Compound Interest

Percentage Accurate: 27.6% → 93.6%

Time: 8.8s

Alternatives: 17

Speedup: 8.9×

• could not determine a ground truth

  1. i = 3.949537721392261e-288
  2. n = 7.82585471463092e+28

Specification

Math

\[\begin{array}{l} \\ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))

C

double code(double i, double n) {
	return 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(i, n)
use fmin_fmax_functions
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = 100.0d0 * ((((1.0d0 + (i / n)) ** n) - 1.0d0) / (i / n))
end function

Java

public static double code(double i, double n) {
	return 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

Python

def code(i, n):
	return 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))

Julia

function code(i, n)
	return Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
end

MATLAB

function tmp = code(i, n)
	tmp = 100.0 * ((((1.0 + (i / n)) ^ n) - 1.0) / (i / n));
end

Wolfram

code[i_, n_] := N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 27.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))

C

double code(double i, double n) {
	return 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(i, n)
use fmin_fmax_functions
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = 100.0d0 * ((((1.0d0 + (i / n)) ** n) - 1.0d0) / (i / n))
end function

Java

public static double code(double i, double n) {
	return 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

Python

def code(i, n):
	return 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))

Julia

function code(i, n)
	return Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
end

MATLAB

function tmp = code(i, n)
	tmp = 100.0 * ((((1.0 + (i / n)) ^ n) - 1.0) / (i / n));
end

Wolfram

code[i_, n_] := N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{i}{n}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;t\_0 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;100 \cdot n\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))))
   (if (<= t_0 0.0)
     (* (* (/ (expm1 (* (log1p (/ i n)) n)) i) n) 100.0)
     (if (<= t_0 INFINITY) t_0 (* 100.0 n)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = ((expm1((log1p((i / n)) * n)) / i) * n) * 100.0;
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = 100.0 * n;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = ((Math.expm1((Math.log1p((i / n)) * n)) / i) * n) * 100.0;
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = 100.0 * n;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))
	tmp = 0
	if t_0 <= 0.0:
		tmp = ((math.expm1((math.log1p((i / n)) * n)) / i) * n) * 100.0
	elif t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = 100.0 * n
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(expm1(Float64(log1p(Float64(i / n)) * n)) / i) * n) * 100.0);
	elseif (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = Float64(100.0 * n);
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(N[(N[(Exp[N[(N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[t$95$0, Infinity], t$95$0, N[(100.0 * n), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < 0.0

   1. Initial program 26.2%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 34.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]
   4. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\log \left(\frac{i}{n} + 1\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \color{blue}{\left(\frac{i}{n} + 1\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      3. lift-/.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \left(\color{blue}{\frac{i}{n}} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \color{blue}{\left(1 + \frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      5. lower-log1p.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      6. lift-/.f64 96.6

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{i}{n}}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

   5. Applied rewrites 96.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

   if 0.0 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < +inf.0

   1. Initial program 98.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   if +inf.0 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n)))

   1. Initial program 0.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \color{blue}{n} \]
   3. Step-by-step derivation

   4. Applied rewrites 79.3%

      \[\leadsto 100 \cdot \color{blue}{n} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{i}{n}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;t\_0 \leq \infty:\\ \;\;\;\;\left(\frac{{\left(\frac{i}{n} + 1\right)}^{n} - 1}{i} \cdot n\right) \cdot 100\\ \mathbf{else}:\\ \;\;\;\;100 \cdot n\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))))
   (if (<= t_0 0.0)
     (* (* (/ (expm1 (* (log1p (/ i n)) n)) i) n) 100.0)
     (if (<= t_0 INFINITY)
       (* (* (/ (- (pow (+ (/ i n) 1.0) n) 1.0) i) n) 100.0)
       (* 100.0 n)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = ((expm1((log1p((i / n)) * n)) / i) * n) * 100.0;
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = (((pow(((i / n) + 1.0), n) - 1.0) / i) * n) * 100.0;
	} else {
		tmp = 100.0 * n;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = ((Math.expm1((Math.log1p((i / n)) * n)) / i) * n) * 100.0;
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = (((Math.pow(((i / n) + 1.0), n) - 1.0) / i) * n) * 100.0;
	} else {
		tmp = 100.0 * n;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))
	tmp = 0
	if t_0 <= 0.0:
		tmp = ((math.expm1((math.log1p((i / n)) * n)) / i) * n) * 100.0
	elif t_0 <= math.inf:
		tmp = (((math.pow(((i / n) + 1.0), n) - 1.0) / i) * n) * 100.0
	else:
		tmp = 100.0 * n
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(expm1(Float64(log1p(Float64(i / n)) * n)) / i) * n) * 100.0);
	elseif (t_0 <= Inf)
		tmp = Float64(Float64(Float64(Float64((Float64(Float64(i / n) + 1.0) ^ n) - 1.0) / i) * n) * 100.0);
	else
		tmp = Float64(100.0 * n);
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(N[(N[(Exp[N[(N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[t$95$0, Infinity], N[(N[(N[(N[(N[Power[N[(N[(i / n), $MachinePrecision] + 1.0), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], N[(100.0 * n), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < 0.0

   1. Initial program 26.2%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 34.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]
   4. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\log \left(\frac{i}{n} + 1\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \color{blue}{\left(\frac{i}{n} + 1\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      3. lift-/.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \left(\color{blue}{\frac{i}{n}} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \color{blue}{\left(1 + \frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      5. lower-log1p.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      6. lift-/.f64 96.6

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{i}{n}}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

   5. Applied rewrites 96.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

   if 0.0 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < +inf.0

   1. Initial program 98.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 58.8%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]
   4. Step-by-step derivation

      1. lift-expm1.f64 N/A

         \[\leadsto \left(\frac{\color{blue}{e^{\log \left(\frac{i}{n} + 1\right) \cdot n} - 1}}{i} \cdot n\right) \cdot 100 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\frac{e^{\color{blue}{\log \left(\frac{i}{n} + 1\right) \cdot n}} - 1}{i} \cdot n\right) \cdot 100 \]

      3. lift-log.f64 N/A

         \[\leadsto \left(\frac{e^{\color{blue}{\log \left(\frac{i}{n} + 1\right)} \cdot n} - 1}{i} \cdot n\right) \cdot 100 \]

      4. lift-+.f64 N/A

         \[\leadsto \left(\frac{e^{\log \color{blue}{\left(\frac{i}{n} + 1\right)} \cdot n} - 1}{i} \cdot n\right) \cdot 100 \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{e^{\log \left(\color{blue}{\frac{i}{n}} + 1\right) \cdot n} - 1}{i} \cdot n\right) \cdot 100 \]

      6. exp-to-pow N/A

         \[\leadsto \left(\frac{\color{blue}{{\left(\frac{i}{n} + 1\right)}^{n}} - 1}{i} \cdot n\right) \cdot 100 \]

      7. +-commutative N/A

         \[\leadsto \left(\frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{i} \cdot n\right) \cdot 100 \]

      8. lower--.f64 N/A

         \[\leadsto \left(\frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{i} \cdot n\right) \cdot 100 \]

      9. lower-pow.f64 N/A

         \[\leadsto \left(\frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{i} \cdot n\right) \cdot 100 \]

      10. +-commutative N/A

          \[\leadsto \left(\frac{{\color{blue}{\left(\frac{i}{n} + 1\right)}}^{n} - 1}{i} \cdot n\right) \cdot 100 \]

      11. lift-/.f64 N/A

          \[\leadsto \left(\frac{{\left(\color{blue}{\frac{i}{n}} + 1\right)}^{n} - 1}{i} \cdot n\right) \cdot 100 \]

      12. lift-+.f64 98.1

          \[\leadsto \left(\frac{{\color{blue}{\left(\frac{i}{n} + 1\right)}}^{n} - 1}{i} \cdot n\right) \cdot 100 \]

   5. Applied rewrites 98.1%

      \[\leadsto \left(\frac{\color{blue}{{\left(\frac{i}{n} + 1\right)}^{n} - 1}}{i} \cdot n\right) \cdot 100 \]

   if +inf.0 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n)))

   1. Initial program 0.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \color{blue}{n} \]
   3. Step-by-step derivation

   4. Applied rewrites 79.3%

      \[\leadsto 100 \cdot \color{blue}{n} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{i}{n}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;t\_0 \leq 10^{+18}:\\ \;\;\;\;100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))))
   (if (<= t_0 0.0)
     (* (* (/ (expm1 (* (log1p (/ i n)) n)) i) n) 100.0)
     (if (<= t_0 1e+18)
       (* 100.0 (/ (- (pow (/ i n) n) 1.0) (/ i n)))
       (* (* (/ (expm1 i) i) n) 100.0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = ((expm1((log1p((i / n)) * n)) / i) * n) * 100.0;
	} else if (t_0 <= 1e+18) {
		tmp = 100.0 * ((pow((i / n), n) - 1.0) / (i / n));
	} else {
		tmp = ((expm1(i) / i) * n) * 100.0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = ((Math.expm1((Math.log1p((i / n)) * n)) / i) * n) * 100.0;
	} else if (t_0 <= 1e+18) {
		tmp = 100.0 * ((Math.pow((i / n), n) - 1.0) / (i / n));
	} else {
		tmp = ((Math.expm1(i) / i) * n) * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))
	tmp = 0
	if t_0 <= 0.0:
		tmp = ((math.expm1((math.log1p((i / n)) * n)) / i) * n) * 100.0
	elif t_0 <= 1e+18:
		tmp = 100.0 * ((math.pow((i / n), n) - 1.0) / (i / n))
	else:
		tmp = ((math.expm1(i) / i) * n) * 100.0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(expm1(Float64(log1p(Float64(i / n)) * n)) / i) * n) * 100.0);
	elseif (t_0 <= 1e+18)
		tmp = Float64(100.0 * Float64(Float64((Float64(i / n) ^ n) - 1.0) / Float64(i / n)));
	else
		tmp = Float64(Float64(Float64(expm1(i) / i) * n) * 100.0);
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(N[(N[(Exp[N[(N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[t$95$0, 1e+18], N[(100.0 * N[(N[(N[Power[N[(i / n), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < 0.0

   1. Initial program 26.2%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 34.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]
   4. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\log \left(\frac{i}{n} + 1\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \color{blue}{\left(\frac{i}{n} + 1\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      3. lift-/.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \left(\color{blue}{\frac{i}{n}} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\log \color{blue}{\left(1 + \frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      5. lower-log1p.f64 N/A

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

      6. lift-/.f64 96.6

         \[\leadsto \left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{i}{n}}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

   5. Applied rewrites 96.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n\right)}{i} \cdot n\right) \cdot 100 \]

   if 0.0 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < 1e18

   1. Initial program 96.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around inf

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. lift-/.f64 95.2

         \[\leadsto 100 \cdot \frac{{\left(\frac{i}{\color{blue}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

   4. Applied rewrites 95.2%

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

   if 1e18 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n)))

   1. Initial program 19.2%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 20.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 82.4%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)\\ \mathbf{if}\;n \leq -7 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\frac{100 \cdot \mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 2.95 \cdot 10^{-111}:\\ \;\;\;\;100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* (/ (expm1 i) i) (* 100.0 n))))
   (if (<= n -7e-72)
     t_0
     (if (<= n -2e-311)
       (/ (* 100.0 (expm1 (* (log (+ (/ i n) 1.0)) n))) (/ i n))
       (if (<= n 2.95e-111)
         (* 100.0 (/ (fma (log i) n (* (- (log n)) n)) (/ i n)))
         t_0)))))

C

double code(double i, double n) {
	double t_0 = (expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = (100.0 * expm1((log(((i / n) + 1.0)) * n))) / (i / n);
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (fma(log(i), n, (-log(n) * n)) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(i, n)
	t_0 = Float64(Float64(expm1(i) / i) * Float64(100.0 * n))
	tmp = 0.0
	if (n <= -7e-72)
		tmp = t_0;
	elseif (n <= -2e-311)
		tmp = Float64(Float64(100.0 * expm1(Float64(log(Float64(Float64(i / n) + 1.0)) * n))) / Float64(i / n));
	elseif (n <= 2.95e-111)
		tmp = Float64(100.0 * Float64(fma(log(i), n, Float64(Float64(-log(n)) * n)) / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * N[(100.0 * n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -7e-72], t$95$0, If[LessEqual[n, -2e-311], N[(N[(100.0 * N[(Exp[N[(N[Log[N[(N[(i / n), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2.95e-111], N[(100.0 * N[(N[(N[Log[i], $MachinePrecision] * n + N[((-N[Log[n], $MachinePrecision]) * n), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if n < -7.00000000000000001e-72 or 2.95e-111 < n

   1. Initial program 22.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 20.7%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right)} \cdot 100 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(n \cdot 100\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

      6. lower-*.f64 86.5

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

   8. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

   if -7.00000000000000001e-72 < n < -1.9999999999999e-311

   1. Initial program 52.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]

   3. Applied rewrites 69.9%

      \[\leadsto \color{blue}{\frac{100 \cdot \mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{\frac{i}{n}}} \]

   if -1.9999999999999e-311 < n < 2.95e-111

   1. Initial program 30.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{n \cdot \left(\log i + -1 \cdot \log n\right)}}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      3. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \left(\mathsf{neg}\left(\log n\right)\right)\right) \cdot n}{\frac{i}{n}} \]

      4. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \log \left(\frac{1}{n}\right)\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      6. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      7. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      8. lower-/.f64 43.0

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

   4. Applied rewrites 43.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(i \cdot \frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lift-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      3. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      4. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      5. *-commutative N/A

         \[\leadsto 100 \cdot \frac{n \cdot \color{blue}{\log \left(i \cdot \frac{1}{n}\right)}}{\frac{i}{n}} \]

      6. sum-log N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(\log i + \color{blue}{\log \left(\frac{1}{n}\right)}\right)}{\frac{i}{n}} \]

      7. distribute-rgt-in N/A

         \[\leadsto 100 \cdot \frac{\log i \cdot n + \color{blue}{\log \left(\frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]

      8. lower-fma.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, \color{blue}{n}, \log \left(\frac{1}{n}\right) \cdot n\right)}{\frac{i}{n}} \]

      9. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \log \left(\frac{1}{n}\right) \cdot n\right)}{\frac{i}{n}} \]

      10. log-rec N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(\mathsf{neg}\left(\log n\right)\right) \cdot n\right)}{\frac{i}{n}} \]

      11. mul-1-neg N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-1 \cdot \log n\right) \cdot n\right)}{\frac{i}{n}} \]

      12. lower-*.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-1 \cdot \log n\right) \cdot n\right)}{\frac{i}{n}} \]

      13. mul-1-neg N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(\mathsf{neg}\left(\log n\right)\right) \cdot n\right)}{\frac{i}{n}} \]

      14. lower-neg.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]

      15. lower-log.f64 72.5

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]

   6. Applied rewrites 72.5%

      \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, \color{blue}{n}, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)\\ \mathbf{if}\;n \leq -7 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq -2 \cdot 10^{-311}:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 2.95 \cdot 10^{-111}:\\ \;\;\;\;100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* (/ (expm1 i) i) (* 100.0 n))))
   (if (<= n -7e-72)
     t_0
     (if (<= n -2e-311)
       (* 100.0 (/ (expm1 (* (log (+ (/ i n) 1.0)) n)) (/ i n)))
       (if (<= n 2.95e-111)
         (* 100.0 (/ (fma (log i) n (* (- (log n)) n)) (/ i n)))
         t_0)))))

C

double code(double i, double n) {
	double t_0 = (expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = 100.0 * (expm1((log(((i / n) + 1.0)) * n)) / (i / n));
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (fma(log(i), n, (-log(n) * n)) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(i, n)
	t_0 = Float64(Float64(expm1(i) / i) * Float64(100.0 * n))
	tmp = 0.0
	if (n <= -7e-72)
		tmp = t_0;
	elseif (n <= -2e-311)
		tmp = Float64(100.0 * Float64(expm1(Float64(log(Float64(Float64(i / n) + 1.0)) * n)) / Float64(i / n)));
	elseif (n <= 2.95e-111)
		tmp = Float64(100.0 * Float64(fma(log(i), n, Float64(Float64(-log(n)) * n)) / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * N[(100.0 * n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -7e-72], t$95$0, If[LessEqual[n, -2e-311], N[(100.0 * N[(N[(Exp[N[(N[Log[N[(N[(i / n), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2.95e-111], N[(100.0 * N[(N[(N[Log[i], $MachinePrecision] * n + N[((-N[Log[n], $MachinePrecision]) * n), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if n < -7.00000000000000001e-72 or 2.95e-111 < n

   1. Initial program 22.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 20.7%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right)} \cdot 100 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(n \cdot 100\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

      6. lower-*.f64 86.5

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

   8. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

   if -7.00000000000000001e-72 < n < -1.9999999999999e-311

   1. Initial program 52.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      2. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      3. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      4. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      5. pow-to-exp N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}} \]

      6. lower-expm1.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{\mathsf{expm1}\left(\log \left(1 + \frac{i}{n}\right) \cdot n\right)}}{\frac{i}{n}} \]

      7. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(\color{blue}{\log \left(1 + \frac{i}{n}\right) \cdot n}\right)}{\frac{i}{n}} \]

      8. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(\color{blue}{\log \left(1 + \frac{i}{n}\right)} \cdot n\right)}{\frac{i}{n}} \]

      9. +-commutative N/A

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(\log \color{blue}{\left(\frac{i}{n} + 1\right)} \cdot n\right)}{\frac{i}{n}} \]

      10. lower-+.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(\log \color{blue}{\left(\frac{i}{n} + 1\right)} \cdot n\right)}{\frac{i}{n}} \]

      11. lift-/.f64 69.8

          \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(\log \left(\color{blue}{\frac{i}{n}} + 1\right) \cdot n\right)}{\frac{i}{n}} \]

   3. Applied rewrites 69.8%

      \[\leadsto 100 \cdot \frac{\color{blue}{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}}{\frac{i}{n}} \]

   if -1.9999999999999e-311 < n < 2.95e-111

   1. Initial program 30.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{n \cdot \left(\log i + -1 \cdot \log n\right)}}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      3. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \left(\mathsf{neg}\left(\log n\right)\right)\right) \cdot n}{\frac{i}{n}} \]

      4. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \log \left(\frac{1}{n}\right)\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      6. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      7. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      8. lower-/.f64 43.0

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

   4. Applied rewrites 43.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(i \cdot \frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lift-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      3. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      4. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      5. *-commutative N/A

         \[\leadsto 100 \cdot \frac{n \cdot \color{blue}{\log \left(i \cdot \frac{1}{n}\right)}}{\frac{i}{n}} \]

      6. sum-log N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(\log i + \color{blue}{\log \left(\frac{1}{n}\right)}\right)}{\frac{i}{n}} \]

      7. distribute-rgt-in N/A

         \[\leadsto 100 \cdot \frac{\log i \cdot n + \color{blue}{\log \left(\frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]

      8. lower-fma.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, \color{blue}{n}, \log \left(\frac{1}{n}\right) \cdot n\right)}{\frac{i}{n}} \]

      9. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \log \left(\frac{1}{n}\right) \cdot n\right)}{\frac{i}{n}} \]

      10. log-rec N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(\mathsf{neg}\left(\log n\right)\right) \cdot n\right)}{\frac{i}{n}} \]

      11. mul-1-neg N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-1 \cdot \log n\right) \cdot n\right)}{\frac{i}{n}} \]

      12. lower-*.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-1 \cdot \log n\right) \cdot n\right)}{\frac{i}{n}} \]

      13. mul-1-neg N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(\mathsf{neg}\left(\log n\right)\right) \cdot n\right)}{\frac{i}{n}} \]

      14. lower-neg.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]

      15. lower-log.f64 72.5

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]

   6. Applied rewrites 72.5%

      \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, \color{blue}{n}, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)\\ \mathbf{if}\;n \leq -7 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\frac{100 \cdot \mathsf{expm1}\left(\log \left(\frac{i}{n}\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 2.95 \cdot 10^{-111}:\\ \;\;\;\;100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* (/ (expm1 i) i) (* 100.0 n))))
   (if (<= n -7e-72)
     t_0
     (if (<= n -2e-311)
       (/ (* 100.0 (expm1 (* (log (/ i n)) n))) (/ i n))
       (if (<= n 2.95e-111)
         (* 100.0 (/ (fma (log i) n (* (- (log n)) n)) (/ i n)))
         t_0)))))

C

double code(double i, double n) {
	double t_0 = (expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = (100.0 * expm1((log((i / n)) * n))) / (i / n);
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (fma(log(i), n, (-log(n) * n)) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(i, n)
	t_0 = Float64(Float64(expm1(i) / i) * Float64(100.0 * n))
	tmp = 0.0
	if (n <= -7e-72)
		tmp = t_0;
	elseif (n <= -2e-311)
		tmp = Float64(Float64(100.0 * expm1(Float64(log(Float64(i / n)) * n))) / Float64(i / n));
	elseif (n <= 2.95e-111)
		tmp = Float64(100.0 * Float64(fma(log(i), n, Float64(Float64(-log(n)) * n)) / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * N[(100.0 * n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -7e-72], t$95$0, If[LessEqual[n, -2e-311], N[(N[(100.0 * N[(Exp[N[(N[Log[N[(i / n), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2.95e-111], N[(100.0 * N[(N[(N[Log[i], $MachinePrecision] * n + N[((-N[Log[n], $MachinePrecision]) * n), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if n < -7.00000000000000001e-72 or 2.95e-111 < n

   1. Initial program 22.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 20.7%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right)} \cdot 100 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(n \cdot 100\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

      6. lower-*.f64 86.5

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

   8. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

   if -7.00000000000000001e-72 < n < -1.9999999999999e-311

   1. Initial program 52.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around inf

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. lift-/.f64 51.3

         \[\leadsto 100 \cdot \frac{{\left(\frac{i}{\color{blue}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

   4. Applied rewrites 51.3%

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]

   6. Applied rewrites 65.7%

      \[\leadsto \color{blue}{\frac{100 \cdot \mathsf{expm1}\left(\log \left(\frac{i}{n}\right) \cdot n\right)}{\frac{i}{n}}} \]

   if -1.9999999999999e-311 < n < 2.95e-111

   1. Initial program 30.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{n \cdot \left(\log i + -1 \cdot \log n\right)}}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      3. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \left(\mathsf{neg}\left(\log n\right)\right)\right) \cdot n}{\frac{i}{n}} \]

      4. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \log \left(\frac{1}{n}\right)\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      6. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      7. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      8. lower-/.f64 43.0

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

   4. Applied rewrites 43.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(i \cdot \frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lift-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      3. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      4. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      5. *-commutative N/A

         \[\leadsto 100 \cdot \frac{n \cdot \color{blue}{\log \left(i \cdot \frac{1}{n}\right)}}{\frac{i}{n}} \]

      6. sum-log N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(\log i + \color{blue}{\log \left(\frac{1}{n}\right)}\right)}{\frac{i}{n}} \]

      7. distribute-rgt-in N/A

         \[\leadsto 100 \cdot \frac{\log i \cdot n + \color{blue}{\log \left(\frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]

      8. lower-fma.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, \color{blue}{n}, \log \left(\frac{1}{n}\right) \cdot n\right)}{\frac{i}{n}} \]

      9. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \log \left(\frac{1}{n}\right) \cdot n\right)}{\frac{i}{n}} \]

