Octave 3.8, jcobi/4

Percentage Accurate: 30.1% → 91.4%

Time: 3.2s

Alternatives: 5

Speedup: 5.1×

• Could not converge on a ground truth

  1. alpha = 1.7533746046869366e+195
  2. beta = -1.7030234586554808e+258
  3. i = -1.7593880419529947e+99

Specification

\[\left(\alpha > -1 \land \beta > -1\right) \land i > 1\]

Math

\[\begin{array}{l} t_0 := i \cdot \left(\left(\alpha + \beta\right) + i\right)\\ t_1 := \left(\alpha + \beta\right) + 2 \cdot i\\ t_2 := t\_1 \cdot t\_1\\ \frac{\frac{t\_0 \cdot \left(\beta \cdot \alpha + t\_0\right)}{t\_2}}{t\_2 - 1} \end{array} \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  (let* ((t_0 (* i (+ (+ alpha beta) i)))
       (t_1 (+ (+ alpha beta) (* 2.0 i)))
       (t_2 (* t_1 t_1)))
  (/ (/ (* t_0 (+ (* beta alpha) t_0)) t_2) (- t_2 1.0))))

C

double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Fortran

real(8) function code(alpha, beta, i)
use fmin_fmax_functions
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = i * ((alpha + beta) + i)
    t_1 = (alpha + beta) + (2.0d0 * i)
    t_2 = t_1 * t_1
    code = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0d0)
end function

Java

public static double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Python

def code(alpha, beta, i):
	t_0 = i * ((alpha + beta) + i)
	t_1 = (alpha + beta) + (2.0 * i)
	t_2 = t_1 * t_1
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0)

Julia

function code(alpha, beta, i)
	t_0 = Float64(i * Float64(Float64(alpha + beta) + i))
	t_1 = Float64(Float64(alpha + beta) + Float64(2.0 * i))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(Float64(t_0 * Float64(Float64(beta * alpha) + t_0)) / t_2) / Float64(t_2 - 1.0))
end

MATLAB

function tmp = code(alpha, beta, i)
	t_0 = i * ((alpha + beta) + i);
	t_1 = (alpha + beta) + (2.0 * i);
	t_2 = t_1 * t_1;
	tmp = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
end

Wolfram

code[alpha_, beta_, i_] := Block[{t$95$0 = N[(i * N[(N[(alpha + beta), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(N[(t$95$0 * N[(N[(beta * alpha), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] / N[(t$95$2 - 1.0), $MachinePrecision]), $MachinePrecision]]]]

Initial Program: 30.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := i \cdot \left(\left(\alpha + \beta\right) + i\right)\\ t_1 := \left(\alpha + \beta\right) + 2 \cdot i\\ t_2 := t\_1 \cdot t\_1\\ \frac{\frac{t\_0 \cdot \left(\beta \cdot \alpha + t\_0\right)}{t\_2}}{t\_2 - 1} \end{array} \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  (let* ((t_0 (* i (+ (+ alpha beta) i)))
       (t_1 (+ (+ alpha beta) (* 2.0 i)))
       (t_2 (* t_1 t_1)))
  (/ (/ (* t_0 (+ (* beta alpha) t_0)) t_2) (- t_2 1.0))))

C

double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Fortran

real(8) function code(alpha, beta, i)
use fmin_fmax_functions
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = i * ((alpha + beta) + i)
    t_1 = (alpha + beta) + (2.0d0 * i)
    t_2 = t_1 * t_1
    code = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0d0)
end function

Java

public static double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Python

def code(alpha, beta, i):
	t_0 = i * ((alpha + beta) + i)
	t_1 = (alpha + beta) + (2.0 * i)
	t_2 = t_1 * t_1
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0)

Julia

function code(alpha, beta, i)
	t_0 = Float64(i * Float64(Float64(alpha + beta) + i))
	t_1 = Float64(Float64(alpha + beta) + Float64(2.0 * i))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(Float64(t_0 * Float64(Float64(beta * alpha) + t_0)) / t_2) / Float64(t_2 - 1.0))
end

MATLAB

function tmp = code(alpha, beta, i)
	t_0 = i * ((alpha + beta) + i);
	t_1 = (alpha + beta) + (2.0 * i);
	t_2 = t_1 * t_1;
	tmp = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
end

Wolfram

code[alpha_, beta_, i_] := Block[{t$95$0 = N[(i * N[(N[(alpha + beta), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(N[(t$95$0 * N[(N[(beta * alpha), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] / N[(t$95$2 - 1.0), $MachinePrecision]), $MachinePrecision]]]]

Alternative 1: 91.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq 3.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{\alpha \cdot 0}{\beta}}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\left(0.0625 + 0.0625 \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - 0.125 \cdot \frac{\alpha + \beta}{i}\\ \end{array} \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  (if (<= i 3.4e-19)
  (/ (/ (* alpha 0.0) beta) beta)
  (-
   (+ 0.0625 (* 0.0625 (/ (fma 2.0 alpha (* 2.0 beta)) i)))
   (* 0.125 (/ (+ alpha beta) i)))))

C

double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 3.4e-19) {
		tmp = ((alpha * 0.0) / beta) / beta;
	} else {
		tmp = (0.0625 + (0.0625 * (fma(2.0, alpha, (2.0 * beta)) / i))) - (0.125 * ((alpha + beta) / i));
	}
	return tmp;
}

Julia

function code(alpha, beta, i)
	tmp = 0.0
	if (i <= 3.4e-19)
		tmp = Float64(Float64(Float64(alpha * 0.0) / beta) / beta);
	else
		tmp = Float64(Float64(0.0625 + Float64(0.0625 * Float64(fma(2.0, alpha, Float64(2.0 * beta)) / i))) - Float64(0.125 * Float64(Float64(alpha + beta) / i)));
	end
	return tmp
end

Wolfram

code[alpha_, beta_, i_] := If[LessEqual[i, 3.4e-19], N[(N[(N[(alpha * 0.0), $MachinePrecision] / beta), $MachinePrecision] / beta), $MachinePrecision], N[(N[(0.0625 + N[(0.0625 * N[(N[(2.0 * alpha + N[(2.0 * beta), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(N[(alpha + beta), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 3.4000000000000002e-19

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right)} \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \color{blue}{\beta}\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \color{blue}{\left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left(\color{blue}{{\left(\alpha + \beta\right)}^{2}} - 1\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - \color{blue}{1}\right)} \]

      7. lower-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      8. lower-+.f64 53.0%

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

   5. Taylor expanded in beta around inf

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. lower-pow.f64 31.3%

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lift-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. unpow2 N/A

         \[\leadsto \frac{\alpha \cdot i}{\beta \cdot \beta} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

      6. lower-/.f64 31.3%

         \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

   9. Applied rewrites 31.3%

      \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

   10. Taylor expanded in undef-var around zero

       \[\leadsto \frac{\frac{\alpha \cdot 0}{\beta}}{\beta} \]
   11. Step-by-step derivation

   12. Applied rewrites 87.1%

       \[\leadsto \frac{\frac{\alpha \cdot 0}{\beta}}{\beta} \]

   if 3.4000000000000002e-19 < i

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right)} \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \color{blue}{\beta}\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \color{blue}{\left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left(\color{blue}{{\left(\alpha + \beta\right)}^{2}} - 1\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - \color{blue}{1}\right)} \]

      7. lower-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      8. lower-+.f64 53.0%

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot \alpha + 2 \cdot \beta}{i}\right) - \frac{1}{8} \cdot \frac{\alpha + \beta}{i}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot \alpha + 2 \cdot \beta}{i}\right) - \color{blue}{\frac{1}{8} \cdot \frac{\alpha + \beta}{i}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot \alpha + 2 \cdot \beta}{i}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{\alpha + \beta}{i} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot \alpha + 2 \cdot \beta}{i}\right) - \frac{1}{8} \cdot \frac{\alpha + \beta}{i} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot \alpha + 2 \cdot \beta}{i}\right) - \frac{1}{8} \cdot \frac{\alpha + \beta}{i} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - \frac{1}{8} \cdot \frac{\alpha + \beta}{i} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - \frac{1}{8} \cdot \frac{\alpha + \beta}{i} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - \frac{1}{8} \cdot \color{blue}{\frac{\alpha + \beta}{i}} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - \frac{1}{8} \cdot \frac{\alpha + \beta}{\color{blue}{i}} \]

      9. lower-+.f64 50.5%

         \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - 0.125 \cdot \frac{\alpha + \beta}{i} \]

   7. Applied rewrites 50.5%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{\mathsf{fma}\left(2, \alpha, 2 \cdot \beta\right)}{i}\right) - 0.125 \cdot \frac{\alpha + \beta}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq 5.2 \cdot 10^{+235}:\\ \;\;\;\;\frac{\frac{\alpha \cdot 0}{\beta}}{\beta}\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  (if (<= i 5.2e+235) (/ (/ (* alpha 0.0) beta) beta) 0.0625))

C

double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 5.2e+235) {
		tmp = ((alpha * 0.0) / beta) / beta;
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta, i)
use fmin_fmax_functions
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= 5.2d+235) then
        tmp = ((alpha * 0.0d0) / beta) / beta
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 5.2e+235) {
		tmp = ((alpha * 0.0) / beta) / beta;
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(alpha, beta, i):
	tmp = 0
	if i <= 5.2e+235:
		tmp = ((alpha * 0.0) / beta) / beta
	else:
		tmp = 0.0625
	return tmp

Julia

function code(alpha, beta, i)
	tmp = 0.0
	if (i <= 5.2e+235)
		tmp = Float64(Float64(Float64(alpha * 0.0) / beta) / beta);
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (i <= 5.2e+235)
		tmp = ((alpha * 0.0) / beta) / beta;
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_, i_] := If[LessEqual[i, 5.2e+235], N[(N[(N[(alpha * 0.0), $MachinePrecision] / beta), $MachinePrecision] / beta), $MachinePrecision], 0.0625]

Derivation

1. Split input into 2 regimes

2. if i < 5.1999999999999996e235

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right)} \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \color{blue}{\beta}\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \color{blue}{\left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left(\color{blue}{{\left(\alpha + \beta\right)}^{2}} - 1\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - \color{blue}{1}\right)} \]

      7. lower-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      8. lower-+.f64 53.0%

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

   5. Taylor expanded in beta around inf

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. lower-pow.f64 31.3%

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lift-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. unpow2 N/A

         \[\leadsto \frac{\alpha \cdot i}{\beta \cdot \beta} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

      6. lower-/.f64 31.3%

         \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

   9. Applied rewrites 31.3%

      \[\leadsto \frac{\frac{\alpha \cdot i}{\beta}}{\beta} \]

   10. Taylor expanded in undef-var around zero

       \[\leadsto \frac{\frac{\alpha \cdot 0}{\beta}}{\beta} \]
   11. Step-by-step derivation

   12. Applied rewrites 87.1%

       \[\leadsto \frac{\frac{\alpha \cdot 0}{\beta}}{\beta} \]

   if 5.1999999999999996e235 < i

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 13.0%

      \[\leadsto \color{blue}{0.0625} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 62.3% accurate, 5.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq 65000000:\\ \;\;\;\;0 \cdot \frac{\alpha}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  (if (<= i 65000000.0) (* 0.0 (/ alpha (* beta beta))) 0.0625))

C

double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 65000000.0) {
		tmp = 0.0 * (alpha / (beta * beta));
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta, i)
use fmin_fmax_functions
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= 65000000.0d0) then
        tmp = 0.0d0 * (alpha / (beta * beta))
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 65000000.0) {
		tmp = 0.0 * (alpha / (beta * beta));
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(alpha, beta, i):
	tmp = 0
	if i <= 65000000.0:
		tmp = 0.0 * (alpha / (beta * beta))
	else:
		tmp = 0.0625
	return tmp

Julia

function code(alpha, beta, i)
	tmp = 0.0
	if (i <= 65000000.0)
		tmp = Float64(0.0 * Float64(alpha / Float64(beta * beta)));
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (i <= 65000000.0)
		tmp = 0.0 * (alpha / (beta * beta));
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_, i_] := If[LessEqual[i, 65000000.0], N[(0.0 * N[(alpha / N[(beta * beta), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0625]

Derivation

1. Split input into 2 regimes

2. if i < 6.5e7

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right)} \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \color{blue}{\beta}\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \color{blue}{\left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left(\color{blue}{{\left(\alpha + \beta\right)}^{2}} - 1\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - \color{blue}{1}\right)} \]

      7. lower-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      8. lower-+.f64 53.0%

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

   5. Taylor expanded in beta around inf

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. lower-pow.f64 31.3%

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. *-commutative N/A

         \[\leadsto \frac{i \cdot \alpha}{{\beta}^{2}} \]

      4. associate-/l* N/A

         \[\leadsto i \cdot \frac{\alpha}{\color{blue}{{\beta}^{2}}} \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \frac{\alpha}{\color{blue}{{\beta}^{2}}} \]

      6. lower-/.f64 34.0%

         \[\leadsto i \cdot \frac{\alpha}{{\beta}^{\color{blue}{2}}} \]

      7. lift-pow.f64 N/A

         \[\leadsto i \cdot \frac{\alpha}{{\beta}^{2}} \]

      8. unpow2 N/A

         \[\leadsto i \cdot \frac{\alpha}{\beta \cdot \beta} \]

      9. lower-*.f64 34.0%

         \[\leadsto i \cdot \frac{\alpha}{\beta \cdot \beta} \]

   9. Applied rewrites 34.0%

      \[\leadsto i \cdot \frac{\alpha}{\color{blue}{\beta \cdot \beta}} \]

   10. Taylor expanded in undef-var around zero

       \[\leadsto 0 \cdot \frac{\alpha}{\color{blue}{\beta} \cdot \beta} \]
   11. Step-by-step derivation

   12. Applied rewrites 60.8%

       \[\leadsto 0 \cdot \frac{\alpha}{\color{blue}{\beta} \cdot \beta} \]

   if 6.5e7 < i

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 13.0%

      \[\leadsto \color{blue}{0.0625} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 39.2% accurate, 5.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq 5.5 \cdot 10^{+25}:\\ \;\;\;\;i \cdot \frac{\alpha}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  (if (<= i 5.5e+25) (* i (/ alpha (* beta beta))) 0.0625))

C

double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 5.5e+25) {
		tmp = i * (alpha / (beta * beta));
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta, i)
use fmin_fmax_functions
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= 5.5d+25) then
        tmp = i * (alpha / (beta * beta))
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta, double i) {
	double tmp;
	if (i <= 5.5e+25) {
		tmp = i * (alpha / (beta * beta));
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(alpha, beta, i):
	tmp = 0
	if i <= 5.5e+25:
		tmp = i * (alpha / (beta * beta))
	else:
		tmp = 0.0625
	return tmp

Julia

function code(alpha, beta, i)
	tmp = 0.0
	if (i <= 5.5e+25)
		tmp = Float64(i * Float64(alpha / Float64(beta * beta)));
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (i <= 5.5e+25)
		tmp = i * (alpha / (beta * beta));
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_, i_] := If[LessEqual[i, 5.5e+25], N[(i * N[(alpha / N[(beta * beta), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0625]

Derivation

1. Split input into 2 regimes

2. if i < 5.5000000000000002e25

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\color{blue}{\left(\alpha + \beta\right)} \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \color{blue}{\beta}\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \color{blue}{\left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left(\color{blue}{{\left(\alpha + \beta\right)}^{2}} - 1\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - \color{blue}{1}\right)} \]

      7. lower-pow.f64 N/A

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

      8. lower-+.f64 53.0%

         \[\leadsto \frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)} \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\frac{\alpha \cdot \left(\beta \cdot i\right)}{\left(\alpha + \beta\right) \cdot \left({\left(\alpha + \beta\right)}^{2} - 1\right)}} \]

   5. Taylor expanded in beta around inf

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. lower-pow.f64 31.3%

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\alpha \cdot i}{\color{blue}{{\beta}^{2}}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{\color{blue}{2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\alpha \cdot i}{{\beta}^{2}} \]

      3. *-commutative N/A

         \[\leadsto \frac{i \cdot \alpha}{{\beta}^{2}} \]

      4. associate-/l* N/A

         \[\leadsto i \cdot \frac{\alpha}{\color{blue}{{\beta}^{2}}} \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \frac{\alpha}{\color{blue}{{\beta}^{2}}} \]

      6. lower-/.f64 34.0%

         \[\leadsto i \cdot \frac{\alpha}{{\beta}^{\color{blue}{2}}} \]

      7. lift-pow.f64 N/A

         \[\leadsto i \cdot \frac{\alpha}{{\beta}^{2}} \]

      8. unpow2 N/A

         \[\leadsto i \cdot \frac{\alpha}{\beta \cdot \beta} \]

      9. lower-*.f64 34.0%

         \[\leadsto i \cdot \frac{\alpha}{\beta \cdot \beta} \]

   9. Applied rewrites 34.0%

      \[\leadsto i \cdot \frac{\alpha}{\color{blue}{\beta \cdot \beta}} \]

   if 5.5000000000000002e25 < i

   1. Initial program 30.1%

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 13.0%

      \[\leadsto \color{blue}{0.0625} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 13.0% accurate, 75.0× speedup

Math

\[0.0625 \]

FPCore

(FPCore (alpha beta i)
  :precision binary64
  0.0625)

C

double code(double alpha, double beta, double i) {
	return 0.0625;
}

Fortran

real(8) function code(alpha, beta, i)
use fmin_fmax_functions
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    code = 0.0625d0
end function

Java

public static double code(double alpha, double beta, double i) {
	return 0.0625;
}

Python

def code(alpha, beta, i):
	return 0.0625

Julia

function code(alpha, beta, i)
	return 0.0625
end

MATLAB

function tmp = code(alpha, beta, i)
	tmp = 0.0625;
end

Wolfram

code[alpha_, beta_, i_] := 0.0625

Derivation

1. Initial program 30.1%

   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1} \]

2. Taylor expanded in i around inf

   \[\leadsto \color{blue}{\frac{1}{16}} \]
3. Step-by-step derivation

4. Applied rewrites 13.0%

   \[\leadsto \color{blue}{0.0625} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025313 -o setup:search
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :precision binary64
  :pre (and (and (> alpha -1.0) (> beta -1.0)) (> i 1.0))
  (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)))