Average Error: 0.3 → 0.3
Time: 5.0s
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 0.3

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

  2. Final simplification0.3

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

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 4.5s)Debug log

sample30.0ms

Algorithm
intervals

simplify1.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ a (- (acos a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 22
Calls

1 calls. Slowest were:

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

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify37.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

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

prune149.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (/ (- (acos a)) a))
0.2b
(/ (- (acos a)) a)

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 44
Calls

2 calls. Slowest were:

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

series31.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

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

simplify68.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

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

prune300.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (- (acos a)) (/ 1 a))
0.2b
(/ 1 (* (- (acos a)) (/ 1 a)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
2 → 50
Calls

2 calls. Slowest were:

8.0ms
(* (- (acos a)) (/ 1 a))
6.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

series43.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

24.0ms
(* (- (acos a)) (/ 1 a))
19.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify381.0ms

Counts
24 → 56
Calls

24 calls. Slowest were:

261.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
27.0ms
(* (- (acos a)) (/ 1 a))
19.0ms
(+ (log (- (acos a))) (log (/ 1 a)))

prune261.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize5.0ms

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)))

simplify1.4s

Counts
58 → 72
Calls

58 calls. Slowest were:

738.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
103.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
79.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune443.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

end0.0ms

sample1.1s

Algorithm
intervals