Average Error: 0.1 → 0.1
Time: 7.8s
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. Initial simplification0.1

    \[\leadsto 0.954929658551372 \cdot x - \left(0.12900613773279798 \cdot x\right) \cdot \left(x \cdot x\right)\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

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

  6. Applied distribute-rgt-out--0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2018365 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 5.8s)Debug log

start805.0ms

Algorithm
intervals

setup142.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

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)))

rewrite10.0ms

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)))

series185.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

119.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 x) (* x x)))
66.0ms
(* (* 0.12900613773279798 x) (* x x))

simplify683.0ms

Counts
10 → 31
Calls

10 calls. Slowest were:

360.0ms
(* (* (* (* 0.12900613773279798 x) (* 0.12900613773279798 x)) (* 0.12900613773279798 x)) (* (* (* x x) (* x x)) (* x x)))
112.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 x) (* x x))))
66.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune332.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
3 → 31
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)

series83.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

52.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
16.0ms
(* (* (* 0.12900613773279798 x) x) x)
14.0ms
(* (* 0.12900613773279798 x) x)

simplify293.0ms

Counts
12 → 40
Calls

12 calls. Slowest were:

82.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* (* 0.12900613773279798 x) x) x)))
55.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
55.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune458.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

series76.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

64.0ms
(* x (- 0.954929658551372 (* (* 0.12900613773279798 x) x)))
12.0ms
(* (* 0.12900613773279798 x) x)

simplify616.0ms

Counts
15 → 32
Calls

15 calls. Slowest were:

236.0ms
(+ (* 0.954929658551372 0.954929658551372) (+ (* (* (* 0.12900613773279798 x) x) (* (* 0.12900613773279798 x) x)) (* 0.954929658551372 (* (* 0.12900613773279798 x) x))))
67.0ms
(* x (- (* (* 0.12900613773279798 x) x)))
60.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune336.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

23.7b
(sqrt (* (* 0.12900613773279798 x) x))
23.7b
(sqrt (* (* 0.12900613773279798 x) x))
0.3b
(* (sqrt (* (* 0.12900613773279798 x) x)) (sqrt (* (* 0.12900613773279798 x) x)))
0.2b
(* (* 0.12900613773279798 x) x)

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 53
Calls

4 calls. Slowest were:

8.0ms
(* (sqrt (* (* 0.12900613773279798 x) x)) (sqrt (* (* 0.12900613773279798 x) x)))
3.0ms
(* (* 0.12900613773279798 x) x)
1.0ms
(sqrt (* (* 0.12900613773279798 x) x))

series150.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

82.0ms
(* (sqrt (* (* 0.12900613773279798 x) x)) (sqrt (* (* 0.12900613773279798 x) x)))
25.0ms
(sqrt (* (* 0.12900613773279798 x) x))
24.0ms
(sqrt (* (* 0.12900613773279798 x) x))
19.0ms
(* (* 0.12900613773279798 x) x)

simplify616.0ms

Counts
32 → 65
Calls

32 calls. Slowest were:

309.0ms
(* (* (* (sqrt (* (* 0.12900613773279798 x) x)) (sqrt (* (* 0.12900613773279798 x) x))) (sqrt (* (* 0.12900613773279798 x) x))) (* (* (sqrt (* (* 0.12900613773279798 x) x)) (sqrt (* (* 0.12900613773279798 x) x))) (sqrt (* (* 0.12900613773279798 x) x))))
70.0ms
(* (* (* 0.12900613773279798 x) x) (* (* 0.12900613773279798 x) x))
44.0ms
(* (* (* 0.12900613773279798 x) x) (* (* 0.12900613773279798 x) x))

prune765.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms