VandenBroeck and Keller, Equation (6)

Average Error: 16.7 → 12.6

Time: 8.7s

Precision: binary64

• could not determine a ground truth for program body

  1. F = 3.718988740058123e+107
  2. l = 4003682086000171.5

Math

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↓

\[\]

C

double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) - ((double) (((double) (1.0 / ((double) (F * F)))) * ((double) tan(((double) (((double) M_PI) * l))))))));
}

↓

double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) + ((double) (1.0 * ((double) (((double) (-1.0 / ((double) (F / ((double) tan(((double) (((double) M_PI) * l)))))))) / F))))));
}

Error

Bits error versus F

Bits error versus l

Derivation

1. Initial program 16.7

   \[\]

2. Simplified 16.5

   \[\leadsto \]
3. Using strategy rm

4. Applied associate-/r* 12.6

   \[\leadsto \]
5. Using strategy rm

6. Applied clear-num 12.6

   \[\leadsto \]

7. Final simplification 12.6

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))