Compound Interest

Percentage Accurate: 28.2% → 98.6%

Time: 17.6s

Alternatives: 17

Speedup: 8.7×

• could not determine a ground truth

  1. i = -2.0000000000000001e231
  2. n = 1.99999999999999997e77

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

real(8) function code(i, n)
    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: 28.2% 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

real(8) function code(i, n)
    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: 98.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot {\left(\frac{i}{n}\right)}^{n}\\ t_1 := \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-27}:\\ \;\;\;\;\frac{n \cdot \left(t\_0 - 100\right)}{i}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{t\_0 + -100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (pow (/ i n) n)))
        (t_1 (/ (+ (pow (+ 1.0 (/ i n)) n) -1.0) (/ i n))))
   (if (<= t_1 -2e-27)
     (/ (* n (- t_0 100.0)) i)
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
       (if (<= t_1 INFINITY)
         (/ (+ t_0 -100.0) (/ i n))
         (* 100.0 (/ n (+ 1.0 (* i -0.5)))))))))

C

double code(double i, double n) {
	double t_0 = 100.0 * pow((i / n), n);
	double t_1 = (pow((1.0 + (i / n)), n) + -1.0) / (i / n);
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = (n * (t_0 - 100.0)) / i;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1((n * log1p((i / n)))) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (t_0 + -100.0) / (i / n);
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * Math.pow((i / n), n);
	double t_1 = (Math.pow((1.0 + (i / n)), n) + -1.0) / (i / n);
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = (n * (t_0 - 100.0)) / i;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1((n * Math.log1p((i / n)))) / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (t_0 + -100.0) / (i / n);
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * math.pow((i / n), n)
	t_1 = (math.pow((1.0 + (i / n)), n) + -1.0) / (i / n)
	tmp = 0
	if t_1 <= -2e-27:
		tmp = (n * (t_0 - 100.0)) / i
	elif t_1 <= 0.0:
		tmp = 100.0 * (math.expm1((n * math.log1p((i / n)))) / (i / n))
	elif t_1 <= math.inf:
		tmp = (t_0 + -100.0) / (i / n)
	else:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * (Float64(i / n) ^ n))
	t_1 = Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= -2e-27)
		tmp = Float64(Float64(n * Float64(t_0 - 100.0)) / i);
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(Float64(n * log1p(Float64(i / n)))) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(t_0 + -100.0) / Float64(i / n));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[Power[N[(i / n), $MachinePrecision], n], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-27], N[(N[(n * N[(t$95$0 - 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(t$95$0 + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n)) < -2.0000000000000001e-27

   1. Initial program 99.7%

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

      1. associate-*r/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-in 99.7%

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

      4. metadata-eval 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in i around inf 99.7%

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

   6. Taylor expanded in n around inf 100.0%

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

   if -2.0000000000000001e-27 < (/.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 18.6%

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

      1. sub-neg 18.6%

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

      2. metadata-eval 18.6%

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

   4. Applied egg-rr 18.6%

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

      1. metadata-eval 18.6%

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

      2. sub-neg 18.6%

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

      3. exp-to-pow 18.6%

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

      4. log1p-undefine 41.5%

         \[\leadsto 100 \cdot \frac{e^{\color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)} \cdot n} - 1}{\frac{i}{n}} \]

      5. *-commutative 41.5%

         \[\leadsto 100 \cdot \frac{e^{\color{blue}{n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)}} - 1}{\frac{i}{n}} \]

      6. expm1-undefine 99.7%

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

   6. Simplified 99.7%

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

   if -0.0 < (/.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 99.2%

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

      1. associate-*r/ 99.4%

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

      2. sub-neg 99.4%

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

      3. distribute-rgt-in 99.4%

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

      4. metadata-eval 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in i around inf 99.4%

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

   if +inf.0 < (/.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. Step-by-step derivation

      1. associate-/r/ 1.9%

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

      2. associate-*r* 1.9%

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

      3. *-commutative 1.9%

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

      4. associate-*r/ 1.9%

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

      5. sub-neg 1.9%

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

      6. distribute-lft-in 1.9%

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

      7. metadata-eval 1.9%

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

      8. metadata-eval 1.9%

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

      9. metadata-eval 1.9%

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

      10. fma-define 1.9%

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

      11. metadata-eval 1.9%

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

   3. Simplified 1.9%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 1.9%

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

      1. sub-neg 1.9%

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

      2. metadata-eval 1.9%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 1.9%

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

      4. distribute-lft-in 1.9%

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

      5. metadata-eval 1.9%

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

      6. sub-neg 1.9%

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

      7. expm1-define 87.5%

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

   7. Simplified 87.5%

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

      1. clear-num 87.6%

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

      2. un-div-inv 87.4%

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

      3. *-un-lft-identity 87.4%

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

      4. times-frac 87.5%

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

      5. metadata-eval 87.5%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 87.5%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 87.5%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 87.7%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 87.7%

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

   11. Simplified 87.7%

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

   12. Taylor expanded in i around 0 100.0%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + -0.5 \cdot i}} \]
   13. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto 100 \cdot \frac{n}{1 + \color{blue}{i \cdot -0.5}} \]

   14. Simplified 100.0%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot -0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq -2 \cdot 10^{-27}:\\ \;\;\;\;\frac{n \cdot \left(100 \cdot {\left(\frac{i}{n}\right)}^{n} - 100\right)}{i}\\ \mathbf{elif}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq \infty:\\ \;\;\;\;\frac{100 \cdot {\left(\frac{i}{n}\right)}^{n} + -100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\frac{i}{n}\right)}^{n}\\ t_1 := \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{t\_0 + -1}{\frac{i}{n}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{100 \cdot t\_0 + -100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (/ i n) n))
        (t_1 (/ (+ (pow (+ 1.0 (/ i n)) n) -1.0) (/ i n))))
   (if (<= t_1 -1e-89)
     (* 100.0 (/ (+ t_0 -1.0) (/ i n)))
     (if (<= t_1 0.0)
       (* 100.0 (/ n (/ i (expm1 i))))
       (if (<= t_1 INFINITY)
         (/ (+ (* 100.0 t_0) -100.0) (/ i n))
         (* 100.0 (/ n (+ 1.0 (* i -0.5)))))))))

C

double code(double i, double n) {
	double t_0 = pow((i / n), n);
	double t_1 = (pow((1.0 + (i / n)), n) + -1.0) / (i / n);
	double tmp;
	if (t_1 <= -1e-89) {
		tmp = 100.0 * ((t_0 + -1.0) / (i / n));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((100.0 * t_0) + -100.0) / (i / n);
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = Math.pow((i / n), n);
	double t_1 = (Math.pow((1.0 + (i / n)), n) + -1.0) / (i / n);
	double tmp;
	if (t_1 <= -1e-89) {
		tmp = 100.0 * ((t_0 + -1.0) / (i / n));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((100.0 * t_0) + -100.0) / (i / n);
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((i / n), n)
	t_1 = (math.pow((1.0 + (i / n)), n) + -1.0) / (i / n)
	tmp = 0
	if t_1 <= -1e-89:
		tmp = 100.0 * ((t_0 + -1.0) / (i / n))
	elif t_1 <= 0.0:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif t_1 <= math.inf:
		tmp = ((100.0 * t_0) + -100.0) / (i / n)
	else:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(i / n) ^ n
	t_1 = Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= -1e-89)
		tmp = Float64(100.0 * Float64(Float64(t_0 + -1.0) / Float64(i / n)));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(100.0 * t_0) + -100.0) / Float64(i / n));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[Power[N[(i / n), $MachinePrecision], n], $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-89], N[(100.0 * N[(N[(t$95$0 + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(100.0 * t$95$0), $MachinePrecision] + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 i n)) n) #s(literal 1 binary64)) (/.f64 i n)) < -1.00000000000000004e-89

   1. Initial program 91.8%

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

   3. Taylor expanded in i around inf 91.8%

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

   if -1.00000000000000004e-89 < (/.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 17.2%

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

      1. associate-/r/ 17.2%

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

      2. associate-*r* 17.2%

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

      3. *-commutative 17.2%

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

      4. associate-*r/ 17.2%

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

      5. sub-neg 17.2%

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

      6. distribute-lft-in 17.2%

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

      7. metadata-eval 17.2%

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

      8. metadata-eval 17.2%

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

      9. metadata-eval 17.2%

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

      10. fma-define 17.2%

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

      11. metadata-eval 17.2%

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

   3. Simplified 17.2%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 35.3%

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

      1. sub-neg 35.3%

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

      2. metadata-eval 35.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 35.3%

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

      4. distribute-lft-in 35.3%

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

      5. metadata-eval 35.3%

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

      6. sub-neg 35.3%

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

      7. expm1-define 81.2%

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

   7. Simplified 81.2%

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

      1. clear-num 81.3%

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

      2. un-div-inv 81.2%

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

      3. *-un-lft-identity 81.2%

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

      4. times-frac 81.2%

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

      5. metadata-eval 81.2%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 81.2%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 81.2%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 81.2%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 81.3%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 81.3%

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

   11. Simplified 81.3%

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

   if -0.0 < (/.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 99.2%

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

      1. associate-*r/ 99.4%

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

      2. sub-neg 99.4%

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

      3. distribute-rgt-in 99.4%

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

      4. metadata-eval 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in i around inf 99.4%

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

   if +inf.0 < (/.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. Step-by-step derivation

      1. associate-/r/ 1.9%

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

      2. associate-*r* 1.9%

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

      3. *-commutative 1.9%

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

      4. associate-*r/ 1.9%

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

      5. sub-neg 1.9%

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

      6. distribute-lft-in 1.9%

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

      7. metadata-eval 1.9%

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

      8. metadata-eval 1.9%

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

      9. metadata-eval 1.9%

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

      10. fma-define 1.9%

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

      11. metadata-eval 1.9%

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

   3. Simplified 1.9%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 1.9%

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

      1. sub-neg 1.9%

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

      2. metadata-eval 1.9%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 1.9%

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

      4. distribute-lft-in 1.9%

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

      5. metadata-eval 1.9%

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

      6. sub-neg 1.9%

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

      7. expm1-define 87.5%

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

   7. Simplified 87.5%

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

      1. clear-num 87.6%

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

      2. un-div-inv 87.4%

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

      3. *-un-lft-identity 87.4%

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

      4. times-frac 87.5%

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

      5. metadata-eval 87.5%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 87.5%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 87.5%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 87.7%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 87.7%

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

   11. Simplified 87.7%

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

   12. Taylor expanded in i around 0 100.0%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + -0.5 \cdot i}} \]
   13. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto 100 \cdot \frac{n}{1 + \color{blue}{i \cdot -0.5}} \]

   14. Simplified 100.0%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot -0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq -1 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ \mathbf{elif}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq 0:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq \infty:\\ \;\;\;\;\frac{100 \cdot {\left(\frac{i}{n}\right)}^{n} + -100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -5.5 \cdot 10^{-33} \lor \neg \left(n \leq 1.25\right):\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -5.5e-33) (not (<= n 1.25)))
   (* 100.0 (/ n (/ i (expm1 i))))
   (* 100.0 (/ n (+ 1.0 (* i (* i 0.08333333333333333)))))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -5.5e-33) || !(n <= 1.25)) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -5.5e-33) || !(n <= 1.25)) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -5.5e-33) or not (n <= 1.25):
		tmp = 100.0 * (n / (i / math.expm1(i)))
	else:
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -5.5e-33) || !(n <= 1.25))
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(i * 0.08333333333333333)))));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -5.5e-33], N[Not[LessEqual[n, 1.25]], $MachinePrecision]], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(i * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -5.5e-33 or 1.25 < n

   1. Initial program 23.7%

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

      1. associate-/r/ 24.2%

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

      2. associate-*r* 24.2%

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

      3. *-commutative 24.2%

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

      4. associate-*r/ 24.2%

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

      5. sub-neg 24.2%

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

      6. distribute-lft-in 24.2%

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

      7. metadata-eval 24.2%

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

      8. metadata-eval 24.2%

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

      9. metadata-eval 24.2%

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

      10. fma-define 24.2%

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

      11. metadata-eval 24.2%

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

   3. Simplified 24.2%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 39.7%

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

      1. sub-neg 39.7%

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

      2. metadata-eval 39.7%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 39.7%

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

      4. distribute-lft-in 39.7%

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

      5. metadata-eval 39.7%

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

      6. sub-neg 39.7%

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

      7. expm1-define 89.5%

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

   7. Simplified 89.5%

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

      1. clear-num 89.5%

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

      2. un-div-inv 89.4%

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

      3. *-un-lft-identity 89.4%

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

      4. times-frac 89.5%

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

      5. metadata-eval 89.5%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 89.5%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 89.5%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 89.5%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 89.6%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 89.6%

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

   11. Simplified 89.6%

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

   if -5.5e-33 < n < 1.25

   1. Initial program 26.3%

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

      1. associate-/r/ 26.4%

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

      2. associate-*r* 26.4%

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

      3. *-commutative 26.4%

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

      4. associate-*r/ 26.4%

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

      5. sub-neg 26.4%

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

      6. distribute-lft-in 26.4%

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

      7. metadata-eval 26.4%

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

      8. metadata-eval 26.4%

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

      9. metadata-eval 26.4%

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

      10. fma-define 26.4%

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

      11. metadata-eval 26.4%

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

   3. Simplified 26.4%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 14.4%

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

      1. sub-neg 14.4%

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

      2. metadata-eval 14.4%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 14.4%

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

      4. distribute-lft-in 14.4%

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

      5. metadata-eval 14.4%

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

      6. sub-neg 14.4%

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

      7. expm1-define 56.9%

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

   7. Simplified 56.9%

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

      1. clear-num 56.9%

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

      2. un-div-inv 56.8%

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

      3. *-un-lft-identity 56.8%

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

      4. times-frac 56.8%

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

      5. metadata-eval 56.8%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 56.8%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 56.8%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 56.8%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 56.9%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 56.9%

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

   11. Simplified 56.9%

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

   12. Taylor expanded in i around 0 69.5%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]

   13. Taylor expanded in i around inf 69.5%

       \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(0.08333333333333333 \cdot i\right)}} \]
   14. Step-by-step derivation

       1. *-commutative 69.5%

          \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(i \cdot 0.08333333333333333\right)}} \]

   15. Simplified 69.5%

       \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(i \cdot 0.08333333333333333\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -5.5 \cdot 10^{-33} \lor \neg \left(n \leq 1.25\right):\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 1.3 \cdot 10^{+116}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot \left(100 \cdot {\left(\frac{i}{n}\right)}^{n} - 100\right)}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i 1.3e+116)
   (* 100.0 (/ n (/ i (expm1 i))))
   (/ (* n (- (* 100.0 (pow (/ i n) n)) 100.0)) i)))

C

double code(double i, double n) {
	double tmp;
	if (i <= 1.3e+116) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else {
		tmp = (n * ((100.0 * pow((i / n), n)) - 100.0)) / i;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= 1.3e+116) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else {
		tmp = (n * ((100.0 * Math.pow((i / n), n)) - 100.0)) / i;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= 1.3e+116:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	else:
		tmp = (n * ((100.0 * math.pow((i / n), n)) - 100.0)) / i
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= 1.3e+116)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	else
		tmp = Float64(Float64(n * Float64(Float64(100.0 * (Float64(i / n) ^ n)) - 100.0)) / i);
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[i, 1.3e+116], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * N[(N[(100.0 * N[Power[N[(i / n), $MachinePrecision], n], $MachinePrecision]), $MachinePrecision] - 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 1.29999999999999993e116

   1. Initial program 18.2%

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

      1. associate-/r/ 18.6%

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

      2. associate-*r* 18.6%

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

      3. *-commutative 18.6%

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

      4. associate-*r/ 18.6%

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

      5. sub-neg 18.6%

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

      6. distribute-lft-in 18.6%

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

      7. metadata-eval 18.6%

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

      8. metadata-eval 18.6%

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

      9. metadata-eval 18.6%

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

      10. fma-define 18.6%

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

      11. metadata-eval 18.6%

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

   3. Simplified 18.6%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 27.6%

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

      1. sub-neg 27.6%

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

      2. metadata-eval 27.6%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 27.6%

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

      4. distribute-lft-in 27.6%

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

      5. metadata-eval 27.6%

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

      6. sub-neg 27.6%

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

      7. expm1-define 82.8%

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

   7. Simplified 82.8%

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

      1. clear-num 82.9%

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

      2. un-div-inv 82.8%

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

      3. *-un-lft-identity 82.8%

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

      4. times-frac 82.8%

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

      5. metadata-eval 82.8%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 82.8%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 82.8%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 82.8%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 83.0%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 83.0%

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

   11. Simplified 83.0%

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

   if 1.29999999999999993e116 < i

   1. Initial program 62.3%

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

      1. associate-*r/ 62.4%

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

      2. sub-neg 62.4%

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

      3. distribute-rgt-in 62.4%

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

      4. metadata-eval 62.4%

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

      5. metadata-eval 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in i around inf 78.3%

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

   6. Taylor expanded in n around inf 78.5%

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

Alternative 5: 78.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 1.32 \cdot 10^{+116}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i 1.32e+116)
   (* 100.0 (/ n (/ i (expm1 i))))
   (* 100.0 (/ (+ (pow (/ i n) n) -1.0) (/ i n)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= 1.32e+116) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else {
		tmp = 100.0 * ((pow((i / n), n) + -1.0) / (i / n));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= 1.32e+116) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else {
		tmp = 100.0 * ((Math.pow((i / n), n) + -1.0) / (i / n));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= 1.32e+116:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	else:
		tmp = 100.0 * ((math.pow((i / n), n) + -1.0) / (i / n))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= 1.32e+116)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	else
		tmp = Float64(100.0 * Float64(Float64((Float64(i / n) ^ n) + -1.0) / Float64(i / n)));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[i, 1.32e+116], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(N[(N[Power[N[(i / n), $MachinePrecision], n], $MachinePrecision] + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 1.32000000000000002e116

   1. Initial program 18.2%

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

      1. associate-/r/ 18.6%

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

      2. associate-*r* 18.6%

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

      3. *-commutative 18.6%

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

      4. associate-*r/ 18.6%

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

      5. sub-neg 18.6%

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

      6. distribute-lft-in 18.6%

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

      7. metadata-eval 18.6%

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

      8. metadata-eval 18.6%

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

      9. metadata-eval 18.6%

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

      10. fma-define 18.6%

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

      11. metadata-eval 18.6%

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

   3. Simplified 18.6%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 27.6%

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

      1. sub-neg 27.6%

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

      2. metadata-eval 27.6%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 27.6%

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

      4. distribute-lft-in 27.6%

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

      5. metadata-eval 27.6%

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

      6. sub-neg 27.6%

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

      7. expm1-define 82.8%

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

   7. Simplified 82.8%

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

      1. clear-num 82.9%

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

      2. un-div-inv 82.8%

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

      3. *-un-lft-identity 82.8%

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

      4. times-frac 82.8%

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

      5. metadata-eval 82.8%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 82.8%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 82.8%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 82.8%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 83.0%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 83.0%

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

   11. Simplified 83.0%

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

   if 1.32000000000000002e116 < i

   1. Initial program 62.3%

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

   3. Taylor expanded in i around inf 78.2%

      \[\leadsto 100 \cdot \frac{{\color{blue}{\left(\frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 1.32 \cdot 10^{+116}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{{\left(\frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 5 \cdot 10^{+198}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left({\left(\frac{i}{n}\right)}^{\left(n + -1\right)} - \frac{n}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i 5e+198)
   (* 100.0 (/ n (/ i (expm1 i))))
   (* 100.0 (- (pow (/ i n) (+ n -1.0)) (/ n i)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= 5e+198) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else {
		tmp = 100.0 * (pow((i / n), (n + -1.0)) - (n / i));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= 5e+198) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else {
		tmp = 100.0 * (Math.pow((i / n), (n + -1.0)) - (n / i));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= 5e+198:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	else:
		tmp = 100.0 * (math.pow((i / n), (n + -1.0)) - (n / i))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= 5e+198)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	else
		tmp = Float64(100.0 * Float64((Float64(i / n) ^ Float64(n + -1.0)) - Float64(n / i)));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[i, 5e+198], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(N[Power[N[(i / n), $MachinePrecision], N[(n + -1.0), $MachinePrecision]], $MachinePrecision] - N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 5.00000000000000049e198

   1. Initial program 20.5%

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

      1. associate-/r/ 20.8%

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

      2. associate-*r* 20.9%

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

      3. *-commutative 20.9%

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

      4. associate-*r/ 20.9%

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

      5. sub-neg 20.9%

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

      6. distribute-lft-in 20.9%

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

      7. metadata-eval 20.9%

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

      8. metadata-eval 20.9%

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

      9. metadata-eval 20.9%

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

      10. fma-define 20.9%

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

      11. metadata-eval 20.9%

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

   3. Simplified 20.9%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 29.3%

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

      1. sub-neg 29.3%

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

      2. metadata-eval 29.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 29.3%

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

      4. distribute-lft-in 29.3%

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

      5. metadata-eval 29.3%

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

      6. sub-neg 29.3%

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

      7. expm1-define 81.0%

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

   7. Simplified 81.0%

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

      1. clear-num 81.1%

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

      2. un-div-inv 80.9%

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

      3. *-un-lft-identity 80.9%

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

      4. times-frac 81.0%

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

      5. metadata-eval 81.0%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 81.0%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 81.0%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 81.0%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 81.1%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 81.1%

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

   11. Simplified 81.1%

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

   if 5.00000000000000049e198 < i

   1. Initial program 68.2%

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

   3. Taylor expanded in i around inf 72.6%

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

      1. div-sub 72.6%

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

      2. pow1 72.6%

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

      3. pow-div 90.8%

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

      4. clear-num 90.7%

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

   5. Applied egg-rr 90.7%

      \[\leadsto 100 \cdot \color{blue}{\left({\left(\frac{i}{n}\right)}^{\left(n - 1\right)} - \frac{n}{i}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 5 \cdot 10^{+198}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left({\left(\frac{i}{n}\right)}^{\left(n + -1\right)} - \frac{n}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -4.8 \cdot 10^{+181}:\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + i \cdot 4.166666666666667\right)\right)\right)\\ \mathbf{elif}\;n \leq 1.3:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(n \cdot 100\right) \cdot \left(1 + i \cdot \left(0.5 + i \cdot \left(0.16666666666666666 + i \cdot 0.041666666666666664\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -4.8e+181)
   (*
    n
    (+
     100.0
     (* i (+ 50.0 (* i (+ 16.666666666666668 (* i 4.166666666666667)))))))
   (if (<= n 1.3)
     (* 100.0 (/ n (+ 1.0 (* i (- (* i 0.08333333333333333) 0.5)))))
     (*
      (* n 100.0)
      (+
       1.0
       (*
        i
        (+ 0.5 (* i (+ 0.16666666666666666 (* i 0.041666666666666664))))))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -4.8e+181) {
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))));
	} else if (n <= 1.3) {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	} else {
		tmp = (n * 100.0) * (1.0 + (i * (0.5 + (i * (0.16666666666666666 + (i * 0.041666666666666664))))));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-4.8d+181)) then
        tmp = n * (100.0d0 + (i * (50.0d0 + (i * (16.666666666666668d0 + (i * 4.166666666666667d0))))))
    else if (n <= 1.3d0) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * ((i * 0.08333333333333333d0) - 0.5d0))))
    else
        tmp = (n * 100.0d0) * (1.0d0 + (i * (0.5d0 + (i * (0.16666666666666666d0 + (i * 0.041666666666666664d0))))))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -4.8e+181) {
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))));
	} else if (n <= 1.3) {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	} else {
		tmp = (n * 100.0) * (1.0 + (i * (0.5 + (i * (0.16666666666666666 + (i * 0.041666666666666664))))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -4.8e+181:
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))))
	elif n <= 1.3:
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))))
	else:
		tmp = (n * 100.0) * (1.0 + (i * (0.5 + (i * (0.16666666666666666 + (i * 0.041666666666666664))))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -4.8e+181)
		tmp = Float64(n * Float64(100.0 + Float64(i * Float64(50.0 + Float64(i * Float64(16.666666666666668 + Float64(i * 4.166666666666667)))))));
	elseif (n <= 1.3)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(Float64(i * 0.08333333333333333) - 0.5)))));
	else
		tmp = Float64(Float64(n * 100.0) * Float64(1.0 + Float64(i * Float64(0.5 + Float64(i * Float64(0.16666666666666666 + Float64(i * 0.041666666666666664)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -4.8e+181)
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))));
	elseif (n <= 1.3)
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	else
		tmp = (n * 100.0) * (1.0 + (i * (0.5 + (i * (0.16666666666666666 + (i * 0.041666666666666664))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -4.8e+181], N[(n * N[(100.0 + N[(i * N[(50.0 + N[(i * N[(16.666666666666668 + N[(i * 4.166666666666667), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.3], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(N[(i * 0.08333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * 100.0), $MachinePrecision] * N[(1.0 + N[(i * N[(0.5 + N[(i * N[(0.16666666666666666 + N[(i * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if n < -4.80000000000000004e181

   1. Initial program 7.6%

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

      1. associate-/r/ 8.3%

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

      2. associate-*r* 8.3%

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

      3. *-commutative 8.3%

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

      4. associate-*r/ 8.3%

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

      5. sub-neg 8.3%

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

      6. distribute-lft-in 8.3%

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

      7. metadata-eval 8.3%

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

      8. metadata-eval 8.3%

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

      9. metadata-eval 8.3%

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

      10. fma-define 8.3%

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

      11. metadata-eval 8.3%

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

   3. Simplified 8.3%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 45.3%

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

      1. sub-neg 45.3%

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

      2. metadata-eval 45.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 45.3%

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

      4. distribute-lft-in 45.3%

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

      5. metadata-eval 45.3%

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

      6. sub-neg 45.3%

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

      7. expm1-define 95.4%

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

   7. Simplified 95.4%

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

   8. Taylor expanded in i around 0 78.0%

      \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + 4.166666666666667 \cdot i\right)\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto n \cdot \left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + \color{blue}{i \cdot 4.166666666666667}\right)\right)\right) \]

   10. Simplified 78.0%

       \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + i \cdot 4.166666666666667\right)\right)\right)} \]

   if -4.80000000000000004e181 < n < 1.30000000000000004

   1. Initial program 28.6%

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

      1. associate-/r/ 28.8%

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

      2. associate-*r* 28.8%

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

      3. *-commutative 28.8%

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

      4. associate-*r/ 28.9%

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

      5. sub-neg 28.9%

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

      6. distribute-lft-in 28.8%

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

      7. metadata-eval 28.8%

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

      8. metadata-eval 28.8%

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

      9. metadata-eval 28.8%

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

      10. fma-define 28.9%

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

      11. metadata-eval 28.9%

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

   3. Simplified 28.9%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 19.6%

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

      1. sub-neg 19.6%

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

      2. metadata-eval 19.6%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 19.6%

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

      4. distribute-lft-in 19.6%

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

      5. metadata-eval 19.6%

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

      6. sub-neg 19.6%

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

      7. expm1-define 66.3%

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

   7. Simplified 66.3%

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

      1. clear-num 66.4%

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

      2. un-div-inv 66.3%

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

      3. *-un-lft-identity 66.3%

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

      4. times-frac 66.3%

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

      5. metadata-eval 66.3%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 66.3%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 66.3%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 66.3%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 66.4%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 66.4%

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

   11. Simplified 66.4%

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

   12. Taylor expanded in i around 0 64.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]

   if 1.30000000000000004 < n

   1. Initial program 27.2%

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

      1. associate-/r/ 27.7%

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

      2. associate-*r* 27.7%

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

      3. *-commutative 27.7%

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

      4. associate-*r/ 27.7%

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

      5. sub-neg 27.7%

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

      6. distribute-lft-in 27.7%

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

      7. metadata-eval 27.7%

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

      8. metadata-eval 27.7%

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

      9. metadata-eval 27.7%

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

      10. fma-define 27.7%

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

      11. metadata-eval 27.7%

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

   3. Simplified 27.7%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. metadata-eval 47.1%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 47.1%

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

      4. distribute-lft-in 47.1%

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

      5. metadata-eval 47.1%

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

      6. sub-neg 47.1%

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

      7. expm1-define 93.7%

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

   7. Simplified 93.7%

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

      1. clear-num 93.7%

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

      2. un-div-inv 93.6%

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

      3. *-un-lft-identity 93.6%

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

      4. times-frac 93.7%

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

      5. metadata-eval 93.7%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 93.7%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 93.7%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 93.8%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 93.8%

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

   11. Simplified 93.8%

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

   12. Taylor expanded in n around 0 47.1%

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

       1. expm1-define 93.8%

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

       2. associate-*r/ 93.8%

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

       3. associate-*l* 93.7%

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

   14. Simplified 93.7%

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

   15. Taylor expanded in i around 0 80.5%

       \[\leadsto \left(100 \cdot n\right) \cdot \color{blue}{\left(1 + i \cdot \left(0.5 + i \cdot \left(0.16666666666666666 + 0.041666666666666664 \cdot i\right)\right)\right)} \]
   16. Step-by-step derivation

       1. *-commutative 80.5%

          \[\leadsto \left(100 \cdot n\right) \cdot \left(1 + i \cdot \left(0.5 + i \cdot \left(0.16666666666666666 + \color{blue}{i \cdot 0.041666666666666664}\right)\right)\right) \]

   17. Simplified 80.5%

       \[\leadsto \left(100 \cdot n\right) \cdot \color{blue}{\left(1 + i \cdot \left(0.5 + i \cdot \left(0.16666666666666666 + i \cdot 0.041666666666666664\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -4.8 \cdot 10^{+181}:\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + i \cdot 4.166666666666667\right)\right)\right)\\ \mathbf{elif}\;n \leq 1.3:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(n \cdot 100\right) \cdot \left(1 + i \cdot \left(0.5 + i \cdot \left(0.16666666666666666 + i \cdot 0.041666666666666664\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.4% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -7.2 \cdot 10^{+180} \lor \neg \left(n \leq 1.05\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + i \cdot 4.166666666666667\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -7.2e+180) (not (<= n 1.05)))
   (*
    n
    (+
     100.0
     (* i (+ 50.0 (* i (+ 16.666666666666668 (* i 4.166666666666667)))))))
   (* 100.0 (/ n (+ 1.0 (* i (- (* i 0.08333333333333333) 0.5)))))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -7.2e+180) || !(n <= 1.05)) {
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-7.2d+180)) .or. (.not. (n <= 1.05d0))) then
        tmp = n * (100.0d0 + (i * (50.0d0 + (i * (16.666666666666668d0 + (i * 4.166666666666667d0))))))
    else
        tmp = 100.0d0 * (n / (1.0d0 + (i * ((i * 0.08333333333333333d0) - 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -7.2e+180) || !(n <= 1.05)) {
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -7.2e+180) or not (n <= 1.05):
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))))
	else:
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -7.2e+180) || !(n <= 1.05))
		tmp = Float64(n * Float64(100.0 + Float64(i * Float64(50.0 + Float64(i * Float64(16.666666666666668 + Float64(i * 4.166666666666667)))))));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(Float64(i * 0.08333333333333333) - 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -7.2e+180) || ~((n <= 1.05)))
		tmp = n * (100.0 + (i * (50.0 + (i * (16.666666666666668 + (i * 4.166666666666667))))));
	else
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -7.2e+180], N[Not[LessEqual[n, 1.05]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * N[(50.0 + N[(i * N[(16.666666666666668 + N[(i * 4.166666666666667), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(N[(i * 0.08333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -7.2000000000000004e180 or 1.05000000000000004 < 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. associate-/r/ 19.8%

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

      2. associate-*r* 19.8%

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

      3. *-commutative 19.8%

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

      4. associate-*r/ 19.8%

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

      5. sub-neg 19.8%

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

      6. distribute-lft-in 19.8%

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

      7. metadata-eval 19.8%

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

      8. metadata-eval 19.8%

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

      9. metadata-eval 19.8%

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

      10. fma-define 19.8%

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

      11. metadata-eval 19.8%

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

   3. Simplified 19.8%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 46.4%

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

      1. sub-neg 46.4%

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

      2. metadata-eval 46.4%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 46.4%

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

      4. distribute-lft-in 46.3%

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

      5. metadata-eval 46.3%

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

      6. sub-neg 46.3%

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

      7. expm1-define 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in i around 0 79.5%

      \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + 4.166666666666667 \cdot i\right)\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 79.5%

         \[\leadsto n \cdot \left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + \color{blue}{i \cdot 4.166666666666667}\right)\right)\right) \]

   10. Simplified 79.5%

       \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + i \cdot 4.166666666666667\right)\right)\right)} \]

   if -7.2000000000000004e180 < n < 1.05000000000000004

   1. Initial program 28.6%

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

      1. associate-/r/ 28.8%

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

      2. associate-*r* 28.8%

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

      3. *-commutative 28.8%

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

      4. associate-*r/ 28.9%

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

      5. sub-neg 28.9%

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

      6. distribute-lft-in 28.8%

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

      7. metadata-eval 28.8%

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

      8. metadata-eval 28.8%

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

      9. metadata-eval 28.8%

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

      10. fma-define 28.9%

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

      11. metadata-eval 28.9%

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

   3. Simplified 28.9%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 19.6%

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

      1. sub-neg 19.6%

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

      2. metadata-eval 19.6%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 19.6%

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

      4. distribute-lft-in 19.6%

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

      5. metadata-eval 19.6%

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

      6. sub-neg 19.6%

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

      7. expm1-define 66.3%

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

   7. Simplified 66.3%

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

      1. clear-num 66.4%

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

      2. un-div-inv 66.3%

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

      3. *-un-lft-identity 66.3%

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

      4. times-frac 66.3%

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

      5. metadata-eval 66.3%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 66.3%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 66.3%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 66.3%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 66.4%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 66.4%

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

   11. Simplified 66.4%

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

   12. Taylor expanded in i around 0 64.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -7.2 \cdot 10^{+180} \lor \neg \left(n \leq 1.05\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot \left(16.666666666666668 + i \cdot 4.166666666666667\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -5.2 \cdot 10^{+153} \lor \neg \left(n \leq 1\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -5.2e+153) (not (<= n 1.0)))
   (* n (+ 100.0 (* i (+ 50.0 (* i 16.666666666666668)))))
   (* 100.0 (/ n (+ 1.0 (* i (- (* i 0.08333333333333333) 0.5)))))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -5.2e+153) || !(n <= 1.0)) {
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-5.2d+153)) .or. (.not. (n <= 1.0d0))) then
        tmp = n * (100.0d0 + (i * (50.0d0 + (i * 16.666666666666668d0))))
    else
        tmp = 100.0d0 * (n / (1.0d0 + (i * ((i * 0.08333333333333333d0) - 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -5.2e+153) || !(n <= 1.0)) {
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -5.2e+153) or not (n <= 1.0):
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))))
	else:
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -5.2e+153) || !(n <= 1.0))
		tmp = Float64(n * Float64(100.0 + Float64(i * Float64(50.0 + Float64(i * 16.666666666666668)))));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(Float64(i * 0.08333333333333333) - 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -5.2e+153) || ~((n <= 1.0)))
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))));
	else
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -5.2e+153], N[Not[LessEqual[n, 1.0]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * N[(50.0 + N[(i * 16.666666666666668), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(N[(i * 0.08333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -5.1999999999999998e153 or 1 < n

   1. Initial program 18.8%

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

      1. associate-/r/ 19.4%

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

      2. associate-*r* 19.4%

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

      3. *-commutative 19.4%

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

      4. associate-*r/ 19.4%

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

      5. sub-neg 19.4%

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

      6. distribute-lft-in 19.4%

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

      7. metadata-eval 19.4%

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

      8. metadata-eval 19.4%

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

      9. metadata-eval 19.4%

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

      10. fma-define 19.4%

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

      11. metadata-eval 19.4%

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

   3. Simplified 19.4%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 46.7%

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

      1. sub-neg 46.7%

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

      2. metadata-eval 46.7%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 46.7%

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

      4. distribute-lft-in 46.7%

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

      5. metadata-eval 46.7%

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

      6. sub-neg 46.7%

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

      7. expm1-define 94.8%

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

   7. Simplified 94.8%

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

   8. Taylor expanded in i around 0 74.1%

      \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + 16.666666666666668 \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto n \cdot \left(100 + i \cdot \left(50 + \color{blue}{i \cdot 16.666666666666668}\right)\right) \]

   10. Simplified 74.1%

       \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)} \]

   if -5.1999999999999998e153 < n < 1

   1. Initial program 29.5%

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

      1. associate-/r/ 29.6%

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

      2. associate-*r* 29.7%

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

      3. *-commutative 29.7%

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

      4. associate-*r/ 29.7%

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

      5. sub-neg 29.7%

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

      6. distribute-lft-in 29.7%

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

      7. metadata-eval 29.7%

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

      8. metadata-eval 29.7%

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

      9. metadata-eval 29.7%

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

      10. fma-define 29.7%

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

      11. metadata-eval 29.7%

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

   3. Simplified 29.7%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 17.8%

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

      1. sub-neg 17.8%

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

      2. metadata-eval 17.8%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 17.8%

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

      4. distribute-lft-in 17.8%

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

      5. metadata-eval 17.8%

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

      6. sub-neg 17.8%

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

      7. expm1-define 64.4%

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

   7. Simplified 64.4%

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

      1. clear-num 64.4%

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

      2. un-div-inv 64.3%

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

      3. *-un-lft-identity 64.3%

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

      4. times-frac 64.4%

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

      5. metadata-eval 64.4%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 64.4%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 64.4%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 64.4%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 64.5%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 64.5%

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

   11. Simplified 64.5%

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

   12. Taylor expanded in i around 0 65.6%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -5.2 \cdot 10^{+153} \lor \neg \left(n \leq 1\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 50 + i \cdot 16.666666666666668\\ \mathbf{if}\;n \leq -4.1 \cdot 10^{+154}:\\ \;\;\;\;n \cdot \left(100 + i \cdot t\_0\right)\\ \mathbf{elif}\;n \leq 1:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + i \cdot \left(n \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (+ 50.0 (* i 16.666666666666668))))
   (if (<= n -4.1e+154)
     (* n (+ 100.0 (* i t_0)))
     (if (<= n 1.0)
       (* 100.0 (/ n (+ 1.0 (* i (- (* i 0.08333333333333333) 0.5)))))
       (+ (* n 100.0) (* i (* n t_0)))))))

C

double code(double i, double n) {
	double t_0 = 50.0 + (i * 16.666666666666668);
	double tmp;
	if (n <= -4.1e+154) {
		tmp = n * (100.0 + (i * t_0));
	} else if (n <= 1.0) {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	} else {
		tmp = (n * 100.0) + (i * (n * t_0));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 50.0d0 + (i * 16.666666666666668d0)
    if (n <= (-4.1d+154)) then
        tmp = n * (100.0d0 + (i * t_0))
    else if (n <= 1.0d0) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * ((i * 0.08333333333333333d0) - 0.5d0))))
    else
        tmp = (n * 100.0d0) + (i * (n * t_0))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double t_0 = 50.0 + (i * 16.666666666666668);
	double tmp;
	if (n <= -4.1e+154) {
		tmp = n * (100.0 + (i * t_0));
	} else if (n <= 1.0) {
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	} else {
		tmp = (n * 100.0) + (i * (n * t_0));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 50.0 + (i * 16.666666666666668)
	tmp = 0
	if n <= -4.1e+154:
		tmp = n * (100.0 + (i * t_0))
	elif n <= 1.0:
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))))
	else:
		tmp = (n * 100.0) + (i * (n * t_0))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(50.0 + Float64(i * 16.666666666666668))
	tmp = 0.0
	if (n <= -4.1e+154)
		tmp = Float64(n * Float64(100.0 + Float64(i * t_0)));
	elseif (n <= 1.0)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(Float64(i * 0.08333333333333333) - 0.5)))));
	else
		tmp = Float64(Float64(n * 100.0) + Float64(i * Float64(n * t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = 50.0 + (i * 16.666666666666668);
	tmp = 0.0;
	if (n <= -4.1e+154)
		tmp = n * (100.0 + (i * t_0));
	elseif (n <= 1.0)
		tmp = 100.0 * (n / (1.0 + (i * ((i * 0.08333333333333333) - 0.5))));
	else
		tmp = (n * 100.0) + (i * (n * t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(50.0 + N[(i * 16.666666666666668), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -4.1e+154], N[(n * N[(100.0 + N[(i * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.0], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(N[(i * 0.08333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * 100.0), $MachinePrecision] + N[(i * N[(n * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if n < -4.1e154

   1. Initial program 8.5%

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

      1. associate-/r/ 9.2%

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

      2. associate-*r* 9.2%

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

      3. *-commutative 9.2%

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

      4. associate-*r/ 9.2%

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

      5. sub-neg 9.2%

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

      6. distribute-lft-in 9.2%

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

      7. metadata-eval 9.2%

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

      8. metadata-eval 9.2%

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

      9. metadata-eval 9.2%

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

      10. fma-define 9.2%

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

      11. metadata-eval 9.2%

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

   3. Simplified 9.2%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 46.2%

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

      1. sub-neg 46.2%

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

      2. metadata-eval 46.2%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 46.2%

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

      4. distribute-lft-in 46.2%

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

      5. metadata-eval 46.2%

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

      6. sub-neg 46.2%

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

      7. expm1-define 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in i around 0 73.1%

      \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + 16.666666666666668 \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.1%

         \[\leadsto n \cdot \left(100 + i \cdot \left(50 + \color{blue}{i \cdot 16.666666666666668}\right)\right) \]

   10. Simplified 73.1%

       \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)} \]

   if -4.1e154 < n < 1

   1. Initial program 29.5%

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

      1. associate-/r/ 29.6%

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

      2. associate-*r* 29.7%

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

      3. *-commutative 29.7%

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

      4. associate-*r/ 29.7%

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

      5. sub-neg 29.7%

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

      6. distribute-lft-in 29.7%

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

      7. metadata-eval 29.7%

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

      8. metadata-eval 29.7%

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

      9. metadata-eval 29.7%

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

      10. fma-define 29.7%

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

      11. metadata-eval 29.7%

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

   3. Simplified 29.7%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 17.8%

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

      1. sub-neg 17.8%

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

      2. metadata-eval 17.8%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 17.8%

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

      4. distribute-lft-in 17.8%

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

      5. metadata-eval 17.8%

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

      6. sub-neg 17.8%

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

      7. expm1-define 64.4%

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

   7. Simplified 64.4%

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

      1. clear-num 64.4%

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

      2. un-div-inv 64.3%

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

      3. *-un-lft-identity 64.3%

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

      4. times-frac 64.4%

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

      5. metadata-eval 64.4%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 64.4%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 64.4%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 64.4%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 64.5%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 64.5%

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

   11. Simplified 64.5%

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

   12. Taylor expanded in i around 0 65.6%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]

   if 1 < n

   1. Initial program 27.2%

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

      1. associate-/r/ 27.7%

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

      2. associate-*r* 27.7%

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

      3. *-commutative 27.7%

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

      4. associate-*r/ 27.7%

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

      5. sub-neg 27.7%

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

      6. distribute-lft-in 27.7%

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

      7. metadata-eval 27.7%

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

      8. metadata-eval 27.7%

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

      9. metadata-eval 27.7%

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

      10. fma-define 27.7%

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

      11. metadata-eval 27.7%

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

   3. Simplified 27.7%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. metadata-eval 47.1%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 47.1%

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

      4. distribute-lft-in 47.1%

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

      5. metadata-eval 47.1%

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

      6. sub-neg 47.1%

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

      7. expm1-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in i around 0 80.5%

      \[\leadsto \color{blue}{100 \cdot n + i \cdot \left(50 \cdot n + i \cdot \left(4.166666666666667 \cdot \left(i \cdot n\right) + 16.666666666666668 \cdot n\right)\right)} \]

   9. Taylor expanded in i around 0 74.9%

      \[\leadsto 100 \cdot n + \color{blue}{i \cdot \left(16.666666666666668 \cdot \left(i \cdot n\right) + 50 \cdot n\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 74.9%

          \[\leadsto 100 \cdot n + i \cdot \left(\color{blue}{\left(16.666666666666668 \cdot i\right) \cdot n} + 50 \cdot n\right) \]

       2. distribute-rgt-out 74.9%

          \[\leadsto 100 \cdot n + i \cdot \color{blue}{\left(n \cdot \left(16.666666666666668 \cdot i + 50\right)\right)} \]

       3. *-commutative 74.9%

          \[\leadsto 100 \cdot n + i \cdot \left(n \cdot \left(\color{blue}{i \cdot 16.666666666666668} + 50\right)\right) \]

   11. Simplified 74.9%

       \[\leadsto 100 \cdot n + \color{blue}{i \cdot \left(n \cdot \left(i \cdot 16.666666666666668 + 50\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -4.1 \cdot 10^{+154}:\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \mathbf{elif}\;n \leq 1:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333 - 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + i \cdot \left(n \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.0% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -8.5 \cdot 10^{+126} \lor \neg \left(n \leq 1.1\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -8.5e+126) (not (<= n 1.1)))
   (* n (+ 100.0 (* i (+ 50.0 (* i 16.666666666666668)))))
   (* 100.0 (/ n (+ 1.0 (* i (* i 0.08333333333333333)))))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -8.5e+126) || !(n <= 1.1)) {
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-8.5d+126)) .or. (.not. (n <= 1.1d0))) then
        tmp = n * (100.0d0 + (i * (50.0d0 + (i * 16.666666666666668d0))))
    else
        tmp = 100.0d0 * (n / (1.0d0 + (i * (i * 0.08333333333333333d0))))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -8.5e+126) || !(n <= 1.1)) {
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -8.5e+126) or not (n <= 1.1):
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))))
	else:
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -8.5e+126) || !(n <= 1.1))
		tmp = Float64(n * Float64(100.0 + Float64(i * Float64(50.0 + Float64(i * 16.666666666666668)))));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(i * 0.08333333333333333)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -8.5e+126) || ~((n <= 1.1)))
		tmp = n * (100.0 + (i * (50.0 + (i * 16.666666666666668))));
	else
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -8.5e+126], N[Not[LessEqual[n, 1.1]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * N[(50.0 + N[(i * 16.666666666666668), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(i * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -8.49999999999999944e126 or 1.1000000000000001 < n

   1. Initial program 20.4%

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

      1. associate-/r/ 21.0%

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

      2. associate-*r* 21.0%

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

      3. *-commutative 21.0%

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

      4. associate-*r/ 21.0%

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

      5. sub-neg 21.0%

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

      6. distribute-lft-in 21.0%

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

      7. metadata-eval 21.0%

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

      8. metadata-eval 21.0%

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

      9. metadata-eval 21.0%

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

      10. fma-define 21.0%

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

      11. metadata-eval 21.0%

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

   3. Simplified 21.0%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 47.3%

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

      1. sub-neg 47.3%

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

      2. metadata-eval 47.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 47.3%

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

      4. distribute-lft-in 47.3%

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

      5. metadata-eval 47.3%

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

      6. sub-neg 47.3%

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

      7. expm1-define 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in i around 0 71.7%

      \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + 16.666666666666668 \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.7%

         \[\leadsto n \cdot \left(100 + i \cdot \left(50 + \color{blue}{i \cdot 16.666666666666668}\right)\right) \]

   10. Simplified 71.7%

       \[\leadsto n \cdot \color{blue}{\left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)} \]

   if -8.49999999999999944e126 < n < 1.1000000000000001

   1. Initial program 28.8%

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

      1. associate-/r/ 28.9%

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

      2. associate-*r* 29.0%

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

      3. *-commutative 29.0%

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

      4. associate-*r/ 29.0%

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

      5. sub-neg 29.0%

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

      6. distribute-lft-in 29.0%

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

      7. metadata-eval 29.0%

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

      8. metadata-eval 29.0%

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

      9. metadata-eval 29.0%

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

      10. fma-define 29.0%

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

      11. metadata-eval 29.0%

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

   3. Simplified 29.0%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 14.7%

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

      1. sub-neg 14.7%

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

      2. metadata-eval 14.7%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 14.7%

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

      4. distribute-lft-in 14.7%

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

      5. metadata-eval 14.7%

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

      6. sub-neg 14.7%

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

      7. expm1-define 62.1%

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

   7. Simplified 62.1%

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

      1. clear-num 62.1%

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

      2. un-div-inv 62.0%

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

      3. *-un-lft-identity 62.0%

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

      4. times-frac 62.1%

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

      5. metadata-eval 62.1%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 62.1%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 62.1%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 62.1%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 62.2%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 62.2%

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

   11. Simplified 62.2%

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

   12. Taylor expanded in i around 0 67.2%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]

   13. Taylor expanded in i around inf 67.2%

       \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(0.08333333333333333 \cdot i\right)}} \]
   14. Step-by-step derivation

       1. *-commutative 67.2%

          \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(i \cdot 0.08333333333333333\right)}} \]

   15. Simplified 67.2%

       \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(i \cdot 0.08333333333333333\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -8.5 \cdot 10^{+126} \lor \neg \left(n \leq 1.1\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.7% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -6.2 \cdot 10^{+180}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{elif}\;n \leq 0.7:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + 50 \cdot \left(i \cdot n\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -6.2e+180)
   (* n (+ 100.0 (* i 50.0)))
   (if (<= n 0.7)
     (* 100.0 (/ n (+ 1.0 (* i (* i 0.08333333333333333)))))
     (+ (* n 100.0) (* 50.0 (* i n))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -6.2e+180) {
		tmp = n * (100.0 + (i * 50.0));
	} else if (n <= 0.7) {
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	} else {
		tmp = (n * 100.0) + (50.0 * (i * n));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-6.2d+180)) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else if (n <= 0.7d0) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (i * 0.08333333333333333d0))))
    else
        tmp = (n * 100.0d0) + (50.0d0 * (i * n))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -6.2e+180) {
		tmp = n * (100.0 + (i * 50.0));
	} else if (n <= 0.7) {
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	} else {
		tmp = (n * 100.0) + (50.0 * (i * n));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -6.2e+180:
		tmp = n * (100.0 + (i * 50.0))
	elif n <= 0.7:
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))))
	else:
		tmp = (n * 100.0) + (50.0 * (i * n))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -6.2e+180)
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	elseif (n <= 0.7)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(i * 0.08333333333333333)))));
	else
		tmp = Float64(Float64(n * 100.0) + Float64(50.0 * Float64(i * n)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -6.2e+180)
		tmp = n * (100.0 + (i * 50.0));
	elseif (n <= 0.7)
		tmp = 100.0 * (n / (1.0 + (i * (i * 0.08333333333333333))));
	else
		tmp = (n * 100.0) + (50.0 * (i * n));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -6.2e+180], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 0.7], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(i * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * 100.0), $MachinePrecision] + N[(50.0 * N[(i * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if n < -6.19999999999999997e180

   1. Initial program 7.6%

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

      1. associate-/r/ 8.3%

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

      2. associate-*r* 8.3%

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

      3. *-commutative 8.3%

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

      4. associate-*r/ 8.3%

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

      5. sub-neg 8.3%

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

      6. distribute-lft-in 8.3%

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

      7. metadata-eval 8.3%

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

      8. metadata-eval 8.3%

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

      9. metadata-eval 8.3%

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

      10. fma-define 8.3%

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

      11. metadata-eval 8.3%

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

   3. Simplified 8.3%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 45.3%

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

      1. sub-neg 45.3%

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

      2. metadata-eval 45.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 45.3%

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

      4. distribute-lft-in 45.3%

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

      5. metadata-eval 45.3%

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

      6. sub-neg 45.3%

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

      7. expm1-define 95.4%

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

   7. Simplified 95.4%

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

   8. Taylor expanded in i around 0 69.8%

      \[\leadsto \color{blue}{50 \cdot \left(i \cdot n\right) + 100 \cdot n} \]
   9. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto \color{blue}{100 \cdot n + 50 \cdot \left(i \cdot n\right)} \]

      2. associate-*r* 69.8%

         \[\leadsto 100 \cdot n + \color{blue}{\left(50 \cdot i\right) \cdot n} \]

      3. distribute-rgt-in 69.8%

         \[\leadsto \color{blue}{n \cdot \left(100 + 50 \cdot i\right)} \]

      4. *-commutative 69.8%

         \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   if -6.19999999999999997e180 < n < 0.69999999999999996

   1. Initial program 28.6%

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

      1. associate-/r/ 28.8%

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

      2. associate-*r* 28.8%

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

      3. *-commutative 28.8%

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

      4. associate-*r/ 28.9%

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

      5. sub-neg 28.9%

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

      6. distribute-lft-in 28.8%

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

      7. metadata-eval 28.8%

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

      8. metadata-eval 28.8%

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

      9. metadata-eval 28.8%

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

      10. fma-define 28.9%

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

      11. metadata-eval 28.9%

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

   3. Simplified 28.9%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 19.6%

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

      1. sub-neg 19.6%

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

      2. metadata-eval 19.6%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 19.6%

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

      4. distribute-lft-in 19.6%

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

      5. metadata-eval 19.6%

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

      6. sub-neg 19.6%

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

      7. expm1-define 66.3%

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

   7. Simplified 66.3%

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

      1. clear-num 66.4%

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

      2. un-div-inv 66.3%

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

      3. *-un-lft-identity 66.3%

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

      4. times-frac 66.3%

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

      5. metadata-eval 66.3%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 66.3%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 66.3%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 66.3%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 66.4%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 66.4%