      10. log-rec N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(\mathsf{neg}\left(\log n\right)\right) \cdot n\right)}{\frac{i}{n}} \]

      11. mul-1-neg N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-1 \cdot \log n\right) \cdot n\right)}{\frac{i}{n}} \]

      12. lower-*.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-1 \cdot \log n\right) \cdot n\right)}{\frac{i}{n}} \]

      13. mul-1-neg N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(\mathsf{neg}\left(\log n\right)\right) \cdot n\right)}{\frac{i}{n}} \]

      14. lower-neg.f64 N/A

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]

      15. lower-log.f64 72.5

          \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, n, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]

   6. Applied rewrites 72.5%

      \[\leadsto 100 \cdot \frac{\mathsf{fma}\left(\log i, \color{blue}{n}, \left(-\log n\right) \cdot n\right)}{\frac{i}{n}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)\\ \mathbf{if}\;n \leq -7 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\frac{100 \cdot \mathsf{expm1}\left(\log \left(\frac{i}{n}\right) \cdot n\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 2.95 \cdot 10^{-111}:\\ \;\;\;\;100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* (/ (expm1 i) i) (* 100.0 n))))
   (if (<= n -7e-72)
     t_0
     (if (<= n -2e-311)
       (/ (* 100.0 (expm1 (* (log (/ i n)) n))) (/ i n))
       (if (<= n 2.95e-111)
         (* 100.0 (/ (* (+ (- (log n)) (log i)) n) (/ i n)))
         t_0)))))

C

double code(double i, double n) {
	double t_0 = (expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = (100.0 * expm1((log((i / n)) * n))) / (i / n);
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (((-log(n) + log(i)) * n) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = (Math.expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = (100.0 * Math.expm1((Math.log((i / n)) * n))) / (i / n);
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (((-Math.log(n) + Math.log(i)) * n) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = (math.expm1(i) / i) * (100.0 * n)
	tmp = 0
	if n <= -7e-72:
		tmp = t_0
	elif n <= -2e-311:
		tmp = (100.0 * math.expm1((math.log((i / n)) * n))) / (i / n)
	elif n <= 2.95e-111:
		tmp = 100.0 * (((-math.log(n) + math.log(i)) * n) / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(Float64(expm1(i) / i) * Float64(100.0 * n))
	tmp = 0.0
	if (n <= -7e-72)
		tmp = t_0;
	elseif (n <= -2e-311)
		tmp = Float64(Float64(100.0 * expm1(Float64(log(Float64(i / n)) * n))) / Float64(i / n));
	elseif (n <= 2.95e-111)
		tmp = Float64(100.0 * Float64(Float64(Float64(Float64(-log(n)) + log(i)) * n) / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * N[(100.0 * n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -7e-72], t$95$0, If[LessEqual[n, -2e-311], N[(N[(100.0 * N[(Exp[N[(N[Log[N[(i / n), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2.95e-111], N[(100.0 * N[(N[(N[((-N[Log[n], $MachinePrecision]) + N[Log[i], $MachinePrecision]), $MachinePrecision] * n), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if n < -7.00000000000000001e-72 or 2.95e-111 < n

   1. Initial program 22.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 20.7%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right)} \cdot 100 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(n \cdot 100\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

      6. lower-*.f64 86.5

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

   8. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

   if -7.00000000000000001e-72 < n < -1.9999999999999e-311

   1. Initial program 52.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around inf

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. lift-/.f64 51.3

         \[\leadsto 100 \cdot \frac{{\left(\frac{i}{\color{blue}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

   4. Applied rewrites 51.3%

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]

   6. Applied rewrites 65.7%

      \[\leadsto \color{blue}{\frac{100 \cdot \mathsf{expm1}\left(\log \left(\frac{i}{n}\right) \cdot n\right)}{\frac{i}{n}}} \]

   if -1.9999999999999e-311 < n < 2.95e-111

   1. Initial program 30.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{n \cdot \left(\log i + -1 \cdot \log n\right)}}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      3. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \left(\mathsf{neg}\left(\log n\right)\right)\right) \cdot n}{\frac{i}{n}} \]

      4. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \log \left(\frac{1}{n}\right)\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      6. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      7. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      8. lower-/.f64 43.0

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

   4. Applied rewrites 43.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(i \cdot \frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      2. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      3. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      4. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\log \left(\frac{1}{n} \cdot i\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\left(\log \left(\frac{1}{n}\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      6. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\left(\mathsf{neg}\left(\log n\right)\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      7. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(-1 \cdot \log n + \log i\right) \cdot n}{\frac{i}{n}} \]

      8. lower-+.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(-1 \cdot \log n + \log i\right) \cdot n}{\frac{i}{n}} \]

      9. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\left(\mathsf{neg}\left(\log n\right)\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      10. lower-neg.f64 N/A

          \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      11. lower-log.f64 N/A

          \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      12. lower-log.f64 72.5

          \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

   6. Applied rewrites 72.5%

      \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 81.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)\\ \mathbf{if}\;n \leq -7 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;n \leq 2.95 \cdot 10^{-111}:\\ \;\;\;\;100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* (/ (expm1 i) i) (* 100.0 n))))
   (if (<= n -7e-72)
     t_0
     (if (<= n -2e-311)
       (* (* (/ (expm1 (* (log (/ i n)) n)) i) n) 100.0)
       (if (<= n 2.95e-111)
         (* 100.0 (/ (* (+ (- (log n)) (log i)) n) (/ i n)))
         t_0)))))

C

double code(double i, double n) {
	double t_0 = (expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = ((expm1((log((i / n)) * n)) / i) * n) * 100.0;
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (((-log(n) + log(i)) * n) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = (Math.expm1(i) / i) * (100.0 * n);
	double tmp;
	if (n <= -7e-72) {
		tmp = t_0;
	} else if (n <= -2e-311) {
		tmp = ((Math.expm1((Math.log((i / n)) * n)) / i) * n) * 100.0;
	} else if (n <= 2.95e-111) {
		tmp = 100.0 * (((-Math.log(n) + Math.log(i)) * n) / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = (math.expm1(i) / i) * (100.0 * n)
	tmp = 0
	if n <= -7e-72:
		tmp = t_0
	elif n <= -2e-311:
		tmp = ((math.expm1((math.log((i / n)) * n)) / i) * n) * 100.0
	elif n <= 2.95e-111:
		tmp = 100.0 * (((-math.log(n) + math.log(i)) * n) / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(Float64(expm1(i) / i) * Float64(100.0 * n))
	tmp = 0.0
	if (n <= -7e-72)
		tmp = t_0;
	elseif (n <= -2e-311)
		tmp = Float64(Float64(Float64(expm1(Float64(log(Float64(i / n)) * n)) / i) * n) * 100.0);
	elseif (n <= 2.95e-111)
		tmp = Float64(100.0 * Float64(Float64(Float64(Float64(-log(n)) + log(i)) * n) / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * N[(100.0 * n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -7e-72], t$95$0, If[LessEqual[n, -2e-311], N[(N[(N[(N[(Exp[N[(N[Log[N[(i / n), $MachinePrecision]], $MachinePrecision] * n), $MachinePrecision]] - 1), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[n, 2.95e-111], N[(100.0 * N[(N[(N[((-N[Log[n], $MachinePrecision]) + N[Log[i], $MachinePrecision]), $MachinePrecision] * n), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if n < -7.00000000000000001e-72 or 2.95e-111 < n

   1. Initial program 22.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 20.7%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.6%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right)} \cdot 100 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(n \cdot 100\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

      6. lower-*.f64 86.5

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

   8. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

   if -7.00000000000000001e-72 < n < -1.9999999999999e-311

   1. Initial program 52.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around inf

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. lift-/.f64 51.3

         \[\leadsto 100 \cdot \frac{{\left(\frac{i}{\color{blue}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

   4. Applied rewrites 51.3%

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      3. lower-*.f64 51.3

         \[\leadsto \color{blue}{\frac{{\left(\frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   6. Applied rewrites 64.9%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n}\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   if -1.9999999999999e-311 < n < 2.95e-111

   1. Initial program 30.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{n \cdot \left(\log i + -1 \cdot \log n\right)}}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      2. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + -1 \cdot \log n\right) \cdot \color{blue}{n}}{\frac{i}{n}} \]

      3. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \left(\mathsf{neg}\left(\log n\right)\right)\right) \cdot n}{\frac{i}{n}} \]

      4. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\log i + \log \left(\frac{1}{n}\right)\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      6. lower-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      7. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      8. lower-/.f64 43.0

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

   4. Applied rewrites 43.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(i \cdot \frac{1}{n}\right) \cdot n}}{\frac{i}{n}} \]
   5. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      2. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      3. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{\log \left(i \cdot \frac{1}{n}\right) \cdot n}{\frac{i}{n}} \]

      4. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\log \left(\frac{1}{n} \cdot i\right) \cdot n}{\frac{i}{n}} \]

      5. sum-log N/A

         \[\leadsto 100 \cdot \frac{\left(\log \left(\frac{1}{n}\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      6. log-rec N/A

         \[\leadsto 100 \cdot \frac{\left(\left(\mathsf{neg}\left(\log n\right)\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      7. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(-1 \cdot \log n + \log i\right) \cdot n}{\frac{i}{n}} \]

      8. lower-+.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(-1 \cdot \log n + \log i\right) \cdot n}{\frac{i}{n}} \]

      9. mul-1-neg N/A

         \[\leadsto 100 \cdot \frac{\left(\left(\mathsf{neg}\left(\log n\right)\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      10. lower-neg.f64 N/A

          \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      11. lower-log.f64 N/A

          \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

      12. lower-log.f64 72.5

          \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]

   6. Applied rewrites 72.5%

      \[\leadsto 100 \cdot \frac{\left(\left(-\log n\right) + \log i\right) \cdot n}{\frac{i}{n}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 81.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -9.4 \cdot 10^{-169}:\\ \;\;\;\;\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)\\ \mathbf{elif}\;n \leq 1.18 \cdot 10^{-200}:\\ \;\;\;\;\left(\frac{1 - 1}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;n \leq 2.45:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -9.4e-169)
   (* (/ (expm1 i) i) (* 100.0 n))
   (if (<= n 1.18e-200)
     (* (* (/ (- 1.0 1.0) i) n) 100.0)
     (if (<= n 2.45)
       (* 100.0 (/ i (/ i n)))
       (* 100.0 (/ (* (expm1 i) n) i))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -9.4e-169) {
		tmp = (expm1(i) / i) * (100.0 * n);
	} else if (n <= 1.18e-200) {
		tmp = (((1.0 - 1.0) / i) * n) * 100.0;
	} else if (n <= 2.45) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = 100.0 * ((expm1(i) * n) / i);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -9.4e-169) {
		tmp = (Math.expm1(i) / i) * (100.0 * n);
	} else if (n <= 1.18e-200) {
		tmp = (((1.0 - 1.0) / i) * n) * 100.0;
	} else if (n <= 2.45) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = 100.0 * ((Math.expm1(i) * n) / i);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -9.4e-169:
		tmp = (math.expm1(i) / i) * (100.0 * n)
	elif n <= 1.18e-200:
		tmp = (((1.0 - 1.0) / i) * n) * 100.0
	elif n <= 2.45:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = 100.0 * ((math.expm1(i) * n) / i)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -9.4e-169)
		tmp = Float64(Float64(expm1(i) / i) * Float64(100.0 * n));
	elseif (n <= 1.18e-200)
		tmp = Float64(Float64(Float64(Float64(1.0 - 1.0) / i) * n) * 100.0);
	elseif (n <= 2.45)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = Float64(100.0 * Float64(Float64(expm1(i) * n) / i));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[n, -9.4e-169], N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * N[(100.0 * n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.18e-200], N[(N[(N[(N[(1.0 - 1.0), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[n, 2.45], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(N[(N[(Exp[i] - 1), $MachinePrecision] * n), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if n < -9.39999999999999981e-169

   1. Initial program 26.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 24.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 83.0%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right)} \cdot 100 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(n \cdot 100\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

      6. lower-*.f64 82.8

         \[\leadsto \frac{\mathsf{expm1}\left(i\right)}{i} \cdot \color{blue}{\left(100 \cdot n\right)} \]

   8. Applied rewrites 82.8%

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(i\right)}{i} \cdot \left(100 \cdot n\right)} \]

   if -9.39999999999999981e-169 < n < 1.17999999999999996e-200

   1. Initial program 56.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(1 + i\right)} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(i + \color{blue}{1}\right) - 1}{\frac{i}{n}} \]

      2. lower-+.f64 60.0

         \[\leadsto 100 \cdot \frac{\left(i + \color{blue}{1}\right) - 1}{\frac{i}{n}} \]

   4. Applied rewrites 60.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(i + 1\right)} - 1}{\frac{i}{n}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{1 - 1}{\frac{i}{n}} \]
   6. Step-by-step derivation

   7. Applied rewrites 71.4%

      \[\leadsto 100 \cdot \frac{1 - 1}{\frac{i}{n}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{1 - 1}{\frac{i}{n}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}} \cdot 100} \]

      3. lower-*.f64 71.4

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}} \cdot 100} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{1 - 1}{\color{blue}{\frac{i}{n}}} \cdot 100 \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}}} \cdot 100 \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right)} \cdot 100 \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right)} \cdot 100 \]

      8. lower-/.f64 71.4

         \[\leadsto \left(\color{blue}{\frac{1 - 1}{i}} \cdot n\right) \cdot 100 \]

   9. Applied rewrites 71.4%

      \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right) \cdot 100} \]

   if 1.17999999999999996e-200 < n < 2.4500000000000002

   1. Initial program 15.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]

   if 2.4500000000000002 < n

   1. Initial program 22.3%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 94.8

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 94.8%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 81.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -9.4 \cdot 10^{-169}:\\ \;\;\;\;\left(\frac{\mathsf{expm1}\left(i\right)}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;n \leq 1.18 \cdot 10^{-200}:\\ \;\;\;\;\left(\frac{1 - 1}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;n \leq 2.45:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -9.4e-169)
   (* (* (/ (expm1 i) i) n) 100.0)
   (if (<= n 1.18e-200)
     (* (* (/ (- 1.0 1.0) i) n) 100.0)
     (if (<= n 2.45)
       (* 100.0 (/ i (/ i n)))
       (* 100.0 (/ (* (expm1 i) n) i))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -9.4e-169) {
		tmp = ((expm1(i) / i) * n) * 100.0;
	} else if (n <= 1.18e-200) {
		tmp = (((1.0 - 1.0) / i) * n) * 100.0;
	} else if (n <= 2.45) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = 100.0 * ((expm1(i) * n) / i);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -9.4e-169) {
		tmp = ((Math.expm1(i) / i) * n) * 100.0;
	} else if (n <= 1.18e-200) {
		tmp = (((1.0 - 1.0) / i) * n) * 100.0;
	} else if (n <= 2.45) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = 100.0 * ((Math.expm1(i) * n) / i);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -9.4e-169:
		tmp = ((math.expm1(i) / i) * n) * 100.0
	elif n <= 1.18e-200:
		tmp = (((1.0 - 1.0) / i) * n) * 100.0
	elif n <= 2.45:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = 100.0 * ((math.expm1(i) * n) / i)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -9.4e-169)
		tmp = Float64(Float64(Float64(expm1(i) / i) * n) * 100.0);
	elseif (n <= 1.18e-200)
		tmp = Float64(Float64(Float64(Float64(1.0 - 1.0) / i) * n) * 100.0);
	elseif (n <= 2.45)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = Float64(100.0 * Float64(Float64(expm1(i) * n) / i));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[n, -9.4e-169], N[(N[(N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[n, 1.18e-200], N[(N[(N[(N[(1.0 - 1.0), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[n, 2.45], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(N[(N[(Exp[i] - 1), $MachinePrecision] * n), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if n < -9.39999999999999981e-169

   1. Initial program 26.1%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      2. lift-/.f64 N/A

         \[\leadsto 100 \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \]

      3. lift--.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \]

      4. lift-pow.f64 N/A

         \[\leadsto 100 \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \]

      5. lift-+.f64 N/A

         \[\leadsto 100 \cdot \frac{{\color{blue}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]

      6. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \color{blue}{\frac{i}{n}}\right)}^{n} - 1}{\frac{i}{n}} \]

      7. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\frac{i}{n}}} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \cdot 100} \]

   3. Applied rewrites 24.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{expm1}\left(\log \left(\frac{i}{n} + 1\right) \cdot n\right)}{i} \cdot n\right) \cdot 100} \]

   4. Taylor expanded in i around 0

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]
   5. Step-by-step derivation

   6. Applied rewrites 83.0%

      \[\leadsto \left(\frac{\mathsf{expm1}\left(\color{blue}{i}\right)}{i} \cdot n\right) \cdot 100 \]

   if -9.39999999999999981e-169 < n < 1.17999999999999996e-200

   1. Initial program 56.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(1 + i\right)} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(i + \color{blue}{1}\right) - 1}{\frac{i}{n}} \]

      2. lower-+.f64 60.0

         \[\leadsto 100 \cdot \frac{\left(i + \color{blue}{1}\right) - 1}{\frac{i}{n}} \]

   4. Applied rewrites 60.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(i + 1\right)} - 1}{\frac{i}{n}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{1 - 1}{\frac{i}{n}} \]
   6. Step-by-step derivation

   7. Applied rewrites 71.4%

      \[\leadsto 100 \cdot \frac{1 - 1}{\frac{i}{n}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{1 - 1}{\frac{i}{n}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}} \cdot 100} \]

      3. lower-*.f64 71.4

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}} \cdot 100} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{1 - 1}{\color{blue}{\frac{i}{n}}} \cdot 100 \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}}} \cdot 100 \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right)} \cdot 100 \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right)} \cdot 100 \]

      8. lower-/.f64 71.4

         \[\leadsto \left(\color{blue}{\frac{1 - 1}{i}} \cdot n\right) \cdot 100 \]

   9. Applied rewrites 71.4%

      \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right) \cdot 100} \]

   if 1.17999999999999996e-200 < n < 2.4500000000000002

   1. Initial program 15.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]

   if 2.4500000000000002 < n

   1. Initial program 22.3%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 94.8

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 94.8%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 80.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i}\\ \mathbf{if}\;n \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq 1.18 \cdot 10^{-200}:\\ \;\;\;\;\left(\frac{1 - 1}{i} \cdot n\right) \cdot 100\\ \mathbf{elif}\;n \leq 2.45:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (* (expm1 i) n) i))))
   (if (<= n -1.25e-135)
     t_0
     (if (<= n 1.18e-200)
       (* (* (/ (- 1.0 1.0) i) n) 100.0)
       (if (<= n 2.45) (* 100.0 (/ i (/ i n))) t_0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * ((expm1(i) * n) / i);
	double tmp;
	if (n <= -1.25e-135) {
		tmp = t_0;
	} else if (n <= 1.18e-200) {
		tmp = (((1.0 - 1.0) / i) * n) * 100.0;
	} else if (n <= 2.45) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * ((Math.expm1(i) * n) / i);
	double tmp;
	if (n <= -1.25e-135) {
		tmp = t_0;
	} else if (n <= 1.18e-200) {
		tmp = (((1.0 - 1.0) / i) * n) * 100.0;
	} else if (n <= 2.45) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * ((math.expm1(i) * n) / i)
	tmp = 0
	if n <= -1.25e-135:
		tmp = t_0
	elif n <= 1.18e-200:
		tmp = (((1.0 - 1.0) / i) * n) * 100.0
	elif n <= 2.45:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(Float64(expm1(i) * n) / i))
	tmp = 0.0
	if (n <= -1.25e-135)
		tmp = t_0;
	elseif (n <= 1.18e-200)
		tmp = Float64(Float64(Float64(Float64(1.0 - 1.0) / i) * n) * 100.0);
	elseif (n <= 2.45)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(N[(Exp[i] - 1), $MachinePrecision] * n), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.25e-135], t$95$0, If[LessEqual[n, 1.18e-200], N[(N[(N[(N[(1.0 - 1.0), $MachinePrecision] / i), $MachinePrecision] * n), $MachinePrecision] * 100.0), $MachinePrecision], If[LessEqual[n, 2.45], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if n < -1.25000000000000005e-135 or 2.4500000000000002 < n

   1. Initial program 24.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 86.3

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 86.3%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]

   if -1.25000000000000005e-135 < n < 1.17999999999999996e-200

   1. Initial program 54.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(1 + i\right)} - 1}{\frac{i}{n}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(i + \color{blue}{1}\right) - 1}{\frac{i}{n}} \]

      2. lower-+.f64 56.4

         \[\leadsto 100 \cdot \frac{\left(i + \color{blue}{1}\right) - 1}{\frac{i}{n}} \]

   4. Applied rewrites 56.4%

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(i + 1\right)} - 1}{\frac{i}{n}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{1 - 1}{\frac{i}{n}} \]
   6. Step-by-step derivation

   7. Applied rewrites 67.9%

      \[\leadsto 100 \cdot \frac{1 - 1}{\frac{i}{n}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{100 \cdot \frac{1 - 1}{\frac{i}{n}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}} \cdot 100} \]

      3. lower-*.f64 67.9

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}} \cdot 100} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{1 - 1}{\color{blue}{\frac{i}{n}}} \cdot 100 \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1 - 1}{\frac{i}{n}}} \cdot 100 \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right)} \cdot 100 \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right)} \cdot 100 \]

      8. lower-/.f64 67.9

         \[\leadsto \left(\color{blue}{\frac{1 - 1}{i}} \cdot n\right) \cdot 100 \]

   9. Applied rewrites 67.9%

      \[\leadsto \color{blue}{\left(\frac{1 - 1}{i} \cdot n\right) \cdot 100} \]

   if 1.17999999999999996e-200 < n < 2.4500000000000002

   1. Initial program 15.5%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leq \infty:\\ \;\;\;\;100 \cdot \left(\mathsf{expm1}\left(i\right) \cdot \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot n\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))) INFINITY)
   (* 100.0 (* (expm1 i) (/ n i)))
   (* 100.0 n)))

C

double code(double i, double n) {
	double tmp;
	if ((100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n))) <= ((double) INFINITY)) {
		tmp = 100.0 * (expm1(i) * (n / i));
	} else {
		tmp = 100.0 * n;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if ((100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))) <= Double.POSITIVE_INFINITY) {
		tmp = 100.0 * (Math.expm1(i) * (n / i));
	} else {
		tmp = 100.0 * n;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))) <= math.inf:
		tmp = 100.0 * (math.expm1(i) * (n / i))
	else:
		tmp = 100.0 * n
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n))) <= Inf)
		tmp = Float64(100.0 * Float64(expm1(i) * Float64(n / i)));
	else
		tmp = Float64(100.0 * n);
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * n), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n))) < +inf.0

   1. Initial program 33.8%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 69.6

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 69.6%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{\color{blue}{i}} \]

      2. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

      3. lift-expm1.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. associate-/l* N/A

         \[\leadsto 100 \cdot \left(\left(e^{i} - 1\right) \cdot \color{blue}{\frac{n}{i}}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 100 \cdot \left(\left(e^{i} - 1\right) \cdot \color{blue}{\frac{n}{i}}\right) \]

      6. lift-expm1.f64 N/A

         \[\leadsto 100 \cdot \left(\mathsf{expm1}\left(i\right) \cdot \frac{\color{blue}{n}}{i}\right) \]

      7. lower-/.f64 73.5

         \[\leadsto 100 \cdot \left(\mathsf{expm1}\left(i\right) \cdot \frac{n}{\color{blue}{i}}\right) \]

   6. Applied rewrites 73.5%

      \[\leadsto 100 \cdot \left(\mathsf{expm1}\left(i\right) \cdot \color{blue}{\frac{n}{i}}\right) \]

   if +inf.0 < (*.f64 #s(literal 100 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n)))

   1. Initial program 0.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \color{blue}{n} \]
   3. Step-by-step derivation

   4. Applied rewrites 79.3%

      \[\leadsto 100 \cdot \color{blue}{n} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 61.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \mathsf{fma}\left(n \cdot i, 0.5, n\right)\\ \mathbf{if}\;n \leq -5 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq 1.5:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (fma (* n i) 0.5 n))))
   (if (<= n -5e+132) t_0 (if (<= n 1.5) (* 100.0 (/ i (/ i n))) t_0))))

C

double code(double i, double n) {
	double t_0 = 100.0 * fma((n * i), 0.5, n);
	double tmp;
	if (n <= -5e+132) {
		tmp = t_0;
	} else if (n <= 1.5) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(i, n)
	t_0 = Float64(100.0 * fma(Float64(n * i), 0.5, n))
	tmp = 0.0
	if (n <= -5e+132)
		tmp = t_0;
	elseif (n <= 1.5)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(n * i), $MachinePrecision] * 0.5 + n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -5e+132], t$95$0, If[LessEqual[n, 1.5], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if n < -5.0000000000000001e132 or 1.5 < n

   1. Initial program 20.3%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 94.3

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 94.3%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \left(n + \color{blue}{\frac{1}{2} \cdot \left(i \cdot n\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 100 \cdot \left(\frac{1}{2} \cdot \left(i \cdot n\right) + n\right) \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \left(\left(i \cdot n\right) \cdot \frac{1}{2} + n\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(i \cdot n, \frac{1}{2}, n\right) \]

      4. *-commutative N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(n \cdot i, \frac{1}{2}, n\right) \]

      5. lower-*.f64 66.9

         \[\leadsto 100 \cdot \mathsf{fma}\left(n \cdot i, 0.5, n\right) \]

   7. Applied rewrites 66.9%

      \[\leadsto 100 \cdot \mathsf{fma}\left(n \cdot i, \color{blue}{0.5}, n\right) \]

   if -5.0000000000000001e132 < n < 1.5

   1. Initial program 34.3%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 60.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{i \cdot n}{i}\\ \mathbf{if}\;n \leq -1.26 \cdot 10^{+157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq 9.5 \cdot 10^{-48}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (* i n) i))))
   (if (<= n -1.26e+157) t_0 (if (<= n 9.5e-48) (* 100.0 (/ i (/ i n))) t_0))))

C

double code(double i, double n) {
	double t_0 = 100.0 * ((i * n) / i);
	double tmp;
	if (n <= -1.26e+157) {
		tmp = t_0;
	} else if (n <= 9.5e-48) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(i, n)
use fmin_fmax_functions
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 100.0d0 * ((i * n) / i)
    if (n <= (-1.26d+157)) then
        tmp = t_0
    else if (n <= 9.5d-48) then
        tmp = 100.0d0 * (i / (i / n))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * ((i * n) / i);
	double tmp;
	if (n <= -1.26e+157) {
		tmp = t_0;
	} else if (n <= 9.5e-48) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * ((i * n) / i)
	tmp = 0
	if n <= -1.26e+157:
		tmp = t_0
	elif n <= 9.5e-48:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(Float64(i * n) / i))
	tmp = 0.0
	if (n <= -1.26e+157)
		tmp = t_0;
	elseif (n <= 9.5e-48)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = 100.0 * ((i * n) / i);
	tmp = 0.0;
	if (n <= -1.26e+157)
		tmp = t_0;
	elseif (n <= 9.5e-48)
		tmp = 100.0 * (i / (i / n));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(i * n), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.26e+157], t$95$0, If[LessEqual[n, 9.5e-48], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if n < -1.25999999999999996e157 or 9.50000000000000036e-48 < n

   1. Initial program 19.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 92.4

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 92.4%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]
   6. Step-by-step derivation

   7. Applied rewrites 66.1%

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]

   if -1.25999999999999996e157 < n < 9.50000000000000036e-48

   1. Initial program 35.4%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
   3. Step-by-step derivation

   4. Applied rewrites 55.0%

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 59.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{i \cdot n}{i}\\ \mathbf{if}\;n \leq -5.8 \cdot 10^{+155}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;n \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;100 \cdot \left(i \cdot \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (* i n) i))))
   (if (<= n -5.8e+155) t_0 (if (<= n 3.1e-19) (* 100.0 (* i (/ n i))) t_0))))

C

double code(double i, double n) {
	double t_0 = 100.0 * ((i * n) / i);
	double tmp;
	if (n <= -5.8e+155) {
		tmp = t_0;
	} else if (n <= 3.1e-19) {
		tmp = 100.0 * (i * (n / i));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(i, n)
use fmin_fmax_functions
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 100.0d0 * ((i * n) / i)
    if (n <= (-5.8d+155)) then
        tmp = t_0
    else if (n <= 3.1d-19) then
        tmp = 100.0d0 * (i * (n / i))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * ((i * n) / i);
	double tmp;
	if (n <= -5.8e+155) {
		tmp = t_0;
	} else if (n <= 3.1e-19) {
		tmp = 100.0 * (i * (n / i));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * ((i * n) / i)
	tmp = 0
	if n <= -5.8e+155:
		tmp = t_0
	elif n <= 3.1e-19:
		tmp = 100.0 * (i * (n / i))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(Float64(i * n) / i))
	tmp = 0.0
	if (n <= -5.8e+155)
		tmp = t_0;
	elseif (n <= 3.1e-19)
		tmp = Float64(100.0 * Float64(i * Float64(n / i)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = 100.0 * ((i * n) / i);
	tmp = 0.0;
	if (n <= -5.8e+155)
		tmp = t_0;
	elseif (n <= 3.1e-19)
		tmp = 100.0 * (i * (n / i));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(i * n), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -5.8e+155], t$95$0, If[LessEqual[n, 3.1e-19], N[(100.0 * N[(i * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if n < -5.7999999999999998e155 or 3.0999999999999999e-19 < n

   1. Initial program 20.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 94.0

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 94.0%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]
   6. Step-by-step derivation

   7. Applied rewrites 66.4%

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]

   if -5.7999999999999998e155 < n < 3.0999999999999999e-19

   1. Initial program 34.3%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 51.2

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 51.2%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]
   6. Step-by-step derivation

   7. Applied rewrites 36.2%

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{i \cdot n}{\color{blue}{i}} \]

      2. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]

      3. associate-/l* N/A

         \[\leadsto 100 \cdot \left(i \cdot \color{blue}{\frac{n}{i}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto 100 \cdot \left(i \cdot \color{blue}{\frac{n}{i}}\right) \]

      5. lower-/.f64 54.1

         \[\leadsto 100 \cdot \left(i \cdot \frac{n}{\color{blue}{i}}\right) \]

   9. Applied rewrites 54.1%

      \[\leadsto 100 \cdot \left(i \cdot \color{blue}{\frac{n}{i}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 55.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \left(i \cdot \frac{n}{i}\right)\\ \mathbf{if}\;i \leq -1.85 \cdot 10^{-45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-66}:\\ \;\;\;\;100 \cdot \mathsf{fma}\left(-0.5, i, n\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (* i (/ n i)))))
   (if (<= i -1.85e-45)
     t_0
     (if (<= i 1.55e-66) (* 100.0 (fma -0.5 i n)) t_0))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (i * (n / i));
	double tmp;
	if (i <= -1.85e-45) {
		tmp = t_0;
	} else if (i <= 1.55e-66) {
		tmp = 100.0 * fma(-0.5, i, n);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(i * Float64(n / i)))
	tmp = 0.0
	if (i <= -1.85e-45)
		tmp = t_0;
	elseif (i <= 1.55e-66)
		tmp = Float64(100.0 * fma(-0.5, i, n));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(i * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.85e-45], t$95$0, If[LessEqual[i, 1.55e-66], N[(100.0 * N[(-0.5 * i + n), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.85e-45 or 1.5499999999999999e-66 < i

   1. Initial program 45.0%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in n around inf

      \[\leadsto 100 \cdot \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{\color{blue}{i}} \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto 100 \cdot \frac{\left(e^{i} - 1\right) \cdot n}{i} \]

      4. lower-expm1.f64 65.1

         \[\leadsto 100 \cdot \frac{\mathsf{expm1}\left(i\right) \cdot n}{i} \]

   4. Applied rewrites 65.1%

      \[\leadsto 100 \cdot \color{blue}{\frac{\mathsf{expm1}\left(i\right) \cdot n}{i}} \]

   5. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

      \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto 100 \cdot \frac{i \cdot n}{\color{blue}{i}} \]

      2. lift-*.f64 N/A

         \[\leadsto 100 \cdot \frac{i \cdot n}{i} \]

      3. associate-/l* N/A

         \[\leadsto 100 \cdot \left(i \cdot \color{blue}{\frac{n}{i}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto 100 \cdot \left(i \cdot \color{blue}{\frac{n}{i}}\right) \]

      5. lower-/.f64 27.2

         \[\leadsto 100 \cdot \left(i \cdot \frac{n}{\color{blue}{i}}\right) \]

   9. Applied rewrites 27.2%

      \[\leadsto 100 \cdot \left(i \cdot \color{blue}{\frac{n}{i}}\right) \]

   if -1.85e-45 < i < 1.5499999999999999e-66

   1. Initial program 7.8%

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

   2. Taylor expanded in i around 0

      \[\leadsto 100 \cdot \color{blue}{\left(n + i \cdot \left(n \cdot \left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 100 \cdot \left(i \cdot \left(n \cdot \left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right)\right) + \color{blue}{n}\right) \]

      2. *-commutative N/A

         \[\leadsto 100 \cdot \left(\left(n \cdot \left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right)\right) \cdot i + n\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(n \cdot \left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right), \color{blue}{i}, n\right) \]

      4. *-commutative N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(\left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right) \cdot n, i, n\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(\left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right) \cdot n, i, n\right) \]

      6. lower--.f64 N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(\left(\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{n}\right) \cdot n, i, n\right) \]

      7. associate-*r/ N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(\left(\frac{1}{2} - \frac{\frac{1}{2} \cdot 1}{n}\right) \cdot n, i, n\right) \]

      8. metadata-eval N/A

         \[\leadsto 100 \cdot \mathsf{fma}\left(\left(\frac{1}{2} - \frac{\frac{1}{2}}{n}\right) \cdot n, i, n\right) \]

      9. lower-/.f64 88.7

         \[\leadsto 100 \cdot \mathsf{fma}\left(\left(0.5 - \frac{0.5}{n}\right) \cdot n, i, n\right) \]

   4. Applied rewrites 88.7%

      \[\leadsto 100 \cdot \color{blue}{\mathsf{fma}\left(\left(0.5 - \frac{0.5}{n}\right) \cdot n, i, n\right)} \]

   5. Taylor expanded in n around 0

      \[\leadsto 100 \cdot \mathsf{fma}\left(\frac{-1}{2}, i, n\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 88.7%

      \[\leadsto 100 \cdot \mathsf{fma}\left(-0.5, i, n\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 49.4% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ 100 \cdot n \end{array} \]

FPCore

(FPCore (i n) :precision binary64 (* 100.0 n))

C

double code(double i, double n) {
	return 100.0 * n;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(i, n)
use fmin_fmax_functions
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = 100.0d0 * n
end function

Java

public static double code(double i, double n) {
	return 100.0 * n;
}

Python

def code(i, n):
	return 100.0 * n

Julia

function code(i, n)
	return Float64(100.0 * n)
end

MATLAB

function tmp = code(i, n)
	tmp = 100.0 * n;
end

Wolfram

code[i_, n_] := N[(100.0 * n), $MachinePrecision]

Derivation

1. Initial program 27.6%

   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]

2. Taylor expanded in i around 0

   \[\leadsto 100 \cdot \color{blue}{n} \]
3. Step-by-step derivation

4. Applied rewrites 49.4%

   \[\leadsto 100 \cdot \color{blue}{n} \]
5. Add Preprocessing

Developer Target 1: 34.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{i}{n}\\ 100 \cdot \frac{e^{n \cdot \begin{array}{l} \mathbf{if}\;t\_0 = 1:\\ \;\;\;\;\frac{i}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{i}{n} \cdot \log t\_0}{\left(\frac{i}{n} + 1\right) - 1}\\ \end{array}} - 1}{\frac{i}{n}} \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ i n))))
   (*
    100.0
    (/
     (-
      (exp
       (*
        n
        (if (== t_0 1.0)
          (/ i n)
          (/ (* (/ i n) (log t_0)) (- (+ (/ i n) 1.0) 1.0)))))
      1.0)
     (/ i n)))))

C

double code(double i, double n) {
	double t_0 = 1.0 + (i / n);
	double tmp;
	if (t_0 == 1.0) {
		tmp = i / n;
	} else {
		tmp = ((i / n) * log(t_0)) / (((i / n) + 1.0) - 1.0);
	}
	return 100.0 * ((exp((n * tmp)) - 1.0) / (i / n));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(i, n)
use fmin_fmax_functions
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (i / n)
    if (t_0 == 1.0d0) then
        tmp = i / n
    else
        tmp = ((i / n) * log(t_0)) / (((i / n) + 1.0d0) - 1.0d0)
    end if
    code = 100.0d0 * ((exp((n * tmp)) - 1.0d0) / (i / n))
end function

Java

public static double code(double i, double n) {
	double t_0 = 1.0 + (i / n);
	double tmp;
	if (t_0 == 1.0) {
		tmp = i / n;
	} else {
		tmp = ((i / n) * Math.log(t_0)) / (((i / n) + 1.0) - 1.0);
	}
	return 100.0 * ((Math.exp((n * tmp)) - 1.0) / (i / n));
}

Python

def code(i, n):
	t_0 = 1.0 + (i / n)
	tmp = 0
	if t_0 == 1.0:
		tmp = i / n
	else:
		tmp = ((i / n) * math.log(t_0)) / (((i / n) + 1.0) - 1.0)
	return 100.0 * ((math.exp((n * tmp)) - 1.0) / (i / n))

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n))
	tmp = 0.0
	if (t_0 == 1.0)
		tmp = Float64(i / n);
	else
		tmp = Float64(Float64(Float64(i / n) * log(t_0)) / Float64(Float64(Float64(i / n) + 1.0) - 1.0));
	end
	return Float64(100.0 * Float64(Float64(exp(Float64(n * tmp)) - 1.0) / Float64(i / n)))
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = 1.0 + (i / n);
	tmp = 0.0;
	if (t_0 == 1.0)
		tmp = i / n;
	else
		tmp = ((i / n) * log(t_0)) / (((i / n) + 1.0) - 1.0);
	end
	tmp_2 = 100.0 * ((exp((n * tmp)) - 1.0) / (i / n));
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision]}, N[(100.0 * N[(N[(N[Exp[N[(n * If[Equal[t$95$0, 1.0], N[(i / n), $MachinePrecision], N[(N[(N[(i / n), $MachinePrecision] * N[Log[t$95$0], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(i / n), $MachinePrecision] + 1.0), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2025123 
(FPCore (i n)
  :name "Compound Interest"
  :precision binary64

  :alt
  (! :herbie-platform c (let ((lnbase (if (== (+ 1 (/ i n)) 1) (/ i n) (/ (* (/ i n) (log (+ 1 (/ i n)))) (- (+ (/ i n) 1) 1))))) (* 100 (/ (- (exp (* n lnbase)) 1) (/ i n)))))

  (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))