Average Error: 0.1 → 0.1
Time: 4.9s
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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019002 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 4.6s)Debug log

sample185.0ms

Algorithm
intervals

simplify75.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

75.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 3 expressions with local error:

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

7.0ms
(* (* x x) x)
6.0ms
(* 0.12900613773279798 (* (* x x) x))
5.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

series116.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

59.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
32.0ms
(* (* x x) x)
25.0ms
(* 0.12900613773279798 (* (* x x) x))

simplify277.0ms

Counts
10 → 41
Calls

10 calls. Slowest were:

110.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
57.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
36.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune278.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.12900613773279798 (pow x 3))
0.0b
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

5.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
3.0ms
(* 0.12900613773279798 (pow x 3))

series98.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

70.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
28.0ms
(* 0.12900613773279798 (pow x 3))

simplify251.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

82.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (pow x 3))))
48.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune240.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

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

series64.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

47.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 x) (* x x)))
16.0ms
(* (* 0.12900613773279798 x) (* x x))

simplify575.0ms

Counts
10 → 31
Calls

10 calls. Slowest were:

336.0ms
(* (* (* (* 0.12900613773279798 x) (* 0.12900613773279798 x)) (* 0.12900613773279798 x)) (* (* (* x x) (* x x)) (* x x)))
77.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 x) (* x x))))
38.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune216.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
3 → 31
Calls

3 calls. Slowest were:

14.0ms
(* (* (* 0.12900613773279798 x) x) x)
4.0ms
(* (* 0.12900613773279798 x) x)
4.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))

series78.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

46.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
16.0ms
(* (* 0.12900613773279798 x) x)
16.0ms
(* (* (* 0.12900613773279798 x) x) x)

simplify270.0ms

Counts
12 → 40
Calls

12 calls. Slowest were:

91.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* (* 0.12900613773279798 x) x) x)))
52.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
35.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune317.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes55.0ms

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