Average Error: 0.4 → 0.3
Time: 10.7s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(c + \left(a + b\right)\right) + \left(d + e\right)\]

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
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019022 
(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: 10.0s)Debug log

sample54.0ms

Algorithm
intervals
Results
21.0ms256×pre80true
17.0ms256×body80valid

simplify280.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
280.0ms
(+ (+ (+ (+ e d) c) b) a)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite82.0ms

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
66.0ms
(+ (+ (+ (+ e d) c) b) a)
11.0ms
(+ (+ (+ e d) c) b)
4.0ms
(+ (+ e d) c)

series71.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
36.0ms
(+ (+ (+ (+ e d) c) b) a)
20.0ms
(+ (+ (+ e d) c) b)
14.0ms
(+ (+ e d) c)

simplify80.0ms

Counts
11 → 42
Calls
11 calls:
Slowest
12.0ms
(+ e (+ c d))
12.0ms
(+ a (+ b c))
11.0ms
(+ (+ e d) c)
7.0ms
(+ b (+ c d))
6.0ms
(+ a (+ b c))

prune382.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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
24.0ms
(+ (+ (+ e d) c) (+ b a))
5.0ms
(+ (+ e d) c)

series57.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
43.0ms
(+ (+ (+ e d) c) (+ b a))
14.0ms
(+ (+ e d) c)

simplify2.5s

Counts
17 → 35
Calls
17 calls:
Slowest
543.0ms
(+ (* (+ (pow (+ e d) 3) (pow c 3)) (+ (* b b) (- (* a a) (* b a)))) (* (+ (* (+ e d) (+ e d)) (- (* c c) (* (+ e d) c))) (+ (pow b 3) (pow a 3))))
372.0ms
(* (- (+ e d) c) (+ (* b b) (- (* a a) (* b a))))
307.0ms
(* (+ (* (+ e d) (+ e d)) (- (* c c) (* (+ e d) c))) (- b a))
296.0ms
(* (- (+ e d) c) (- b a))
222.0ms
(* (exp (+ (+ e d) c)) (exp (+ b a)))

prune349.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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-+r+
2×+-commutative
2×pow1
2×add-sqr-sqrt
1×distribute-lft-out
1×sum-log
1×associate-+l+
Counts
2 → 29
Calls
2 calls:
Slowest
4.0ms
(+ (+ e d) (+ c (+ b a)))
1.0ms
(+ c (+ b a))

series53.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
43.0ms
(+ (+ e d) (+ c (+ b a)))
10.0ms
(+ c (+ b a))

simplify1.7s

Counts
17 → 35
Calls
17 calls:
Slowest
288.0ms
(* (exp (+ e d)) (exp (+ c (+ b a))))
251.0ms
(* (- e d) (- c (+ b a)))
222.0ms
(+ (+ e d) (+ c (+ b a)))
192.0ms
(+ (* (+ (pow e 3) (pow d 3)) (+ (* c c) (- (* (+ b a) (+ b a)) (* c (+ b a))))) (* (+ (* e e) (- (* d d) (* e d))) (+ (pow c 3) (pow (+ b a) 3))))
187.0ms
(+ (* (- (* e e) (* d d)) (+ (* c c) (- (* (+ b a) (+ b a)) (* c (+ b a))))) (* (- e d) (+ (pow c 3) (pow (+ b a) 3))))

prune402.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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-+r+
2×+-commutative
2×pow1
2×add-sqr-sqrt
1×distribute-lft-out
1×sum-log
1×associate-+l+
Counts
2 → 29
Calls
2 calls:
Slowest
4.0ms
(+ (+ e (+ c d)) (+ b a))
1.0ms
(+ e (+ c d))

series73.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
56.0ms
(+ (+ e (+ c d)) (+ b a))
17.0ms
(+ e (+ c d))

simplify2.0s

Counts
16 → 35
Calls
16 calls:
Slowest
325.0ms
(* (exp (+ e (+ c d))) (exp (+ b a)))
312.0ms
(* (+ (* e e) (- (* (+ c d) (+ c d)) (* e (+ c d)))) (- b a))
223.0ms
(* (- e (+ c d)) (- b a))
204.0ms
(+ (* (+ (pow e 3) (pow (+ c d) 3)) (+ (* b b) (- (* a a) (* b a)))) (* (+ (* e e) (- (* (+ c d) (+ c d)) (* e (+ c d)))) (+ (pow b 3) (pow a 3))))
203.0ms
(* (- e (+ c d)) (+ (* b b) (- (* a a) (* b a))))

prune378.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes337.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
612.0ms8000×pre80true
394.0ms8000×body80valid