Average Error: 0.4 → 0.2
Time: 28.0s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(c + b\right) + e\right) + \left(d + a\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]

  2. Initial simplification0.2

    \[\leadsto \left(\left(a + d\right) + \left(c + b\right)\right) + e\]
  3. Using strategy rm

  4. Applied associate-+l+0.2

    \[\leadsto \color{blue}{\left(a + d\right) + \left(\left(c + b\right) + e\right)}\]

  5. Final simplification0.2

    \[\leadsto \left(\left(c + b\right) + e\right) + \left(d + a\right)\]

Reproduce

herbie shell --seed 2018365 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))

Details

Time bar (total: 25.2s)Debug log

start63.0ms

Algorithm
intervals

setup311.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (+ a d) (+ c b))
0.2b
(+ (+ (+ a d) (+ c b)) e)

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

25.0ms
(+ (+ (+ a d) (+ c b)) e)
3.0ms
(+ (+ a d) (+ c b))

series108.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

72.0ms
(+ (+ (+ a d) (+ c b)) e)
36.0ms
(+ (+ a d) (+ c b))

simplify2.3s

Counts
17 → 35
Calls

17 calls. Slowest were:

477.0ms
(+ (* (+ (pow a 3) (pow d 3)) (- c b)) (* (+ (* a a) (- (* d d) (* a d))) (- (* c c) (* b b))))
475.0ms
(+ (* (- (* a a) (* d d)) (- c b)) (* (- a d) (- (* c c) (* b b))))
397.0ms
(* (+ (* a a) (- (* d d) (* a d))) (- c b))

prune418.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (+ a d) (+ (+ c b) e))
0.1b
(+ (+ c b) e)

rewrite25.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

19.0ms
(+ (+ a d) (+ (+ c b) e))
4.0ms
(+ (+ c b) e)

series72.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

56.0ms
(+ (+ a d) (+ (+ c b) e))
16.0ms
(+ (+ c b) e)

simplify2.0s

Counts
16 → 35
Calls

16 calls. Slowest were:

423.0ms
(* (- a d) (- (+ c b) e))
348.0ms
(* (exp (+ a d)) (exp (+ (+ c b) e)))
228.0ms
(+ (* (+ (pow a 3) (pow d 3)) (+ (* (+ c b) (+ c b)) (- (* e e) (* (+ c b) e)))) (* (+ (* a a) (- (* d d) (* a d))) (+ (pow (+ c b) 3) (pow e 3))))

prune444.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (+ a d) (+ c (+ b e)))
0.2b
(+ c (+ b e))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

4.0ms
(+ (+ a d) (+ c (+ b e)))
1.0ms
(+ c (+ b e))

series57.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

39.0ms
(+ (+ a d) (+ c (+ b e)))
18.0ms
(+ c (+ b e))

simplify1.9s

Counts
17 → 35
Calls

17 calls. Slowest were:

356.0ms
(* (- a d) (- c (+ b e)))
263.0ms
(+ (* (- (* a a) (* d d)) (+ (* c c) (- (* (+ b e) (+ b e)) (* c (+ b e))))) (* (- a d) (+ (pow c 3) (pow (+ b e) 3))))
257.0ms
(* (exp (+ a d)) (exp (+ c (+ b e))))

prune411.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (+ (* a a) (* d (- d a))) (+ (pow b 3) (pow c 3)))
0.4b
(+ (* b (- b c)) (* c c))
0.4b
(* (+ (* b (- b c)) (* c c)) (+ (pow a 3) (pow d 3)))
0.4b
(* (- (* b b) (* (- b c) c)) (+ (* a a) (* (- d a) d)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Counts
4 → 100
Calls

4 calls. Slowest were:

22.0ms
(* (+ (* b (- b c)) (* c c)) (+ (pow a 3) (pow d 3)))
19.0ms
(* (+ (* a a) (* d (- d a))) (+ (pow b 3) (pow c 3)))
14.0ms
(* (- (* b b) (* (- b c) c)) (+ (* a a) (* (- d a) d)))

series510.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

183.0ms
(* (+ (* b (- b c)) (* c c)) (+ (pow a 3) (pow d 3)))
155.0ms
(* (- (* b b) (* (- b c) c)) (+ (* a a) (* (- d a) d)))
152.0ms
(* (+ (* a a) (* d (- d a))) (+ (pow b 3) (pow c 3)))
20.0ms
(+ (* b (- b c)) (* c c))

simplify12.8s

Counts
87 → 112
Calls

87 calls. Slowest were:

1.1s
(* (+ (pow (* a a) 3) (pow (* d (- d a)) 3)) (- (* (pow b 3) (pow b 3)) (* (pow c 3) (pow c 3))))
810.0ms
(* (+ (pow (* a a) 3) (pow (* d (- d a)) 3)) (+ (pow b 3) (pow c 3)))
652.0ms
(* (+ (pow (* b (- b c)) 3) (pow (* c c) 3)) (+ (pow a 3) (pow d 3)))

prune3.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes547.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms