subtraction fraction

Percentage Accurate: 100.0% → 100.0%

Time: 758.0ms

Alternatives: 2

Speedup: 1.1×

Specification

Math

\[\frac{-\left(f + n\right)}{f - n} \]

FPCore

(FPCore (f n)
  :precision binary64
  (/ (- (+ f n)) (- f n)))

C

double code(double f, double n) {
	return -(f + n) / (f - n);
}

Fortran

real(8) function code(f, n)
use fmin_fmax_functions
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = -(f + n) / (f - n)
end function

Java

public static double code(double f, double n) {
	return -(f + n) / (f - n);
}

Python

def code(f, n):
	return -(f + n) / (f - n)

Julia

function code(f, n)
	return Float64(Float64(-Float64(f + n)) / Float64(f - n))
end

MATLAB

function tmp = code(f, n)
	tmp = -(f + n) / (f - n);
end

Wolfram

code[f_, n_] := N[((-N[(f + n), $MachinePrecision]) / N[(f - n), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{-\left(f + n\right)}{f - n} \]

FPCore

(FPCore (f n)
  :precision binary64
  (/ (- (+ f n)) (- f n)))

C

double code(double f, double n) {
	return -(f + n) / (f - n);
}

Fortran

real(8) function code(f, n)
use fmin_fmax_functions
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = -(f + n) / (f - n)
end function

Java

public static double code(double f, double n) {
	return -(f + n) / (f - n);
}

Python

def code(f, n):
	return -(f + n) / (f - n)

Julia

function code(f, n)
	return Float64(Float64(-Float64(f + n)) / Float64(f - n))
end

MATLAB

function tmp = code(f, n)
	tmp = -(f + n) / (f - n);
end

Wolfram

code[f_, n_] := N[((-N[(f + n), $MachinePrecision]) / N[(f - n), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.6× speedup

Math

\[\frac{n}{n - f} - \frac{f}{f - n} \]

FPCore

(FPCore (f n)
  :precision binary64
  (- (/ n (- n f)) (/ f (- f n))))

C

double code(double f, double n) {
	return (n / (n - f)) - (f / (f - n));
}

Fortran

real(8) function code(f, n)
use fmin_fmax_functions
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = (n / (n - f)) - (f / (f - n))
end function

Java

public static double code(double f, double n) {
	return (n / (n - f)) - (f / (f - n));
}

Python

def code(f, n):
	return (n / (n - f)) - (f / (f - n))

Julia

function code(f, n)
	return Float64(Float64(n / Float64(n - f)) - Float64(f / Float64(f - n)))
end

MATLAB

function tmp = code(f, n)
	tmp = (n / (n - f)) - (f / (f - n));
end

Wolfram

code[f_, n_] := N[(N[(n / N[(n - f), $MachinePrecision]), $MachinePrecision] - N[(f / N[(f - n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{-\left(f + n\right)}{f - n} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{-\left(f + n\right)}{f - n}} \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(-\left(f + n\right)\right)\right)}{\mathsf{neg}\left(\left(f - n\right)\right)}} \]

   3. distribute-frac-neg2 N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{\mathsf{neg}\left(\left(-\left(f + n\right)\right)\right)}{f - n}\right)} \]

   4. lift-neg.f64 N/A

      \[\leadsto \mathsf{neg}\left(\frac{\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\left(f + n\right)\right)\right)}\right)}{f - n}\right) \]

   5. remove-double-neg N/A

      \[\leadsto \mathsf{neg}\left(\frac{\color{blue}{f + n}}{f - n}\right) \]

   6. lift-+.f64 N/A

      \[\leadsto \mathsf{neg}\left(\frac{\color{blue}{f + n}}{f - n}\right) \]

   7. add-flip N/A

      \[\leadsto \mathsf{neg}\left(\frac{\color{blue}{f - \left(\mathsf{neg}\left(n\right)\right)}}{f - n}\right) \]

   8. div-sub N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{f}{f - n} - \frac{\mathsf{neg}\left(n\right)}{f - n}\right)}\right) \]

   9. sub-negate N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(n\right)}{f - n} - \frac{f}{f - n}} \]

   10. lower--.f64 N/A

       \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(n\right)}{f - n} - \frac{f}{f - n}} \]

   11. distribute-frac-neg N/A

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{n}{f - n}\right)\right)} - \frac{f}{f - n} \]

   12. distribute-neg-frac2 N/A

       \[\leadsto \color{blue}{\frac{n}{\mathsf{neg}\left(\left(f - n\right)\right)}} - \frac{f}{f - n} \]

   13. add-sound-/ N/A

       \[\leadsto \color{blue}{\frac{n}{\mathsf{neg}\left(\left(f - n\right)\right)}} - \frac{f}{f - n} \]

   14. lower-/.f64 N/A

       \[\leadsto \color{blue}{\frac{n}{\mathsf{neg}\left(\left(f - n\right)\right)}} - \frac{f}{f - n} \]

   15. lift--.f64 N/A

       \[\leadsto \frac{n}{\mathsf{neg}\left(\color{blue}{\left(f - n\right)}\right)} - \frac{f}{f - n} \]

   16. sub-negate-rev N/A

       \[\leadsto \frac{n}{\color{blue}{n - f}} - \frac{f}{f - n} \]

   17. lower--.f64 N/A

       \[\leadsto \frac{n}{\color{blue}{n - f}} - \frac{f}{f - n} \]

   18. add-sound-/ N/A

       \[\leadsto \frac{n}{n - f} - \color{blue}{\frac{f}{f - n}} \]

   19. lower-/.f64 100.0%

       \[\leadsto \frac{n}{n - f} - \color{blue}{\frac{f}{f - n}} \]

3. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\frac{n}{n - f} - \frac{f}{f - n}} \]
4. Add Preprocessing

Alternative 2: 100.0% accurate, 1.1× speedup

Math

\[\frac{n + f}{n - f} \]

FPCore

(FPCore (f n)
  :precision binary64
  (/ (+ n f) (- n f)))

C

double code(double f, double n) {
	return (n + f) / (n - f);
}

Fortran

real(8) function code(f, n)
use fmin_fmax_functions
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = (n + f) / (n - f)
end function

Java

public static double code(double f, double n) {
	return (n + f) / (n - f);
}

Python

def code(f, n):
	return (n + f) / (n - f)

Julia

function code(f, n)
	return Float64(Float64(n + f) / Float64(n - f))
end

MATLAB

function tmp = code(f, n)
	tmp = (n + f) / (n - f);
end

Wolfram

code[f_, n_] := N[(N[(n + f), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{-\left(f + n\right)}{f - n} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{-\left(f + n\right)}{f - n}} \]

   2. mult-flip N/A

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

   3. *-commutative N/A

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

   4. lift-neg.f64 N/A

      \[\leadsto \frac{1}{f - n} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(f + n\right)\right)\right)} \]

   5. distribute-rgt-neg-out N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{1}{f - n} \cdot \left(f + n\right)\right)} \]

   6. *-commutative N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(f + n\right) \cdot \frac{1}{f - n}}\right) \]

   7. mult-flip N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{f + n}{f - n}}\right) \]

   8. lift-+.f64 N/A

      \[\leadsto \mathsf{neg}\left(\frac{\color{blue}{f + n}}{f - n}\right) \]

   9. div-add N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{f}{f - n} + \frac{n}{f - n}\right)}\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{n}{f - n} + \frac{f}{f - n}\right)}\right) \]

   11. add-to-fraction N/A

       \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{\frac{n}{f - n} \cdot \left(f - n\right) + f}{f - n}}\right) \]

   12. distribute-neg-frac2 N/A

       \[\leadsto \color{blue}{\frac{\frac{n}{f - n} \cdot \left(f - n\right) + f}{\mathsf{neg}\left(\left(f - n\right)\right)}} \]

   13. add-sound-/ N/A

       \[\leadsto \color{blue}{\frac{\frac{n}{f - n} \cdot \left(f - n\right) + f}{\mathsf{neg}\left(\left(f - n\right)\right)}} \]

   14. lower-/.f64 N/A

       \[\leadsto \color{blue}{\frac{\frac{n}{f - n} \cdot \left(f - n\right) + f}{\mathsf{neg}\left(\left(f - n\right)\right)}} \]

3. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\frac{n + f}{n - f}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2025326 -o generate:taylor -o generate:evaluate
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))