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

   11. Simplified 66.4%

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

   12. Taylor expanded in i around 0 64.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(0.08333333333333333 \cdot i - 0.5\right)}} \]

   13. Taylor expanded in i around inf 64.5%

       \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(0.08333333333333333 \cdot i\right)}} \]
   14. Step-by-step derivation

       1. *-commutative 64.5%

          \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(i \cdot 0.08333333333333333\right)}} \]

   15. Simplified 64.5%

       \[\leadsto 100 \cdot \frac{n}{1 + i \cdot \color{blue}{\left(i \cdot 0.08333333333333333\right)}} \]

   if 0.69999999999999996 < n

   1. Initial program 27.2%

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

      1. associate-/r/ 27.7%

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

      2. associate-*r* 27.7%

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

      3. *-commutative 27.7%

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

      4. associate-*r/ 27.7%

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

      5. sub-neg 27.7%

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

      6. distribute-lft-in 27.7%

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

      7. metadata-eval 27.7%

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

      8. metadata-eval 27.7%

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

      9. metadata-eval 27.7%

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

      10. fma-define 27.7%

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

      11. metadata-eval 27.7%

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

   3. Simplified 27.7%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. metadata-eval 47.1%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 47.1%

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

      4. distribute-lft-in 47.1%

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

      5. metadata-eval 47.1%

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

      6. sub-neg 47.1%

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

      7. expm1-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in i around 0 73.2%

      \[\leadsto \color{blue}{50 \cdot \left(i \cdot n\right) + 100 \cdot n} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -6.2 \cdot 10^{+180}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{elif}\;n \leq 0.7:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + 50 \cdot \left(i \cdot n\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.1% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -6.5 \cdot 10^{+180} \lor \neg \left(n \leq 6.2 \cdot 10^{-62}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -6.5e+180) (not (<= n 6.2e-62)))
   (* n (+ 100.0 (* i 50.0)))
   (* 100.0 (/ n (+ 1.0 (* i -0.5))))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -6.5e+180) || !(n <= 6.2e-62)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-6.5d+180)) .or. (.not. (n <= 6.2d-62))) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -6.5e+180) || !(n <= 6.2e-62)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -6.5e+180) or not (n <= 6.2e-62):
		tmp = n * (100.0 + (i * 50.0))
	else:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -6.5e+180) || !(n <= 6.2e-62))
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -6.5e+180) || ~((n <= 6.2e-62)))
		tmp = n * (100.0 + (i * 50.0));
	else
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -6.5e+180], N[Not[LessEqual[n, 6.2e-62]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -6.5e180 or 6.1999999999999999e-62 < n

   1. Initial program 18.5%

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

      1. associate-/r/ 19.0%

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

      2. associate-*r* 19.0%

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

      3. *-commutative 19.0%

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

      4. associate-*r/ 19.0%

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

      5. sub-neg 19.0%

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

      6. distribute-lft-in 19.0%

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

      7. metadata-eval 19.0%

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

      8. metadata-eval 19.0%

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

      9. metadata-eval 19.0%

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

      10. fma-define 19.0%

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

      11. metadata-eval 19.0%

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

   3. Simplified 19.0%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 42.4%

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

      1. sub-neg 42.4%

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

      2. metadata-eval 42.4%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 42.4%

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

      4. distribute-lft-in 42.4%

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

      5. metadata-eval 42.4%

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

      6. sub-neg 42.4%

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

      7. expm1-define 93.4%

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

   7. Simplified 93.4%

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

   8. Taylor expanded in i around 0 72.9%

      \[\leadsto \color{blue}{50 \cdot \left(i \cdot n\right) + 100 \cdot n} \]
   9. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto \color{blue}{100 \cdot n + 50 \cdot \left(i \cdot n\right)} \]

      2. associate-*r* 72.9%

         \[\leadsto 100 \cdot n + \color{blue}{\left(50 \cdot i\right) \cdot n} \]

      3. distribute-rgt-in 72.9%

         \[\leadsto \color{blue}{n \cdot \left(100 + 50 \cdot i\right)} \]

      4. *-commutative 72.9%

         \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   10. Simplified 72.9%

       \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   if -6.5e180 < n < 6.1999999999999999e-62

   1. Initial program 30.1%

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

      1. associate-/r/ 30.2%

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

      2. associate-*r* 30.3%

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

      3. *-commutative 30.3%

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

      4. associate-*r/ 30.3%

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

      5. sub-neg 30.3%

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

      6. distribute-lft-in 30.3%

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

      7. metadata-eval 30.3%

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

      8. metadata-eval 30.3%

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

      9. metadata-eval 30.3%

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

      10. fma-define 30.3%

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

      11. metadata-eval 30.3%

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

   3. Simplified 30.3%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 20.9%

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

      1. sub-neg 20.9%

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

      2. metadata-eval 20.9%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 20.9%

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

      4. distribute-lft-in 20.9%

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

      5. metadata-eval 20.9%

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

      6. sub-neg 20.9%

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

      7. expm1-define 65.0%

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

   7. Simplified 65.0%

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

      1. clear-num 65.0%

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

      2. un-div-inv 64.9%

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

      3. *-un-lft-identity 64.9%

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

      4. times-frac 65.0%

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

      5. metadata-eval 65.0%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 65.0%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 65.0%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 65.1%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 65.1%

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

   11. Simplified 65.1%

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

   12. Taylor expanded in i around 0 61.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + -0.5 \cdot i}} \]
   13. Step-by-step derivation

       1. *-commutative 61.9%

          \[\leadsto 100 \cdot \frac{n}{1 + \color{blue}{i \cdot -0.5}} \]

   14. Simplified 61.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot -0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -6.5 \cdot 10^{+180} \lor \neg \left(n \leq 6.2 \cdot 10^{-62}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.2% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -6.6 \cdot 10^{+180}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{elif}\;n \leq 7.2 \cdot 10^{-62}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + 50 \cdot \left(i \cdot n\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -6.6e+180)
   (* n (+ 100.0 (* i 50.0)))
   (if (<= n 7.2e-62)
     (* 100.0 (/ n (+ 1.0 (* i -0.5))))
     (+ (* n 100.0) (* 50.0 (* i n))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -6.6e+180) {
		tmp = n * (100.0 + (i * 50.0));
	} else if (n <= 7.2e-62) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = (n * 100.0) + (50.0 * (i * n));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-6.6d+180)) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else if (n <= 7.2d-62) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    else
        tmp = (n * 100.0d0) + (50.0d0 * (i * n))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -6.6e+180) {
		tmp = n * (100.0 + (i * 50.0));
	} else if (n <= 7.2e-62) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = (n * 100.0) + (50.0 * (i * n));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -6.6e+180:
		tmp = n * (100.0 + (i * 50.0))
	elif n <= 7.2e-62:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	else:
		tmp = (n * 100.0) + (50.0 * (i * n))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -6.6e+180)
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	elseif (n <= 7.2e-62)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	else
		tmp = Float64(Float64(n * 100.0) + Float64(50.0 * Float64(i * n)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -6.6e+180)
		tmp = n * (100.0 + (i * 50.0));
	elseif (n <= 7.2e-62)
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	else
		tmp = (n * 100.0) + (50.0 * (i * n));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -6.6e+180], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 7.2e-62], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * 100.0), $MachinePrecision] + N[(50.0 * N[(i * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if n < -6.59999999999999978e180

   1. Initial program 7.6%

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

      1. associate-/r/ 8.3%

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

      2. associate-*r* 8.3%

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

      3. *-commutative 8.3%

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

      4. associate-*r/ 8.3%

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

      5. sub-neg 8.3%

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

      6. distribute-lft-in 8.3%

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

      7. metadata-eval 8.3%

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

      8. metadata-eval 8.3%

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

      9. metadata-eval 8.3%

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

      10. fma-define 8.3%

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

      11. metadata-eval 8.3%

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

   3. Simplified 8.3%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 45.3%

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

      1. sub-neg 45.3%

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

      2. metadata-eval 45.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 45.3%

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

      4. distribute-lft-in 45.3%

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

      5. metadata-eval 45.3%

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

      6. sub-neg 45.3%

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

      7. expm1-define 95.4%

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

   7. Simplified 95.4%

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

   8. Taylor expanded in i around 0 69.8%

      \[\leadsto \color{blue}{50 \cdot \left(i \cdot n\right) + 100 \cdot n} \]
   9. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto \color{blue}{100 \cdot n + 50 \cdot \left(i \cdot n\right)} \]

      2. associate-*r* 69.8%

         \[\leadsto 100 \cdot n + \color{blue}{\left(50 \cdot i\right) \cdot n} \]

      3. distribute-rgt-in 69.8%

         \[\leadsto \color{blue}{n \cdot \left(100 + 50 \cdot i\right)} \]

      4. *-commutative 69.8%

         \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   if -6.59999999999999978e180 < n < 7.1999999999999999e-62

   1. Initial program 30.1%

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

      1. associate-/r/ 30.2%

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

      2. associate-*r* 30.3%

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

      3. *-commutative 30.3%

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

      4. associate-*r/ 30.3%

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

      5. sub-neg 30.3%

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

      6. distribute-lft-in 30.3%

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

      7. metadata-eval 30.3%

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

      8. metadata-eval 30.3%

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

      9. metadata-eval 30.3%

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

      10. fma-define 30.3%

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

      11. metadata-eval 30.3%

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

   3. Simplified 30.3%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 20.9%

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

      1. sub-neg 20.9%

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

      2. metadata-eval 20.9%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 20.9%

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

      4. distribute-lft-in 20.9%

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

      5. metadata-eval 20.9%

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

      6. sub-neg 20.9%

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

      7. expm1-define 65.0%

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

   7. Simplified 65.0%

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

      1. clear-num 65.0%

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

      2. un-div-inv 64.9%

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

      3. *-un-lft-identity 64.9%

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

      4. times-frac 65.0%

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

      5. metadata-eval 65.0%

         \[\leadsto \frac{n}{\color{blue}{0.01} \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

   9. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{n}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}}} \]
   10. Step-by-step derivation

       1. *-rgt-identity 65.0%

          \[\leadsto \frac{\color{blue}{n \cdot 1}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       2. *-commutative 65.0%

          \[\leadsto \frac{\color{blue}{1 \cdot n}}{0.01 \cdot \frac{i}{\mathsf{expm1}\left(i\right)}} \]

       3. times-frac 65.1%

          \[\leadsto \color{blue}{\frac{1}{0.01} \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]

       4. metadata-eval 65.1%

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

   11. Simplified 65.1%

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

   12. Taylor expanded in i around 0 61.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + -0.5 \cdot i}} \]
   13. Step-by-step derivation

       1. *-commutative 61.9%

          \[\leadsto 100 \cdot \frac{n}{1 + \color{blue}{i \cdot -0.5}} \]

   14. Simplified 61.9%

       \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot -0.5}} \]

   if 7.1999999999999999e-62 < n

   1. Initial program 24.9%

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

      1. associate-/r/ 25.3%

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

      2. associate-*r* 25.3%

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

      3. *-commutative 25.3%

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

      4. associate-*r/ 25.3%

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

      5. sub-neg 25.3%

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

      6. distribute-lft-in 25.3%

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

      7. metadata-eval 25.3%

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

      8. metadata-eval 25.3%

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

      9. metadata-eval 25.3%

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

      10. fma-define 25.3%

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

      11. metadata-eval 25.3%

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

   3. Simplified 25.3%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 40.7%

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

      1. sub-neg 40.7%

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

      2. metadata-eval 40.7%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 40.7%

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

      4. distribute-lft-in 40.7%

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

      5. metadata-eval 40.7%

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

      6. sub-neg 40.7%

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

      7. expm1-define 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in i around 0 74.7%

      \[\leadsto \color{blue}{50 \cdot \left(i \cdot n\right) + 100 \cdot n} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -6.6 \cdot 10^{+180}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{elif}\;n \leq 7.2 \cdot 10^{-62}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + 50 \cdot \left(i \cdot n\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.0% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.15 \cdot 10^{-122} \lor \neg \left(n \leq 8.6 \cdot 10^{-190}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -1.15e-122) (not (<= n 8.6e-190)))
   (* n (+ 100.0 (* i 50.0)))
   0.0))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -1.15e-122) || !(n <= 8.6e-190)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-1.15d-122)) .or. (.not. (n <= 8.6d-190))) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -1.15e-122) || !(n <= 8.6e-190)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -1.15e-122) or not (n <= 8.6e-190):
		tmp = n * (100.0 + (i * 50.0))
	else:
		tmp = 0.0
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -1.15e-122) || !(n <= 8.6e-190))
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -1.15e-122) || ~((n <= 8.6e-190)))
		tmp = n * (100.0 + (i * 50.0));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -1.15e-122], N[Not[LessEqual[n, 8.6e-190]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if n < -1.15000000000000003e-122 or 8.5999999999999999e-190 < n

   1. Initial program 20.4%

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

      1. associate-/r/ 20.8%

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

      2. associate-*r* 20.8%

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

      3. *-commutative 20.8%

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

      4. associate-*r/ 20.8%

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

      5. sub-neg 20.8%

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

      6. distribute-lft-in 20.8%

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

      7. metadata-eval 20.8%

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

      8. metadata-eval 20.8%

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

      9. metadata-eval 20.8%

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

      10. fma-define 20.8%

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

      11. metadata-eval 20.8%

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

   3. Simplified 20.8%

      \[\leadsto \color{blue}{n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, -100\right)}{i}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around inf 31.3%

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

      1. sub-neg 31.3%

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

      2. metadata-eval 31.3%

         \[\leadsto n \cdot \frac{100 \cdot e^{i} + \color{blue}{-100}}{i} \]

      3. metadata-eval 31.3%

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

      4. distribute-lft-in 31.3%

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

      5. metadata-eval 31.3%

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

      6. sub-neg 31.3%

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

      7. expm1-define 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in i around 0 67.0%

      \[\leadsto \color{blue}{50 \cdot \left(i \cdot n\right) + 100 \cdot n} \]
   9. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto \color{blue}{100 \cdot n + 50 \cdot \left(i \cdot n\right)} \]

      2. associate-*r* 67.0%

         \[\leadsto 100 \cdot n + \color{blue}{\left(50 \cdot i\right) \cdot n} \]

      3. distribute-rgt-in 67.0%

         \[\leadsto \color{blue}{n \cdot \left(100 + 50 \cdot i\right)} \]

      4. *-commutative 67.0%

         \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   10. Simplified 67.0%

       \[\leadsto \color{blue}{\left(100 + 50 \cdot i\right) \cdot n} \]

   if -1.15000000000000003e-122 < n < 8.5999999999999999e-190

   1. Initial program 50.2%

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

      1. associate-*r/ 50.2%

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

      2. sub-neg 50.2%

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

      3. distribute-rgt-in 50.2%

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

      4. metadata-eval 50.2%

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

      5. metadata-eval 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in i around 0 61.3%

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

   6. Taylor expanded in i around 0 61.3%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -1.15 \cdot 10^{-122} \lor \neg \left(n \leq 8.6 \cdot 10^{-190}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.4% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 10^{-14}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -7.5e-7) 0.0 (if (<= i 1e-14) (* n 100.0) 0.0)))

C

double code(double i, double n) {
	double tmp;
	if (i <= -7.5e-7) {
		tmp = 0.0;
	} else if (i <= 1e-14) {
		tmp = n * 100.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (i <= (-7.5d-7)) then
        tmp = 0.0d0
    else if (i <= 1d-14) then
        tmp = n * 100.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= -7.5e-7) {
		tmp = 0.0;
	} else if (i <= 1e-14) {
		tmp = n * 100.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -7.5e-7:
		tmp = 0.0
	elif i <= 1e-14:
		tmp = n * 100.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -7.5e-7)
		tmp = 0.0;
	elseif (i <= 1e-14)
		tmp = Float64(n * 100.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (i <= -7.5e-7)
		tmp = 0.0;
	elseif (i <= 1e-14)
		tmp = n * 100.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, -7.5e-7], 0.0, If[LessEqual[i, 1e-14], N[(n * 100.0), $MachinePrecision], 0.0]]

Derivation

1. Split input into 2 regimes

2. if i < -7.5000000000000002e-7 or 9.99999999999999999e-15 < i

   1. Initial program 50.9%

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

      1. associate-*r/ 51.0%

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

      2. sub-neg 51.0%

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

      3. distribute-rgt-in 51.0%

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

      4. metadata-eval 51.0%

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

      5. metadata-eval 51.0%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in i around 0 21.6%

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

   6. Taylor expanded in i around 0 21.6%

      \[\leadsto \color{blue}{0} \]

   if -7.5000000000000002e-7 < i < 9.99999999999999999e-15

   1. Initial program 5.3%

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

   3. Taylor expanded in i around 0 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

Alternative 17: 17.7% accurate, 114.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (i n) :precision binary64 0.0)

C

double code(double i, double n) {
	return 0.0;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = 0.0d0
end function

Java

public static double code(double i, double n) {
	return 0.0;
}

Python

def code(i, n):
	return 0.0

Julia

function code(i, n)
	return 0.0
end

MATLAB

function tmp = code(i, n)
	tmp = 0.0;
end

Wolfram

code[i_, n_] := 0.0

Derivation

1. Initial program 24.6%

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

   1. associate-*r/ 24.6%

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

   2. sub-neg 24.6%

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

   3. distribute-rgt-in 24.6%

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

   4. metadata-eval 24.6%

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

   5. metadata-eval 24.6%

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

3. Simplified 24.6%

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

5. Taylor expanded in i around 0 12.2%

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

6. Taylor expanded in i around 0 12.5%

   \[\leadsto \color{blue}{0} \]
7. Add Preprocessing

Developer Target 1: 34.1% 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

real(8) function code(i, n)
    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 2024137 
(FPCore (i n)
  :name "Compound Interest"
  :precision binary64

  :alt
  (! :herbie-platform default (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))))