Average Error: 0.1 → 0
Time: 4.3s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
\[{d1}^{10}\]

Error

Bits error versus d1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0
Herbie0
\[{d1}^{10}\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
  2. Taylor expanded around inf 0.1

    \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{8}}\right) \cdot d1\]
  3. Taylor expanded around -inf 0

    \[\leadsto \color{blue}{{d1}^{10}}\]
  4. Final simplification0

    \[\leadsto {d1}^{10}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

  (* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1))

Details

Time bar (total: 4.0s)Debug log

sample102.0ms

Algorithm
intervals

simplify89.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

89.0ms
(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* d1 (* d1 d1))
0.1b
(* (* d1 (* d1 d1)) d1)
0.1b
(* (* (* d1 (* d1 d1)) d1) d1)
0.1b
(* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)

rewrite89.0ms

Algorithm
rewrite-expression-head
Counts
4 → 40
Calls

4 calls. Slowest were:

60.0ms
(* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)
20.0ms
(* (* (* d1 (* d1 d1)) d1) d1)
6.0ms
(* (* d1 (* d1 d1)) d1)

series103.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

33.0ms
(* (* (* d1 (* d1 d1)) d1) d1)
32.0ms
(* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)
24.0ms
(* (* d1 (* d1 d1)) d1)
14.0ms
(* d1 (* d1 d1))

simplify38.0ms

Counts
14 → 52
Calls

14 calls. Slowest were:

17.0ms
(* (* (* d1 (* d1 d1)) d1) d1)
3.0ms
(* d1 (* d1 d1))
1.0ms
(pow d1 3)

prune325.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b
(* d1 (pow d1 8))
0.0b
(* (* d1 (pow d1 8)) d1)

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 20
Calls

2 calls. Slowest were:

7.0ms
(* (* d1 (pow d1 8)) d1)
2.0ms
(* d1 (pow d1 8))

series82.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

42.0ms
(* d1 (pow d1 8))
39.0ms
(* (* d1 (pow d1 8)) d1)

simplify13.0ms

Counts
9 → 26
Calls

9 calls. Slowest were:

2.0ms
(cbrt (pow d1 8))
1.0ms
(sqrt (pow d1 8))
1.0ms
(pow d1 9)

prune213.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize3.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune2.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.8s

Algorithm
intervals