Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{0.12900613773279798 \cdot {x}^{3}}\]

  3. Final simplification0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 2.4s)Debug log

start161.0ms

Algorithm
intervals

setup120.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.12900613773279798 (* (* x x) x))
0.1b
(* (* x x) x)

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 20
Calls

2 calls. Slowest were:

7.0ms
(* 0.12900613773279798 (* (* x x) x))
4.0ms
(* (* x x) x)

series62.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

34.0ms
(* (* x x) x)
26.0ms
(* 0.12900613773279798 (* (* x x) x))

simplify27.0ms

Counts
6 → 26
Calls

6 calls. Slowest were:

5.0ms
(* 0.12900613773279798 (pow x 3))
5.0ms
(* 0.12900613773279798 (pow x 3))
5.0ms
(* 0.12900613773279798 (pow x 3))

prune243.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 0.12900613773279798 (pow x 3))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

2.0ms
(* 0.12900613773279798 (pow x 3))

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

28.0ms
(* 0.12900613773279798 (pow x 3))

simplify47.0ms

Counts
7 → 16
Calls

7 calls. Slowest were:

14.0ms
(* 0.12900613773279798 (pow x 3))
11.0ms
(* 0.12900613773279798 (pow x 3))
10.0ms
(* 0.12900613773279798 (pow x 3))

prune208.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.2b
(* (* 0.12900613773279798 x) (* x x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

4.0ms
(* (* 0.12900613773279798 x) (* x x))

series22.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

22.0ms
(* (* 0.12900613773279798 x) (* x x))

simplify725.0ms

Counts
6 → 16
Calls

6 calls. Slowest were:

675.0ms
(* (* (* (* 0.12900613773279798 x) (* 0.12900613773279798 x)) (* 0.12900613773279798 x)) (* (* (* x x) (* x x)) (* x x)))
21.0ms
(+ (log (* 0.12900613773279798 x)) (log (* x x)))
12.0ms
(* (* 0.12900613773279798 x) (* x x))

prune216.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (* 0.12900613773279798 (* x x)) x)
0.2b
(* 0.12900613773279798 (* x x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 18
Calls

2 calls. Slowest were:

6.0ms
(* (* 0.12900613773279798 (* x x)) x)
2.0ms
(* 0.12900613773279798 (* x x))

series39.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

27.0ms
(* (* 0.12900613773279798 (* x x)) x)
12.0ms
(* 0.12900613773279798 (* x x))

simplify30.0ms

Counts
6 → 24
Calls

6 calls. Slowest were:

6.0ms
(* 0.12900613773279798 (pow x 2))
6.0ms
(* 0.12900613773279798 (pow x 3))
5.0ms
(* 0.12900613773279798 (pow x 3))

prune289.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.0b

regimes102.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms