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

Percentage Accurate: 98.5% → 98.5%

Time: 15.7s

Alternatives: 14

Speedup: 1.0×

• 47.4% 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: 98.5% 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: 98.5% 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 99.5%

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

3. Final simplification 99.5%

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

Alternative 2: 88.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ t_2 := \frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+228}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) (- t 1.0)) b)) x) y))
        (t_2 (/ (/ (* (pow z y) x) a) y)))
   (if (<= y -1.32e+228)
     t_2
     (if (<= y -3.2e+171)
       t_1
       (if (<= y -6.2e+141) t_2 (if (<= y 1.15e+132) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	double t_2 = ((pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -1.32e+228) {
		tmp = t_2;
	} else if (y <= -3.2e+171) {
		tmp = t_1;
	} else if (y <= -6.2e+141) {
		tmp = t_2;
	} else if (y <= 1.15e+132) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (exp(((log(a) * (t - 1.0d0)) - b)) * x) / y
    t_2 = (((z ** y) * x) / a) / y
    if (y <= (-1.32d+228)) then
        tmp = t_2
    else if (y <= (-3.2d+171)) then
        tmp = t_1
    else if (y <= (-6.2d+141)) then
        tmp = t_2
    else if (y <= 1.15d+132) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) * x) / y;
	double t_2 = ((Math.pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -1.32e+228) {
		tmp = t_2;
	} else if (y <= -3.2e+171) {
		tmp = t_1;
	} else if (y <= -6.2e+141) {
		tmp = t_2;
	} else if (y <= 1.15e+132) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * (t - 1.0)) - b)) * x) / y
	t_2 = ((math.pow(z, y) * x) / a) / y
	tmp = 0
	if y <= -1.32e+228:
		tmp = t_2
	elif y <= -3.2e+171:
		tmp = t_1
	elif y <= -6.2e+141:
		tmp = t_2
	elif y <= 1.15e+132:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * x) / y)
	t_2 = Float64(Float64(Float64((z ^ y) * x) / a) / y)
	tmp = 0.0
	if (y <= -1.32e+228)
		tmp = t_2;
	elseif (y <= -3.2e+171)
		tmp = t_1;
	elseif (y <= -6.2e+141)
		tmp = t_2;
	elseif (y <= 1.15e+132)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	t_2 = (((z ^ y) * x) / a) / y;
	tmp = 0.0;
	if (y <= -1.32e+228)
		tmp = t_2;
	elseif (y <= -3.2e+171)
		tmp = t_1;
	elseif (y <= -6.2e+141)
		tmp = t_2;
	elseif (y <= 1.15e+132)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.32e+228], t$95$2, If[LessEqual[y, -3.2e+171], t$95$1, If[LessEqual[y, -6.2e+141], t$95$2, If[LessEqual[y, 1.15e+132], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.32e228 or -3.20000000000000011e171 < y < -6.20000000000000007e141 or 1.1500000000000001e132 < 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 b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 58.6

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 94.4%

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

   if -1.32e228 < y < -3.20000000000000011e171 or -6.20000000000000007e141 < y < 1.1500000000000001e132

   1. Initial program 99.3%

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

   3. Taylor expanded in 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 93.9

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

   5. Applied rewrites 93.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+228}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+132}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot \left({z}^{y} \cdot x\right)}{y}\\ \mathbf{elif}\;b \leq 480:\\ \;\;\;\;\left(x - b \cdot x\right) \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.8e+125)
     t_1
     (if (<= b -2.5e-289)
       (/ (* (pow a (- t 1.0)) (* (pow z y) x)) y)
       (if (<= b 480.0) (* (- x (* b x)) (/ (/ (pow z y) a) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -1.8e+125) {
		tmp = t_1;
	} else if (b <= -2.5e-289) {
		tmp = (pow(a, (t - 1.0)) * (pow(z, y) * x)) / y;
	} else if (b <= 480.0) {
		tmp = (x - (b * x)) * ((pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-1.8d+125)) then
        tmp = t_1
    else if (b <= (-2.5d-289)) then
        tmp = ((a ** (t - 1.0d0)) * ((z ** y) * x)) / y
    else if (b <= 480.0d0) then
        tmp = (x - (b * x)) * (((z ** y) / a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -1.8e+125) {
		tmp = t_1;
	} else if (b <= -2.5e-289) {
		tmp = (Math.pow(a, (t - 1.0)) * (Math.pow(z, y) * x)) / y;
	} else if (b <= 480.0) {
		tmp = (x - (b * x)) * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -1.8e+125:
		tmp = t_1
	elif b <= -2.5e-289:
		tmp = (math.pow(a, (t - 1.0)) * (math.pow(z, y) * x)) / y
	elif b <= 480.0:
		tmp = (x - (b * x)) * ((math.pow(z, y) / a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -1.8e+125)
		tmp = t_1;
	elseif (b <= -2.5e-289)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * Float64((z ^ y) * x)) / y);
	elseif (b <= 480.0)
		tmp = Float64(Float64(x - Float64(b * x)) * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -1.8e+125)
		tmp = t_1;
	elseif (b <= -2.5e-289)
		tmp = ((a ^ (t - 1.0)) * ((z ^ y) * x)) / y;
	elseif (b <= 480.0)
		tmp = (x - (b * x)) * (((z ^ y) / a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -1.8e+125], t$95$1, If[LessEqual[b, -2.5e-289], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 480.0], N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000002e125 or 480 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.4

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

   5. Applied rewrites 85.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.4

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

   7. Applied rewrites 85.4%

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

   if -1.8000000000000002e125 < b < -2.50000000000000014e-289

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if -2.50000000000000014e-289 < b < 480

   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

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.2%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot \left({z}^{y} \cdot x\right)}{y}\\ \mathbf{elif}\;b \leq 480:\\ \;\;\;\;\left(x - b \cdot x\right) \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 480:\\ \;\;\;\;\left(x - b \cdot x\right) \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.95e+90)
     t_1
     (if (<= b -2.6e-289)
       (/ (* (pow a (- t 1.0)) x) y)
       (if (<= b 480.0) (* (- x (* b x)) (/ (/ (pow z y) a) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= -2.6e-289) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 480.0) {
		tmp = (x - (b * x)) * ((pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-1.95d+90)) then
        tmp = t_1
    else if (b <= (-2.6d-289)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if (b <= 480.0d0) then
        tmp = (x - (b * x)) * (((z ** y) / a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= -2.6e-289) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 480.0) {
		tmp = (x - (b * x)) * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -1.95e+90:
		tmp = t_1
	elif b <= -2.6e-289:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif b <= 480.0:
		tmp = (x - (b * x)) * ((math.pow(z, y) / a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -1.95e+90)
		tmp = t_1;
	elseif (b <= -2.6e-289)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (b <= 480.0)
		tmp = Float64(Float64(x - Float64(b * x)) * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -1.95e+90)
		tmp = t_1;
	elseif (b <= -2.6e-289)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif (b <= 480.0)
		tmp = (x - (b * x)) * (((z ^ y) / a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -1.95e+90], t$95$1, If[LessEqual[b, -2.6e-289], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 480.0], N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9500000000000001e90 or 480 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.3

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

   5. Applied rewrites 85.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.3

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

   7. Applied rewrites 85.3%

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

   if -1.9500000000000001e90 < b < -2.5999999999999999e-289

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 79.3%

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

   if -2.5999999999999999e-289 < b < 480

   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

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 480:\\ \;\;\;\;\left(x - b \cdot x\right) \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;b \leq 150000:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.95e+90)
     t_1
     (if (<= b -8.8e-265)
       (/ (* (pow a (- t 1.0)) x) y)
       (if (<= b 150000.0) (/ (/ (* (pow z y) x) a) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= -8.8e-265) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 150000.0) {
		tmp = ((pow(z, y) * x) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-1.95d+90)) then
        tmp = t_1
    else if (b <= (-8.8d-265)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if (b <= 150000.0d0) then
        tmp = (((z ** y) * x) / a) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= -8.8e-265) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if (b <= 150000.0) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -1.95e+90:
		tmp = t_1
	elif b <= -8.8e-265:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif b <= 150000.0:
		tmp = ((math.pow(z, y) * x) / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -1.95e+90)
		tmp = t_1;
	elseif (b <= -8.8e-265)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (b <= 150000.0)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -1.95e+90)
		tmp = t_1;
	elseif (b <= -8.8e-265)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif (b <= 150000.0)
		tmp = (((z ^ y) * x) / a) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -1.95e+90], t$95$1, If[LessEqual[b, -8.8e-265], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 150000.0], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9500000000000001e90 or 1.5e5 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.1

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

   5. Applied rewrites 86.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 86.1

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

   7. Applied rewrites 86.1%

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

   if -1.9500000000000001e90 < b < -8.80000000000000042e-265

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 78.0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 78.5%

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

   if -8.80000000000000042e-265 < b < 1.5e5

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.7%

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

Alternative 6: 32.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log a \leq 280:\\ \;\;\;\;\frac{1 - b}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (log a) 280.0) (* (/ (- 1.0 b) a) (/ x y)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (log(a) <= 280.0) {
		tmp = ((1.0 - b) / a) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (log(a) <= 280.0d0) then
        tmp = ((1.0d0 - b) / a) * (x / y)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (Math.log(a) <= 280.0) {
		tmp = ((1.0 - b) / a) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if math.log(a) <= 280.0:
		tmp = ((1.0 - b) / a) * (x / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (log(a) <= 280.0)
		tmp = Float64(Float64(Float64(1.0 - b) / a) * Float64(x / y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (log(a) <= 280.0)
		tmp = ((1.0 - b) / a) * (x / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[Log[a], $MachinePrecision], 280.0], N[(N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 a) < 280

   1. Initial program 99.5%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 52.7%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 31.9%

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

   if 280 < (log.f64 a)

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 59.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 34.9%

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

Alternative 7: 74.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6300000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.95e+90)
     t_1
     (if (<= b 6300000.0) (/ (* (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 <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= 6300000.0) {
		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 <= (-1.95d+90)) then
        tmp = t_1
    else if (b <= 6300000.0d0) 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 <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= 6300000.0) {
		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 <= -1.95e+90:
		tmp = t_1
	elif b <= 6300000.0:
		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 <= -1.95e+90)
		tmp = t_1;
	elseif (b <= 6300000.0)
		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 <= -1.95e+90)
		tmp = t_1;
	elseif (b <= 6300000.0)
		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, -1.95e+90], t$95$1, If[LessEqual[b, 6300000.0], 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 < -1.9500000000000001e90 or 6.3e6 < 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 86.1

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

   5. Applied rewrites 86.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 86.1

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

   7. Applied rewrites 86.1%

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

   if -1.9500000000000001e90 < b < 6.3e6

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.6%

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

Alternative 8: 74.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6300000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.95e+90)
     t_1
     (if (<= b 6300000.0) (* (/ (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 <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= 6300000.0) {
		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 <= (-1.95d+90)) then
        tmp = t_1
    else if (b <= 6300000.0d0) 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 <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= 6300000.0) {
		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 <= -1.95e+90:
		tmp = t_1
	elif b <= 6300000.0:
		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 <= -1.95e+90)
		tmp = t_1;
	elseif (b <= 6300000.0)
		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 <= -1.95e+90)
		tmp = t_1;
	elseif (b <= 6300000.0)
		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, -1.95e+90], t$95$1, If[LessEqual[b, 6300000.0], 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 < -1.9500000000000001e90 or 6.3e6 < 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 86.1

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

   5. Applied rewrites 86.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 86.1

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

   7. Applied rewrites 86.1%

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

   if -1.9500000000000001e90 < b < 6.3e6

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. exp-prod N/A

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

      4. lower-pow.f64 N/A

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

      5. rem-exp-log N/A

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

      6. lower--.f64 N/A

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

      7. lower-exp.f64 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 68.0

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

   10. Applied rewrites 68.0%

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

Alternative 9: 71.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1820000:\\ \;\;\;\;\frac{x}{y} \cdot {a}^{\left(t - 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.95e+90)
     t_1
     (if (<= b 1820000.0) (* (/ x y) (pow a (- t 1.0))) 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 <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= 1820000.0) {
		tmp = (x / y) * pow(a, (t - 1.0));
	} 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 <= (-1.95d+90)) then
        tmp = t_1
    else if (b <= 1820000.0d0) then
        tmp = (x / y) * (a ** (t - 1.0d0))
    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 <= -1.95e+90) {
		tmp = t_1;
	} else if (b <= 1820000.0) {
		tmp = (x / y) * Math.pow(a, (t - 1.0));
	} 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 <= -1.95e+90:
		tmp = t_1
	elif b <= 1820000.0:
		tmp = (x / y) * math.pow(a, (t - 1.0))
	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 <= -1.95e+90)
		tmp = t_1;
	elseif (b <= 1820000.0)
		tmp = Float64(Float64(x / y) * (a ^ Float64(t - 1.0)));
	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 <= -1.95e+90)
		tmp = t_1;
	elseif (b <= 1820000.0)
		tmp = (x / y) * (a ^ (t - 1.0));
	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, -1.95e+90], t$95$1, If[LessEqual[b, 1820000.0], N[(N[(x / y), $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9500000000000001e90 or 1.82e6 < 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 86.1

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

   5. Applied rewrites 86.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 86.1

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

   7. Applied rewrites 86.1%

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

   if -1.9500000000000001e90 < b < 1.82e6

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 61.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 61.9%

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

Alternative 10: 58.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -6.8e+22) t_1 (if (<= b 2.9e-17) (/ 1.0 (/ y (/ x a))) 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 <= -6.8e+22) {
		tmp = t_1;
	} else if (b <= 2.9e-17) {
		tmp = 1.0 / (y / (x / a));
	} 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 <= (-6.8d+22)) then
        tmp = t_1
    else if (b <= 2.9d-17) then
        tmp = 1.0d0 / (y / (x / a))
    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 <= -6.8e+22) {
		tmp = t_1;
	} else if (b <= 2.9e-17) {
		tmp = 1.0 / (y / (x / a));
	} 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 <= -6.8e+22:
		tmp = t_1
	elif b <= 2.9e-17:
		tmp = 1.0 / (y / (x / a))
	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 <= -6.8e+22)
		tmp = t_1;
	elseif (b <= 2.9e-17)
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	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 <= -6.8e+22)
		tmp = t_1;
	elseif (b <= 2.9e-17)
		tmp = 1.0 / (y / (x / a));
	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, -6.8e+22], t$95$1, If[LessEqual[b, 2.9e-17], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8e22 or 2.9000000000000003e-17 < 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 79.3

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

   5. Applied rewrites 79.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 79.3

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

   7. Applied rewrites 79.3%

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

   if -6.8e22 < b < 2.9000000000000003e-17

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 36.0%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 37.1

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

   13. Applied rewrites 37.1%

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

Alternative 11: 34.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.35 \cdot 10^{-246}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.35e-246) (/ (/ (fma (- x) b x) a) y) (* (pow a -1.0) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.35e-246) {
		tmp = (fma(-x, b, x) / a) / y;
	} else {
		tmp = pow(a, -1.0) * (x / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.35e-246)
		tmp = Float64(Float64(fma(Float64(-x), b, x) / a) / y);
	else
		tmp = Float64((a ^ -1.0) * Float64(x / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.35e-246], N[(N[(N[((-x) * b + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[Power[a, -1.0], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.3499999999999999e-246

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 46.4%

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

   if 4.3499999999999999e-246 < b

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 51.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.0%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 23.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 27.7%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.35 \cdot 10^{-246}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.2% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.35 \cdot 10^{-246}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{1 - b}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.35e-246)
   (/ (/ (fma (- x) b x) a) y)
   (if (<= b 2.9e-5) (* (/ (- 1.0 b) a) (/ x y)) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.35e-246) {
		tmp = (fma(-x, b, x) / a) / y;
	} else if (b <= 2.9e-5) {
		tmp = ((1.0 - b) / a) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.35e-246)
		tmp = Float64(Float64(fma(Float64(-x), b, x) / a) / y);
	elseif (b <= 2.9e-5)
		tmp = Float64(Float64(Float64(1.0 - b) / a) * Float64(x / y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.35e-246], N[(N[(N[((-x) * b + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.9e-5], N[(N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 4.3499999999999999e-246

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 46.4%

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

   if 4.3499999999999999e-246 < b < 2.9e-5

   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

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 63.8%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 40.6%

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

   if 2.9e-5 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 50.7

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

   5. Applied rewrites 50.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 36.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 18.6%

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

Alternative 13: 35.4% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e-222) (/ (/ (fma (- x) b x) a) y) (/ 1.0 (/ y (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-222) {
		tmp = (fma(-x, b, x) / a) / y;
	} else {
		tmp = 1.0 / (y / (x / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e-222)
		tmp = Float64(Float64(fma(Float64(-x), b, x) / a) / y);
	else
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e-222], N[(N[(N[((-x) * b + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.00000000000000005e-222

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 64.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 50.0%

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

   if -1.00000000000000005e-222 < b

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 64.4

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 27.4%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 28.2

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

   13. Applied rewrites 28.2%

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

Alternative 14: 30.7% accurate, 14.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in b around 0

   \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
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. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. exp-to-pow N/A

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

   7. lower-pow.f64 N/A

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

   8. exp-prod N/A

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

   9. lower-pow.f64 N/A

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

   10. rem-exp-log N/A

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

   11. lower--.f64 65.9

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

5. Applied rewrites 65.9%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 60.0%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 29.1%

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

Developer Target 1: 72.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024259 
(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))