Average Error: 0.1 → 0.1
Time: 4.4s
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. Using strategy rm

  3. Applied pow30.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019022 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 4.1s)Debug log

sample104.0ms

Algorithm
intervals
Results
58.0ms367×body80valid

simplify44.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

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

series119.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
72.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
30.0ms
(* (* x x) x)
16.0ms
(* 0.12900613773279798 (* (* x x) x))

simplify270.0ms

Counts
10 → 41
Calls
10 calls:
Slowest
114.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
61.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
36.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
35.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
10.0ms
(* 0.12900613773279798 (pow x 3))

prune270.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
5×associate-*r*
4×add-log-exp
3×add-cube-cbrt
3×*-un-lft-identity
3×add-sqr-sqrt
2×add-exp-log
2×add-cbrt-cube
2×pow1
1×flip--
1×*-commutative
1×unpow3
1×diff-log
1×flip3--
1×sub-neg
1×cube-mult
Counts
2 → 25
Calls
2 calls:
Slowest
4.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
2.0ms
(* 0.12900613773279798 (pow x 3))

series79.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
49.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
29.0ms
(* 0.12900613773279798 (pow x 3))

simplify214.0ms

Counts
11 → 31
Calls
11 calls:
Slowest
72.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (pow x 3))))
43.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
40.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
29.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
9.0ms
(* 0.12900613773279798 (pow x 3))

prune222.0ms

Pruning

5 alts after pruning (3 fresh and 2 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))

rewrite9.0ms

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
4.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
3.0ms
(* (* 0.12900613773279798 (* x x)) x)
2.0ms
(* 0.12900613773279798 (* x x))

series92.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
56.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
24.0ms
(* (* 0.12900613773279798 (* x x)) x)
12.0ms
(* 0.12900613773279798 (* x x))

simplify235.0ms

Counts
11 → 40
Calls
11 calls:
Slowest
61.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
42.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
40.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
33.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
20.0ms
(- 0.954929658551372 (* 0.12900613773279798 (* x x)))

prune293.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

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
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
2×associate-*l*
1×flip--
1×diff-log
1×distribute-rgt-out--
1×flip3--
1×sub-neg
Counts
3 → 31
Calls
3 calls:
Slowest
6.0ms
(* (* (* 0.12900613773279798 x) x) x)
4.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
2.0ms
(* (* 0.12900613773279798 x) x)

series84.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
46.0ms
(- (* 0.954929658551372 x) (* (* (* 0.12900613773279798 x) x) x))
20.0ms
(* (* 0.12900613773279798 x) x)
17.0ms
(* (* (* 0.12900613773279798 x) x) x)

simplify307.0ms

Counts
12 → 40
Calls
12 calls:
Slowest
84.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* (* 0.12900613773279798 x) x) x)))
61.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
60.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
58.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
12.0ms
(- 0.954929658551372 (* (* 0.12900613773279798 x) x))

prune257.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s11908×body80valid