / a) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e-177:
		tmp = ((1.0 / a) * x) / y
	else:
		tmp = ((1.0 / a) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e-177)
		tmp = Float64(Float64(Float64(1.0 / a) * x) / y);
	else
		tmp = Float64(Float64(Float64(1.0 / a) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e-177)
		tmp = ((1.0 / a) * x) / y;
	else
		tmp = ((1.0 / a) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e-177], N[(N[(N[(1.0 / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999952e-178

   1. Initial program 99.2%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 35.4%

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

   if -9.99999999999999952e-178 < t

   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 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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 28.0%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 31.0

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

   13. Applied rewrites 31.0%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.1% accurate, 12.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Taylor expanded in b around 0

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. distribute-rgt-in N/A

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

   4. associate-+l+ N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. +-commutative N/A

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

   8. exp-sum N/A

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

   9. lower-*.f64 N/A

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

   10. *-commutative N/A

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

   11. exp-prod N/A

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

   12. lower-pow.f64 N/A

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

   13. rem-exp-log N/A

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

   14. +-commutative N/A

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

   15. mul-1-neg N/A

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

5. Applied rewrites 74.8%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 61.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 31.4%

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

    1. lift-/.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-/l* N/A

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

    4. *-commutative N/A

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

    5. lower-*.f64 N/A

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

    6. lower-/.f64 30.4

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

13. Applied rewrites 30.4%

    \[\leadsto \color{blue}{\frac{\frac{1}{a}}{y} \cdot x} \]
14. Add Preprocessing

Alternative 13: 31.1% accurate, 12.0× speedup

Math

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

FPCore

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

C

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

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 / y) * (1.0d0 / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Taylor expanded in b around 0

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. distribute-rgt-in N/A

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

   4. associate-+l+ N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. +-commutative N/A

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

   8. exp-sum N/A

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

   9. lower-*.f64 N/A

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

   10. *-commutative N/A

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

   11. exp-prod N/A

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

   12. lower-pow.f64 N/A

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

   13. rem-exp-log N/A

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

   14. +-commutative N/A

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

   15. mul-1-neg N/A

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

5. Applied rewrites 74.8%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 61.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 31.4%

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

    1. lift-/.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. *-commutative N/A

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

    4. associate-/l* N/A

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

    5. lower-*.f64 N/A

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

    6. lower-/.f64 30.3

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

13. Applied rewrites 30.3%

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

14. Final simplification 30.3%

    \[\leadsto \frac{x}{y} \cdot \frac{1}{a} \]
15. Add Preprocessing

Developer Target 1: 71.5% 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 2024244 
(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))