Average Error: 0.1 → 0.1
Time: 5.2s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[\left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x\]

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. Using strategy rm

  3. Applied associate-*r*0.1

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x}\]
  4. Using strategy rm

  5. Applied distribute-rgt-out--0.1

    \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)}\]
  6. Using strategy rm

  7. Applied associate-*r*0.1

    \[\leadsto x \cdot \left(0.954929658551372 - \color{blue}{\left(0.12900613773279798 \cdot x\right) \cdot x}\right)\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019007 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 4.8s)Debug log

sample160.0ms

Algorithm
intervals

simplify44.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
3 → 32
Calls

3 calls. Slowest were:

8.0ms
(* 0.12900613773279798 (* (* x x) x))
5.0ms
(* (* x x) x)
5.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

series279.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

173.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
78.0ms
(* 0.12900613773279798 (* (* x x) x))
28.0ms
(* (* x x) x)

simplify255.0ms

Counts
10 → 41
Calls

10 calls. Slowest were:

121.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
41.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
31.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune232.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
3 → 31
Calls

3 calls. Slowest were:

3.0ms
(* (* 0.12900613773279798 (* x x)) x)
2.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
1.0ms
(* 0.12900613773279798 (* x x))

series86.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

57.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
17.0ms
(* (* 0.12900613773279798 (* x x)) x)
12.0ms
(* 0.12900613773279798 (* x x))

simplify203.0ms

Counts
11 → 40
Calls

11 calls. Slowest were:

71.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
31.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
31.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune243.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

3.0ms
(* x (- 0.954929658551372 (* 0.12900613773279798 (* x x))))
2.0ms
(* 0.12900613773279798 (* x x))

series72.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

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

simplify635.0ms

Counts
15 → 32
Calls

15 calls. Slowest were:

189.0ms
(+ (* 0.954929658551372 0.954929658551372) (+ (* (* 0.12900613773279798 (* x x)) (* 0.12900613773279798 (* x x))) (* 0.954929658551372 (* 0.12900613773279798 (* x x)))))
60.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
57.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune249.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

2.0ms
(* (* 0.12900613773279798 x) x)
2.0ms
(* x (- 0.954929658551372 (* (* 0.12900613773279798 x) x)))

series73.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

55.0ms
(* x (- 0.954929658551372 (* (* 0.12900613773279798 x) x)))
18.0ms
(* (* 0.12900613773279798 x) x)

simplify491.0ms

Counts
15 → 32
Calls

15 calls. Slowest were:

162.0ms
(+ (* 0.954929658551372 0.954929658551372) (+ (* (* (* 0.12900613773279798 x) x) (* (* 0.12900613773279798 x) x)) (* 0.954929658551372 (* (* 0.12900613773279798 x) x))))
54.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
47.0ms
(* x (- (* (* 0.12900613773279798 x) x)))

prune256.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals