Average Error: 0.4 → 0.2
Time: 8.0s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(a + \left(b + c\right)\right)\right)\]

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. Using strategy rm

  3. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a\]
  4. Using strategy rm

  5. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(e + d\right) + \left(\left(c + b\right) + a\right)}\]
  6. Using strategy rm

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019010 
(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: 7.3s)Debug log

sample48.0ms

Algorithm
intervals

simplify179.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
179.0ms
(+ (+ (+ (+ e d) c) b) a)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ (+ (+ e d) c) b)
0.3b
(+ (+ (+ (+ e d) c) b) a)
0.3b
(+ (+ e d) c)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
3×flip-+
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×flip3-+
3×*-un-lft-identity
3×associate-+l+
3×+-commutative
3×pow1
3×add-sqr-sqrt
Counts
3 → 33
Calls
3 calls:
Slowest
44.0ms
(+ (+ (+ (+ e d) c) b) a)
10.0ms
(+ (+ (+ e d) c) b)
2.0ms
(+ (+ e d) c)

series65.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
35.0ms
(+ (+ (+ (+ e d) c) b) a)
20.0ms
(+ (+ (+ e d) c) b)
10.0ms
(+ (+ e d) c)

simplify61.0ms

Counts
11 → 42
Calls
11 calls:
Slowest
7.0ms
(+ e (+ c d))
6.0ms
(+ b (+ c d))
6.0ms
(+ (+ e d) c)
6.0ms
(+ e (+ c d))
6.0ms
(+ e (+ c d))

prune410.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (+ e d) (+ c b))
0.3b
(+ (+ (+ e d) (+ c b)) a)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
6×flip-+
6×flip3-+
4×add-log-exp
4×frac-add
4×*-un-lft-identity
2×add-cube-cbrt
2×add-exp-log
2×add-cbrt-cube
2×associate-+l+
2×+-commutative
2×pow1
2×add-sqr-sqrt
1×distribute-lft-out
1×sum-log
1×associate-+r+
Counts
2 → 29
Calls
2 calls:
Slowest
23.0ms
(+ (+ (+ e d) (+ c b)) a)
6.0ms
(+ (+ e d) (+ c b))

series67.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(+ (+ (+ e d) (+ c b)) a)
32.0ms
(+ (+ e d) (+ c b))

simplify2.0s

Counts
17 → 35
Calls
17 calls:
Slowest
410.0ms
(+ (* (+ (pow e 3) (pow d 3)) (- c b)) (* (+ (* e e) (- (* d d) (* e d))) (- (* c c) (* b b))))
395.0ms
(+ (* (- (* e e) (* d d)) (- c b)) (* (- e d) (- (* c c) (* b b))))
362.0ms
(* (+ (* e e) (- (* d d) (* e d))) (- c b))
302.0ms
(* (+ (* e e) (- (* d d) (* e d))) (+ (* c c) (- (* b b) (* c b))))
144.0ms
(* (- e d) (+ (* c c) (- (* b b) (* c b))))

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (+ e d) (+ (+ c b) a))
0.2b
(+ (+ c b) a)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×flip-+
6×flip3-+
4×add-log-exp
4×frac-add
4×*-un-lft-identity
2×add-cube-cbrt
2×add-exp-log
2×add-cbrt-cube
2×associate-+l+
2×+-commutative
2×pow1
2×add-sqr-sqrt
1×distribute-lft-out
1×sum-log
1×associate-+r+
Counts
2 → 29
Calls
2 calls:
Slowest
14.0ms
(+ (+ e d) (+ (+ c b) a))
3.0ms
(+ (+ c b) a)

series45.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(+ (+ e d) (+ (+ c b) a))
10.0ms
(+ (+ c b) a)

simplify1.6s

Counts
16 → 35
Calls
16 calls:
Slowest
344.0ms
(* (- e d) (- (+ c b) a))
244.0ms
(* (exp (+ e d)) (exp (+ (+ c b) a)))
216.0ms
(+ (* (+ (pow e 3) (pow d 3)) (+ (* (+ c b) (+ c b)) (- (* a a) (* (+ c b) a)))) (* (+ (* e e) (- (* d d) (* e d))) (+ (pow (+ c b) 3) (pow a 3))))
168.0ms
(+ (+ e d) (+ (+ c b) a))
164.0ms
(* (+ (* e e) (- (* d d) (* e d))) (- (+ c b) a))

prune409.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
3×flip-+
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×flip3-+
3×*-un-lft-identity
3×+-commutative
3×pow1
3×add-sqr-sqrt
2×associate-+r+
1×associate-+l+
Counts
3 → 33
Calls
3 calls:
Slowest
3.0ms
(+ e (+ d (+ (+ c b) a)))
3.0ms
(+ d (+ (+ c b) a))
2.0ms
(+ (+ c b) a)

series74.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
35.0ms
(+ e (+ d (+ (+ c b) a)))
28.0ms
(+ d (+ (+ c b) a))
10.0ms
(+ (+ c b) a)

simplify62.0ms

Counts
10 → 42
Calls
10 calls:
Slowest
7.0ms
(+ a (+ b c))
6.0ms
(+ a (+ b c))
6.0ms
(+ a (+ b c))
6.0ms
(+ (+ c b) a)
6.0ms
(+ a (+ b c))

prune332.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes376.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample982.0ms

Algorithm
intervals