Average Error: 0.1 → 0.1
Time: 6.3s
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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2018362 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 4.1s)Debug log

start218.0ms

Algorithm
intervals

setup157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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)))

series320.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

200.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
85.0ms
(* 0.12900613773279798 (* (* x x) x))
34.0ms
(* (* x x) x)

simplify443.0ms

Counts
10 → 41
Calls

10 calls. Slowest were:

227.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
67.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
62.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune417.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize9.0ms

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)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

2.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
1.0ms
(* 0.12900613773279798 (pow x 3))

series59.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

40.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
19.0ms
(* 0.12900613773279798 (pow x 3))

simplify298.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

95.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (pow x 3))))
64.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
56.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune411.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
3 → 31
Calls

3 calls. Slowest were:

6.0ms
(* (* 0.12900613773279798 (* x x)) x)
4.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
2.0ms
(* 0.12900613773279798 (* x x))

series120.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

73.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
27.0ms
(* (* 0.12900613773279798 (* x x)) x)
20.0ms
(* 0.12900613773279798 (* x x))

simplify272.0ms

Counts
11 → 40
Calls

11 calls. Slowest were:

80.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
53.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
51.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune361.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

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))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
3 → 31
Calls

3 calls. Slowest were:

7.0ms
(* (* (* 0.12900613773279798 x) x) x)
5.0ms
(* (* 0.12900613773279798 x) x)
4.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))

series72.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

40.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
17.0ms
(* (* 0.12900613773279798 x) x)
16.0ms
(* (* (* 0.12900613773279798 x) x) x)

simplify374.0ms

Counts
12 → 40
Calls

12 calls. Slowest were:

101.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* (* 0.12900613773279798 x) x) x)))
64.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
63.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune457.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms