Average Error: 0.1 → 0.1
Time: 5.8s
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. 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. Using strategy rm

  7. Applied associate-*r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019016 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 5.4s)Debug log

sample230.0ms

Algorithm
intervals
Results
413×(pre true 80)
413×(body real 80)

simplify112.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
111.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.5b
(* 0.12900613773279798 (* (* x x) x))
0.2b
(* (* x x) x)
0.0b
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×*-commutative
1×flip--
1×pow3
1×associate-*l*
1×associate-*r*
1×diff-log
1×flip3--
1×pow-plus
1×sub-neg
1×pow2
Counts
3 → 32
Calls
3 calls:
Slowest
8.0ms
(* 0.12900613773279798 (* (* x x) x))
5.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
5.0ms
(* (* x x) x)

series143.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
79.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
40.0ms
(* 0.12900613773279798 (* (* x x) x))
24.0ms
(* (* x x) x)

simplify312.0ms

Counts
10 → 41
Calls
10 calls:
Slowest
122.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
60.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
53.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
37.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
11.0ms
(* 0.12900613773279798 (pow x 3))

prune285.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×*-commutative
1×flip--
1×associate-*l*
1×associate-*r*
1×diff-log
1×distribute-rgt-out--
1×flip3--
1×sub-neg
Counts
3 → 31
Calls
3 calls:
Slowest
3.0ms
(* (* 0.12900613773279798 (* x x)) x)
2.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
1.0ms
(* 0.12900613773279798 (* x x))

series90.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
59.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
18.0ms
(* (* 0.12900613773279798 (* x x)) x)
13.0ms
(* 0.12900613773279798 (* x x))

simplify263.0ms

Counts
11 → 40
Calls
11 calls:
Slowest
83.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
56.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
39.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
33.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
21.0ms
(- 0.954929658551372 (* 0.12900613773279798 (* x x)))

prune314.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-cube-cbrt
4×associate-*r*
4×*-un-lft-identity
4×add-sqr-sqrt
3×add-log-exp
3×add-exp-log
3×add-cbrt-cube
3×sub-neg
3×pow1
2×flip--
2×*-commutative
2×associate-*r/
2×flip3--
2×distribute-lft-in
2×distribute-rgt-in
Counts
3 → 37
Calls
3 calls:
Slowest
1.0ms
(* x (- 0.954929658551372 (* 0.12900613773279798 (* x x))))
1.0ms
(* 0.12900613773279798 (* x x))
1.0ms
(- 0.954929658551372 (* 0.12900613773279798 (* x x)))

series98.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
45.0ms
(* x (- 0.954929658551372 (* 0.12900613773279798 (* x x))))
35.0ms
(- 0.954929658551372 (* 0.12900613773279798 (* x x)))
18.0ms
(* 0.12900613773279798 (* x x))

simplify574.0ms

Counts
18 → 46
Calls
18 calls:
Slowest
171.0ms
(+ (* 0.954929658551372 0.954929658551372) (+ (* (* 0.12900613773279798 (* x x)) (* 0.12900613773279798 (* x x))) (* 0.954929658551372 (* 0.12900613773279798 (* x x)))))
45.0ms
(* (- (* 0.12900613773279798 (* x x))) x)
44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
41.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
39.0ms
(* x (- (* 0.12900613773279798 (* x x))))

prune419.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-cube-cbrt
4×*-un-lft-identity
4×add-sqr-sqrt
3×add-log-exp
3×add-exp-log
3×associate-*r*
3×add-cbrt-cube
3×sub-neg
3×pow1
2×flip--
2×*-commutative
2×associate-*r/
2×flip3--
2×distribute-lft-in
2×distribute-rgt-in
1×associate-*l*
Counts
3 → 37
Calls
3 calls:
Slowest
4.0ms
(* (* 0.12900613773279798 x) x)
3.0ms
(* x (- 0.954929658551372 (* (* 0.12900613773279798 x) x)))
1.0ms
(- 0.954929658551372 (* (* 0.12900613773279798 x) x))

series108.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
45.0ms
(- 0.954929658551372 (* (* 0.12900613773279798 x) x))
43.0ms
(* x (- 0.954929658551372 (* (* 0.12900613773279798 x) x)))
20.0ms
(* (* 0.12900613773279798 x) x)

simplify656.0ms

Counts
18 → 46
Calls
18 calls:
Slowest
211.0ms
(+ (* 0.954929658551372 0.954929658551372) (+ (* (* (* 0.12900613773279798 x) x) (* (* 0.12900613773279798 x) x)) (* 0.954929658551372 (* (* 0.12900613773279798 x) x))))
50.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
50.0ms
(* (- (* (* 0.12900613773279798 x) x)) x)
44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
39.0ms
(* x (- (* (* 0.12900613773279798 x) x)))

prune339.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes58.0ms

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
Results
12041×(pre true 80)
12041×(body real 80)