Average Error: 0.2 → 0.1
Time: 4.7s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[(\left(-0.12900613773279798\right) \cdot \left({x}^{3}\right) + \left(x \cdot 0.954929658551372\right))_*\]

Error

Bits error versus x

Derivation

  1. Initial program 0.2

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{(\left(-0.12900613773279798\right) \cdot \left({x}^{3}\right) + \left(0.954929658551372 \cdot x\right))_*}\]

  3. Final simplification0.1

    \[\leadsto (\left(-0.12900613773279798\right) \cdot \left({x}^{3}\right) + \left(x \cdot 0.954929658551372\right))_*\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 4.4s)Debug log

sample128.0ms

Algorithm
intervals

simplify67.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

66.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

2.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

series107.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

107.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

simplify162.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

70.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
47.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
43.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune150.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x x) x)
0.1b
(* 0.12900613773279798 (* (* x x) x))
0.0b
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
3 → 40
Calls

3 calls. Slowest were:

4.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
3.0ms
(* 0.12900613773279798 (* (* x x) x))
3.0ms
(* (* x x) x)

series83.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

45.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
21.0ms
(* (* x x) x)
17.0ms
(* 0.12900613773279798 (* (* x x) x))

simplify426.0ms

Counts
12 → 49
Calls

12 calls. Slowest were:

113.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
66.0ms
(fma 0.954929658551372 x (- (* (* (* x x) x) 0.12900613773279798)))
63.0ms
(fma (- (* (* x x) x)) 0.12900613773279798 (* (* (* x x) x) 0.12900613773279798))

prune392.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x x) x)
0.1b
(* 0.12900613773279798 (* (* x x) x))
0.0b
(fma 0.954929658551372 x (- (* 0.12900613773279798 (* (* x x) x))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 34
Calls

3 calls. Slowest were:

6.0ms
(* 0.12900613773279798 (* (* x x) x))
5.0ms
(* (* x x) x)
0.0ms
(fma 0.954929658551372 x (- (* 0.12900613773279798 (* (* x x) x))))

series89.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

56.0ms
(fma 0.954929658551372 x (- (* 0.12900613773279798 (* (* x x) x))))
19.0ms
(* 0.12900613773279798 (* (* x x) x))
15.0ms
(* (* x x) x)

simplify244.0ms

Counts
9 → 43
Calls

9 calls. Slowest were:

69.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
69.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
67.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune386.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 0.12900613773279798 (* x x))
0.1b
(* (* 0.12900613773279798 (* x x)) x)
0.0b
(fma 0.954929658551372 x (- (* (* 0.12900613773279798 (* x x)) x)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
3 → 32
Calls

3 calls. Slowest were:

6.0ms
(* (* 0.12900613773279798 (* x x)) x)
2.0ms
(* 0.12900613773279798 (* x x))
0.0ms
(fma 0.954929658551372 x (- (* (* 0.12900613773279798 (* x x)) x)))

series86.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

54.0ms
(fma 0.954929658551372 x (- (* (* 0.12900613773279798 (* x x)) x)))
19.0ms
(* (* 0.12900613773279798 (* x x)) x)
12.0ms
(* 0.12900613773279798 (* x x))

simplify176.0ms

Counts
9 → 41
Calls

9 calls. Slowest were:

68.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
35.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune388.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals