Average Error: 0.2 → 0.2
Time: 6.6s
Precision: 64
Internal Precision: 128
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{a}{-\cos^{-1} a}\]

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{a}{-\cos^{-1} a}\]

  2. Final simplification0.2

    \[\leadsto \frac{a}{-\cos^{-1} a}\]

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 3.9s)Debug log

start44.0ms

Algorithm
intervals

setup7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ a (- (acos a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 22
Calls

1 calls. Slowest were:

1.0ms
(/ a (- (acos a)))

series16.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

16.0ms
(/ a (- (acos a)))

simplify48.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

23.0ms
(* -1 (/ a (acos a)))
9.0ms
(* -1 (/ a (acos a)))
8.0ms
(* -1 (/ a (acos a)))

prune163.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b
(* a (/ 1 (- (acos a))))
0.0b
(/ 1 (- (acos a)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

3.0ms
(* a (/ 1 (- (acos a))))
3.0ms
(/ 1 (- (acos a)))

series37.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

26.0ms
(* a (/ 1 (- (acos a))))
11.0ms
(/ 1 (- (acos a)))

simplify97.0ms

Counts
23 → 47
Calls

23 calls. Slowest were:

20.0ms
(* -1 (/ a (acos a)))
16.0ms
(* -1 (/ a (acos a)))
15.0ms
(* -1 (/ a (acos a)))

prune386.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 44
Calls

2 calls. Slowest were:

8.0ms
(/ (- (acos a)) a)
3.0ms
(/ 1 (/ (- (acos a)) a))

series51.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

26.0ms
(/ (- (acos a)) a)
25.0ms
(/ 1 (/ (- (acos a)) a))

simplify102.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

16.0ms
(* -1 (/ a (acos a)))
14.0ms
(* -1 (/ a (acos a)))
8.0ms
(* -1 (/ (acos a) a))

prune446.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b
(/ 1 (- (acos a)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 66
Calls

2 calls. Slowest were:

4.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
1.0ms
(/ 1 (- (acos a)))

series21.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

15.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.8s

Counts
58 → 72
Calls

58 calls. Slowest were:

927.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
106.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
99.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune570.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms