Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[(d1 \cdot \left(37 + d2\right) + \left(d3 \cdot d1\right))_*\]

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. Simplified0.0

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

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{d2 \cdot d1 + \left(d3 \cdot d1 + 37 \cdot d1\right)}\]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019002 +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: 10.4s)Debug log

sample70.0ms

Algorithm
intervals

simplify540.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

540.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

28.0ms
(fma (+ d2 d3) d1 (* d1 37))

simplify208.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

80.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
78.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
49.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune116.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

19.0ms
(fma d1 (+ 37 d2) (* d3 d1))

simplify196.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

77.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
69.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
50.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune104.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

16.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
6.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
5.0ms
(* (+ d3 5) d1)

series61.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

23.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
21.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
17.0ms
(* (+ d3 5) d1)

simplify1.3s

Counts
19 → 56
Calls

19 calls. Slowest were:

247.0ms
(* (* (exp (* d1 d2)) (exp (* (+ d3 5) d1))) (exp (* d1 32)))
217.0ms
(* (exp (+ (* d1 d2) (* (+ d3 5) d1))) (exp (* d1 32)))
142.0ms
(* (- (* d3 d3) (* 5 5)) d1)

prune499.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

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))

series193.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

55.0ms
(cbrt (+ d3 5))
51.0ms
(cbrt (+ d3 5))
44.0ms
(* (cbrt (+ d3 5)) (cbrt (+ d3 5)))
43.0ms
(cbrt (+ d3 5))

simplify3.8s

Counts
59 → 95
Calls

59 calls. Slowest were:

537.0ms
(- (+ (* 2/15 (* d3 (pow 25 1/3))) (pow 25 1/3)) (* 1/225 (* (pow d3 2) (pow 25 1/3))))
532.0ms
(- (+ (* 1/15 (* d3 (pow 5 1/3))) (pow 5 1/3)) (* 1/225 (* (pow d3 2) (pow 5 1/3))))
508.0ms
(- (+ (* 1/15 (* d3 (pow 5 1/3))) (pow 5 1/3)) (* 1/225 (* (pow d3 2) (pow 5 1/3))))

prune1.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals