Average Error: 0.1 → 0.1
Time: 6.6s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[(0.954929658551372 \cdot x + \left(\left(\left(-0.12900613773279798\right) \cdot \left(x \cdot x\right)\right) \cdot x\right))_*\]

Error

Bits error versus x

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 fma-neg0.1

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

  6. Final simplification0.1

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

Reproduce

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

Details

Time bar (total: 3.8s)Debug log

start160.0ms

Algorithm
intervals

setup119.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 1 expressions with local error:

0.3b
(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))

series91.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

91.0ms
(fma (- 0.12900613773279798) (pow x 3) (* 0.954929658551372 x))

simplify159.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

71.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
50.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
36.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune193.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.4b
(* 0.12900613773279798 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
3 → 40
Calls

3 calls. Slowest were:

6.0ms
(* 0.12900613773279798 (* (* x x) x))
5.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
4.0ms
(* (* x x) x)

series124.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

70.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))
28.0ms
(* 0.12900613773279798 (* (* x x) x))
26.0ms
(* (* x x) x)

simplify541.0ms

Counts
12 → 49
Calls

12 calls. Slowest were:

128.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* 0.12900613773279798 (* (* x x) x))))
105.0ms
(fma 0.954929658551372 x (- (* (* (* x x) x) 0.12900613773279798)))
74.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune439.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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
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))

series93.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

65.0ms
(- (* 0.954929658551372 x) (* (* 0.12900613773279798 (* x x)) x))
16.0ms
(* (* 0.12900613773279798 (* x x)) x)
12.0ms
(* 0.12900613773279798 (* x x))

simplify517.0ms

Counts
13 → 48
Calls

13 calls. Slowest were:

93.0ms
(/ (exp (* 0.954929658551372 x)) (exp (* (* 0.12900613773279798 (* x x)) x)))
88.0ms
(fma 0.954929658551372 x (- (* x (* 0.12900613773279798 (* x x)))))
74.0ms
(fma (- x) (* 0.12900613773279798 (* x x)) (* x (* 0.12900613773279798 (* x x))))

prune465.0ms

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
(* (* 0.12900613773279798 (* x x)) x)
0.0b
(fma 0.954929658551372 x (- (* (* 0.12900613773279798 (* x x)) x)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
3 → 32
Calls

3 calls. Slowest were:

3.0ms
(* (* 0.12900613773279798 (* x x)) x)
1.0ms
(* 0.12900613773279798 (* x x))
0.0ms
(fma 0.954929658551372 x (- (* (* 0.12900613773279798 (* x x)) x)))

series77.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

42.0ms
(fma 0.954929658551372 x (- (* (* 0.12900613773279798 (* x x)) x)))
23.0ms
(* (* 0.12900613773279798 (* x x)) x)
12.0ms
(* 0.12900613773279798 (* x x))

simplify195.0ms

Counts
9 → 41
Calls

9 calls. Slowest were:

59.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
49.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))
43.0ms
(- (* 0.954929658551372 x) (* 0.12900613773279798 (pow x 3)))

prune474.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms