Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[\left(d3 + d2\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(d2 + d3\right)\]

Derivation

  1. Initial program 0.0

    \[d1 \cdot d2 + d1 \cdot d3\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(d2 + d3\right) \cdot d1}\]

  3. Final simplification0.0

    \[\leadsto \left(d3 + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

  :herbie-target
  (* d1 (+ d2 d3))

  (+ (* d1 d2) (* d1 d3)))

Details

Time bar (total: 6.7s)Debug log

sample50.0ms

Algorithm
intervals

simplify11.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

11.0ms
(+ (* d1 d2) (* d1 d3))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 d3) d1)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

5.0ms
(* (+ d2 d3) d1)

series26.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

26.0ms
(* (+ d2 d3) d1)

simplify265.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

204.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
41.0ms
(* (+ (pow d2 3) (pow d3 3)) d1)
6.0ms
(+ (* d3 d1) (* d2 d1))

prune177.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (* d1 d2) (* d1 d3))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(+ (* d1 d2) (* d1 d3))

series33.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

33.0ms
(+ (* d1 d2) (* d1 d3))

simplify30.0ms

Counts
5 → 18
Calls

5 calls. Slowest were:

11.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
6.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d2 d1) (* d3 d1))

prune524.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

18.6b
(/ (* (- (* d2 d2) (* d3 d3)) d1) (- d2 d3))
9.1b
(* (- (* d2 d2) (* d3 d3)) d1)
3.0b
(- (* d2 d2) (* d3 d3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
3 → 58
Calls

3 calls. Slowest were:

13.0ms
(/ (* (- (* d2 d2) (* d3 d3)) d1) (- d2 d3))
9.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
4.0ms
(- (* d2 d2) (* d3 d3))

series98.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

55.0ms
(/ (* (- (* d2 d2) (* d3 d3)) d1) (- d2 d3))
27.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
17.0ms
(- (* d2 d2) (* d3 d3))

simplify3.6s

Counts
35 → 67
Calls

35 calls. Slowest were:

584.0ms
(* (- (* (* d2 d2) (* d2 d2)) (* (* d3 d3) (* d3 d3))) d1)
556.0ms
(* (- (* (* d2 d2) (* d2 d2)) (* (* d3 d3) (* d3 d3))) d1)
344.0ms
(* (- (pow (* d2 d2) 3) (pow (* d3 d3) 3)) d1)

prune680.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes158.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample985.0ms

Algorithm
intervals