Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[\left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x\]

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. 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. Final simplification0.1

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

Reproduce

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

Details

Time bar (total: 4.7s)Debug log

sample142.0ms

Algorithm
intervals

simplify69.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

68.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series109.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

109.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

simplify162.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

64.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
53.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
43.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune97.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
3 → 40
Calls

3 calls. Slowest were:

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

series78.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

41.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
23.0ms
(* 0.12900613773279798 (* (* x x) x))
14.0ms
(* (* x x) x)

simplify404.0ms

Counts
12 → 49
Calls

12 calls. Slowest were:

97.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
77.0ms
(fma (- (* (* x x) x)) 0.12900613773279798 (* (* (* x x) x) 0.12900613773279798))
60.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune355.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

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 → 39
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))

series82.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

48.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
19.0ms
(* (* 0.12900613773279798 (* x x)) x)
15.0ms
(* 0.12900613773279798 (* x x))

simplify509.0ms

Counts
13 → 48
Calls

13 calls. Slowest were:

117.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
80.0ms
(fma (- x) (* 0.12900613773279798 (* x x)) (* x (* 0.12900613773279798 (* x x))))
69.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune327.0ms

Pruning

4 alts after pruning (3 fresh and 1 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))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 30
Calls

2 calls. Slowest were:

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

series65.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

45.0ms
(* x (- 0.954929658551372 (* 0.12900613773279798 (* x x))))
20.0ms
(* 0.12900613773279798 (* x x))

simplify671.0ms

Counts
15 → 36
Calls

15 calls. Slowest were:

248.0ms
(+ (* 0.954929658551372 0.954929658551372) (+ (* (* 0.12900613773279798 (* x x)) (* 0.12900613773279798 (* x x))) (* 0.954929658551372 (* 0.12900613773279798 (* x x)))))
68.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
56.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune253.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals