Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[(a \cdot \left(b + d\right) + \left(c \cdot a\right))_*\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

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

  2. Initial simplification0.0

    \[\leadsto (a \cdot \left(b + d\right) + \left(a \cdot c\right))_*\]

  3. Final simplification0.0

    \[\leadsto (a \cdot \left(b + d\right) + \left(c \cdot a\right))_*\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

  (* a (+ (+ b c) d)))

Details

Time bar (total: 6.1s)Debug log

start55.0ms

Algorithm
intervals

setup70.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma a (+ b d) (* a c))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma a (+ b d) (* a c))

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

35.0ms
(fma a (+ b d) (* a c))

simplify158.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

82.0ms
(+ (* a d) (+ (* a b) (* a c)))
75.0ms
(+ (* a d) (+ (* a b) (* a c)))
1.0ms
0

prune114.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b
(* a (+ (+ b c) d))
0.0b
(+ (+ b c) d)

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 33
Calls

2 calls. Slowest were:

8.0ms
(* a (+ (+ b c) d))
5.0ms
(+ (+ b c) d)

series50.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

32.0ms
(* a (+ (+ b c) d))
18.0ms
(+ (+ b c) d)

simplify391.0ms

Counts
15 → 39
Calls

15 calls. Slowest were:

172.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
73.0ms
(+ (* a d) (+ (* a b) (* a c)))
39.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune379.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (sqrt (+ b c)) (sqrt (+ b c)) d)
0.1b
(* a (fma (sqrt (+ b c)) (sqrt (+ b c)) d))
0.0b
(sqrt (+ b c))
0.0b
(sqrt (+ b c))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

1.0ms
(* a (fma (sqrt (+ b c)) (sqrt (+ b c)) d))
1.0ms
(sqrt (+ b c))
1.0ms
(sqrt (+ b c))

series208.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

108.0ms
(* a (fma (sqrt (+ b c)) (sqrt (+ b c)) d))
64.0ms
(fma (sqrt (+ b c)) (sqrt (+ b c)) d)
19.0ms
(sqrt (+ b c))
18.0ms
(sqrt (+ b c))

simplify152.0ms

Counts
29 → 69
Calls

29 calls. Slowest were:

39.0ms
(sqrt (- (* b b) (* c c)))
34.0ms
(sqrt (- (* b b) (* c c)))
19.0ms
(sqrt (fma (sqrt (+ b c)) (sqrt (+ b c)) d))

prune639.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ b c))) (sqrt (sqrt (+ b c))))
0.3b
(fma (sqrt (+ b c)) (* (sqrt (sqrt (+ b c))) (sqrt (sqrt (+ b c)))) d)
0.1b
(sqrt (sqrt (+ b c)))
0.1b
(sqrt (sqrt (+ b c)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 96
Calls

4 calls. Slowest were:

7.0ms
(* (sqrt (sqrt (+ b c))) (sqrt (sqrt (+ b c))))
1.0ms
(sqrt (sqrt (+ b c)))
1.0ms
(sqrt (sqrt (+ b c)))

series433.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

171.0ms
(sqrt (sqrt (+ b c)))
160.0ms
(sqrt (sqrt (+ b c)))
82.0ms
(fma (sqrt (+ b c)) (* (sqrt (sqrt (+ b c))) (sqrt (sqrt (+ b c)))) d)
19.0ms
(* (sqrt (sqrt (+ b c))) (sqrt (sqrt (+ b c))))

simplify1.7s

Counts
72 → 108
Calls

72 calls. Slowest were:

246.0ms
(- (+ (pow c 1/4) (* 1/4 (* b (pow (/ 1 (pow c 3)) 1/4)))) (* 3/32 (* (pow b 2) (pow (/ 1 (pow c 7)) 1/4))))
233.0ms
(- (+ (pow c 1/4) (* 1/4 (* b (pow (/ 1 (pow c 3)) 1/4)))) (* 3/32 (* (pow b 2) (pow (/ 1 (pow c 7)) 1/4))))
165.0ms
(* (sqrt (sqrt (+ (pow b 3) (pow c 3)))) (sqrt (sqrt (- (* b b) (* c c)))))

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes300.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms