Average Error: 0.1 → 0.1
Time: 5.3s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - \left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x\]

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 4.9s)Debug log

sample145.0ms

Algorithm
intervals

simplify104.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

104.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 1 expressions with local error:

0.3b
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series64.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

64.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

simplify162.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

69.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
51.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
41.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune129.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(* 0.12900613773279798 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
3 → 40
Calls

3 calls. Slowest were:

6.0ms
(* 0.12900613773279798 (* (* x x) x))
5.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
4.0ms
(* (* x x) x)

series95.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

55.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
27.0ms
(* 0.12900613773279798 (* (* x x) x))
14.0ms
(* (* x x) x)

simplify476.0ms

Counts
12 → 49
Calls

12 calls. Slowest were:

90.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
73.0ms
(fma 0.954929658551372 x (- (* (* (* x x) x) 0.12900613773279798)))
72.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune385.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

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))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 39
Calls

3 calls. Slowest were:

5.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
5.0ms
(* (* 0.12900613773279798 (* x x)) x)
1.0ms
(* 0.12900613773279798 (* x x))

series95.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

59.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
18.0ms
(* 0.12900613773279798 (* x x))
18.0ms
(* (* 0.12900613773279798 (* x x)) x)

simplify493.0ms

Counts
13 → 48
Calls

13 calls. Slowest were:

96.0ms
(fma (- x) (* 0.12900613773279798 (* x x)) (* x (* 0.12900613773279798 (* x x))))
80.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
71.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune342.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
3 → 39
Calls

3 calls. Slowest were:

11.0ms
(* (* (* 0.12900613773279798 x) x) x)
4.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
4.0ms
(* (* 0.12900613773279798 x) x)

series98.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

53.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
28.0ms
(* (* (* 0.12900613773279798 x) x) x)
17.0ms
(* (* 0.12900613773279798 x) x)

simplify417.0ms

Counts
14 → 48
Calls

14 calls. Slowest were:

107.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* (* 0.12900613773279798 x) x) x)))
94.0ms
(fma (- x) (* (* 0.12900613773279798 x) x) (* x (* (* 0.12900613773279798 x) x)))
56.0ms
(fma 0.954929658551372 x (- (* x (* (* 0.12900613773279798 x) x))))

prune335.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

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