Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b \cdot a + c \cdot a\right) + d \cdot a\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019010 
(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: 8.1s)Debug log

sample52.0ms

Algorithm
intervals

simplify51.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
51.0ms
(* a (+ (+ b c) d))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cube-cbrt
3×associate-*r*
3×*-un-lft-identity
3×add-sqr-sqrt
2×add-log-exp
2×flip-+
2×add-exp-log
2×associate-*r/
2×add-cbrt-cube
2×flip3-+
2×pow1
1×*-commutative
1×distribute-lft-in
1×associate-+l+
1×+-commutative
1×distribute-rgt-in
Counts
2 → 26
Calls
2 calls:
Slowest
7.0ms
(* a (+ (+ b c) d))
4.0ms
(+ (+ b c) d)

series50.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
31.0ms
(* a (+ (+ b c) d))
19.0ms
(+ (+ b c) d)

simplify326.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
150.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
41.0ms
(+ (* a d) (+ (* a b) (* a c)))
34.0ms
(+ (* a d) (+ (* a b) (* a c)))
16.0ms
(sqrt (+ (+ b c) d))
15.0ms
(- (+ b c) d)

prune257.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
3×add-cube-cbrt
3×associate-*r*
3×*-un-lft-identity
3×add-sqr-sqrt
2×flip-+
2×add-exp-log
2×associate-*r/
2×add-cbrt-cube
2×flip3-+
2×distribute-lft-in
2×associate-+l+
2×pow1
2×distribute-rgt-in
1×distribute-lft-out
1×*-commutative
1×sum-log
1×+-commutative
Counts
2 → 29
Calls
2 calls:
Slowest
3.0ms
(+ (* a (+ b c)) (* a d))
1.0ms
(* a (+ b c))

series57.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
29.0ms
(* a (+ b c))
29.0ms
(+ (* a (+ b c)) (* a d))

simplify214.0ms

Counts
17 → 35
Calls
17 calls:
Slowest
77.0ms
(* (exp (* a (+ b c))) (exp (* a d)))
36.0ms
(+ (* a d) (+ (* a b) (* a c)))
33.0ms
(+ (* a d) (+ (* a b) (* a c)))
32.0ms
(+ (* b b) (- (* c c) (* b c)))
6.0ms
(+ (+ b c) d)

prune318.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×sum-log
2×flip-+
2×add-cube-cbrt
2×add-exp-log
2×add-cbrt-cube
2×distribute-rgt-out
2×flip3-+
2×*-un-lft-identity
2×+-commutative
2×pow1
2×add-sqr-sqrt
1×distribute-lft-out
1×associate-+l+
Counts
2 → 26
Calls
2 calls:
Slowest
9.0ms
(+ (+ (* b a) (* c a)) (* a d))
4.0ms
(+ (* b a) (* c a))

series51.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
33.0ms
(+ (+ (* b a) (* c a)) (* a d))
18.0ms
(+ (* b a) (* c a))

simplify228.0ms

Counts
12 → 32
Calls
12 calls:
Slowest
63.0ms
(* (exp (+ (* b a) (* c a))) (exp (* a d)))
58.0ms
(* (* (exp (* b a)) (exp (* c a))) (exp (* a d)))
36.0ms
(+ (* a d) (+ (* a b) (* a c)))
23.0ms
(+ (* a d) (+ (* a b) (* a c)))
19.0ms
(* (exp (* b a)) (exp (* c a)))

prune301.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))
0.1b
(sqrt (* a (+ b c)))
0.1b
(sqrt (* a (+ b c)))
0.0b
(+ (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (* a d))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×sqrt-div
9×flip-+
9×flip3-+
9×pow1
6×add-log-exp
6×add-cube-cbrt
6×add-exp-log
6×pow1/2
6×add-cbrt-cube
6×*-un-lft-identity
6×add-sqr-sqrt
4×sqrt-prod
4×associate-*l*
4×associate-*r*
4×frac-times
2×pow-prod-up
2×associate-*l/
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×sqrt-unprod
1×pow-plus
1×rem-square-sqrt
1×sum-log
1×+-commutative
1×pow2
Counts
4 → 67
Calls
4 calls:
Slowest
14.0ms
(+ (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (* a d))
13.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))
1.0ms
(sqrt (* a (+ b c)))
1.0ms
(sqrt (* a (+ b c)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(sqrt (* a (+ b c)))
41.0ms
(+ (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (* a d))
33.0ms
(sqrt (* a (+ b c)))
28.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))

simplify3.0s

Counts
49 → 79
Calls
49 calls:
Slowest
345.0ms
(* (* (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (sqrt (* a (+ b c)))) (* (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (sqrt (* a (+ b c)))))
336.0ms
(* (sqrt (* a (+ (pow b 3) (pow c 3)))) (sqrt (* a (- (* b b) (* c c)))))
312.0ms
(* (* a (+ b c)) (* a (+ b c)))
306.0ms
(* (sqrt (* a (- (* b b) (* c c)))) (sqrt (* a (+ (pow b 3) (pow c 3)))))
293.0ms
(* (* a (+ b c)) (* a (+ b c)))

prune876.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes546.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample1.5s

Algorithm
intervals