Average Error: 0.1 → 0.1
Time: 3.3s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[(d1 \cdot \left(d2 + d3\right) + \left(3 \cdot d1\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{(d1 \cdot \left(d2 + d3\right) + \left(d1 \cdot 3\right))_*}\]

  3. Final simplification0.1

    \[\leadsto (d1 \cdot \left(d2 + d3\right) + \left(3 \cdot d1\right))_*\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))

Details

Time bar (total: 2.9s)Debug log

sample81.0ms

Algorithm
intervals
Results
330×(pre true 80)
317×(body real 80)
5×(body real 320)
5×(body real 640)
2×(body real 1280)
1×(body real 160)

simplify77.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
76.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma d1 (+ d2 d3) (* d1 3))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×log1p-expm1-u
1×fma-udef
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 10
Calls
1 calls:
Slowest
0.0ms
(fma d1 (+ d2 d3) (* d1 3))

series34.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
34.0ms
(fma d1 (+ d2 d3) (* d1 3))

simplify179.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
77.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
52.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
49.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune157.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma d1 (+ 3 d2) (* d3 d1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×log1p-expm1-u
1×fma-udef
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 10
Calls
1 calls:
Slowest
0.0ms
(fma d1 (+ 3 d2) (* d3 d1))

series22.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
22.0ms
(fma d1 (+ 3 d2) (* d3 d1))

simplify193.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
80.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
63.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
50.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune143.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes151.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
10133×(pre true 80)
9609×(body real 80)
214×(body real 640)
145×(body real 320)
90×(body real 1280)
75×(body real 160)