Average Error: 0.1 → 0.1
Time: 6.2s
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 2019016 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

Details

Time bar (total: 5.6s)Debug log

sample170.0ms

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

simplify74.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
74.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 1 expressions with local error:

0.5b
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×log1p-expm1-u
1×fma-udef
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 10
Calls
1 calls:
Slowest
2.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

series76.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
76.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

simplify126.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
49.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
41.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
35.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune115.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize21.0ms

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)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
3×log1p-expm1-u
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×expm1-log1p-u
3×add-sqr-sqrt
2×*-commutative
1×flip--
1×pow3
1×prod-diff
1×associate-*l*
1×associate-*r*
1×diff-log
1×fma-neg
1×flip3--
1×pow-plus
1×sub-neg
1×pow2
Counts
3 → 40
Calls
3 calls:
Slowest
6.0ms
(* 0.12900613773279798 (* (* x x) x))
3.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
2.0ms
(* (* x x) x)

series92.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
61.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
17.0ms
(* 0.12900613773279798 (* (* x x) x))
14.0ms
(* (* x x) x)

simplify412.0ms

Counts
12 → 49
Calls
12 calls:
Slowest
99.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
62.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
57.0ms
(fma (- (* (* x x) x)) 0.12900613773279798 (* (* (* x x) x) 0.12900613773279798))
55.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
53.0ms
(fma 0.954929658551372 x (- (* (* (* x x) x) 0.12900613773279798)))

prune318.0ms

Pruning

4 alts after pruning (3 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))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
3×log1p-expm1-u
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×expm1-log1p-u
3×add-sqr-sqrt
2×*-commutative
1×flip--
1×prod-diff
1×associate-*l*
1×associate-*r*
1×diff-log
1×fma-neg
1×distribute-rgt-out--
1×flip3--
1×sub-neg
Counts
3 → 39
Calls
3 calls:
Slowest
5.0ms
(* (* 0.12900613773279798 (* x x)) x)
2.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
1.0ms
(* 0.12900613773279798 (* x x))

series102.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
60.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
28.0ms
(* (* 0.12900613773279798 (* x x)) x)
14.0ms
(* 0.12900613773279798 (* x x))

simplify534.0ms

Counts
13 → 48
Calls
13 calls:
Slowest
124.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
106.0ms
(fma (- x) (* 0.12900613773279798 (* x x)) (* x (* 0.12900613773279798 (* x x))))
89.0ms
(fma 0.954929658551372 x (- (* x (* 0.12900613773279798 (* x x)))))
58.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
44.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune320.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

29.9b
(cbrt (* (* 0.12900613773279798 (* x x)) x))
29.9b
(cbrt (* (* 0.12900613773279798 (* x x)) x))
29.9b
(cbrt (* (* 0.12900613773279798 (* x x)) x))
0.3b
(* (cbrt (* (* 0.12900613773279798 (* x x)) x)) (cbrt (* (* 0.12900613773279798 (* x x)) x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
7×pow1/3
6×add-cube-cbrt
6×add-exp-log
6×*-un-lft-identity
6×add-sqr-sqrt
5×cbrt-prod
4×add-log-exp
4×log1p-expm1-u
4×associate-*l*
4×associate-*r*
4×add-cbrt-cube
4×expm1-log1p-u
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 59
Calls
4 calls:
Slowest
11.0ms
(* (cbrt (* (* 0.12900613773279798 (* x x)) x)) (cbrt (* (* 0.12900613773279798 (* x x)) x)))
2.0ms
(cbrt (* (* 0.12900613773279798 (* x x)) x))
2.0ms
(cbrt (* (* 0.12900613773279798 (* x x)) x))
2.0ms
(cbrt (* (* 0.12900613773279798 (* x x)) x))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(* (cbrt (* (* 0.12900613773279798 (* x x)) x)) (cbrt (* (* 0.12900613773279798 (* x x)) x)))
83.0ms
(cbrt (* (* 0.12900613773279798 (* x x)) x))
77.0ms
(cbrt (* (* 0.12900613773279798 (* x x)) x))
65.0ms
(cbrt (* (* 0.12900613773279798 (* x x)) x))

simplify561.0ms

Counts
31 → 71
Calls
31 calls:
Slowest
168.0ms
(* (* (* 0.12900613773279798 (* x x)) x) (* (* 0.12900613773279798 (* x x)) x))
109.0ms
(* (* (* 0.12900613773279798 (* x x)) x) (* (* 0.12900613773279798 (* x x)) x))
19.0ms
(* -1 (* (cbrt -0.12900613773279798) x))
19.0ms
(* (cbrt (cbrt (* (* 0.12900613773279798 (* x x)) x))) (cbrt (cbrt (* (* 0.12900613773279798 (* x x)) x))))
18.0ms
(sqrt (cbrt (* (* 0.12900613773279798 (* x x)) x)))

prune691.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

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