Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[(d1 \cdot \left(d2 + 37\right) + \left(d3 \cdot d1\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

  2. Initial simplification0.0

    \[\leadsto (d1 \cdot \left(d2 + 37\right) + \left(d3 \cdot d1\right))_*\]

  3. Final simplification0.0

    \[\leadsto (d1 \cdot \left(d2 + 37\right) + \left(d3 \cdot d1\right))_*\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))

Details

Time bar (total: 9.1s)Debug log

start78.0ms

Algorithm
intervals

setup321.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma d1 (+ d2 37) (* d3 d1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma d1 (+ d2 37) (* d3 d1))

series33.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

33.0ms
(fma d1 (+ d2 37) (* d3 d1))

simplify195.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

83.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
63.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
47.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune109.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
0.0b
(* (+ d3 5) d1)
0.0b
(+ (* d1 d2) (* (+ d3 5) d1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

17.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
5.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
5.0ms
(* (+ d3 5) d1)

series70.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

30.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
26.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
14.0ms
(* (+ d3 5) d1)

simplify1.6s

Counts
19 → 56
Calls

19 calls. Slowest were:

342.0ms
(* (exp (+ (* d1 d2) (* (+ d3 5) d1))) (exp (* d1 32)))
298.0ms
(* (- (* d3 d3) (* 5 5)) d1)
266.0ms
(* (* (exp (* d1 d2)) (exp (* (+ d3 5) d1))) (exp (* d1 32)))

prune753.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ d3 5))
0.7b
(cbrt (+ d3 5))
0.7b
(cbrt (+ d3 5))
0.7b
(* (cbrt (+ d3 5)) (cbrt (+ d3 5)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 83
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (+ d3 5)) (cbrt (+ d3 5)))
1.0ms
(cbrt (+ d3 5))
1.0ms
(cbrt (+ d3 5))

series166.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

54.0ms
(cbrt (+ d3 5))
43.0ms
(cbrt (+ d3 5))
36.0ms
(cbrt (+ d3 5))
33.0ms
(* (cbrt (+ d3 5)) (cbrt (+ d3 5)))

simplify3.7s

Counts
59 → 95
Calls

59 calls. Slowest were:

559.0ms
(- (+ (* 1/15 (* d3 (pow 5 1/3))) (pow 5 1/3)) (* 1/225 (* (pow d3 2) (pow 5 1/3))))
497.0ms
(- (+ (* 2/15 (* d3 (pow 25 1/3))) (pow 25 1/3)) (* 1/225 (* (pow d3 2) (pow 25 1/3))))
476.0ms
(- (+ (* 1/15 (* d3 (pow 5 1/3))) (pow 5 1/3)) (* 1/225 (* (pow d3 2) (pow 5 1/3))))

prune1.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes347.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms