Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 649.0ms

Precision: binary64

Math

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

↓

\[2 \cdot \left(1 \cdot \frac{1}{9} + \left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right)\right)\]

FPCore

(FPCore ()
 :precision binary64
 (*
  2.0
  (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))

↓

(FPCore ()
 :precision binary64
 (*
  2.0
  (+ (* 1.0 (/ 1.0 9.0)) (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))))))

C

double code() {
	return ((double) (2.0 * ((double) (((double) (((double) (1.0 * (1.0 / 9.0))) + ((double) ((1.0 / 9.0) * (1.0 / 9.0))))) + ((double) ((1.0 / 9.0) * 1.0))))));
}

↓

double code() {
	return ((double) (2.0 * ((double) (((double) (1.0 * (1.0 / 9.0))) + ((double) (((double) (1.0 * (1.0 / 9.0))) + ((double) ((1.0 / 9.0) * (1.0 / 9.0)))))))));
}

Target

Original	0
Target	0
Herbie	0

\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

Derivation

1. Initial program 0

   \[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

2. Final simplification 0

   \[\leadsto 2 \cdot \left(1 \cdot \frac{1}{9} + \left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right)\right)\]

Reproduce

herbie shell --seed 2020210 
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"
  :precision binary64

  :herbie-target
  (+ (+ (* (* (/ 1.0 9.0) 1.0) 2.0) (* 2.0 (* (/ 1.0 9.0) (/ 1.0 9.0)))) (* 2.0 (* 1.0 (/ 1.0 9.0))))

  (* 2.0 (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))