Average Error: 0.2 → 0.2
Time: 6.9s
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. Initial simplification0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 3.9s)Debug log

start56.0ms

Algorithm
intervals

setup18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

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)))

series25.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify66.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

18.0ms
(* -1 (/ a (acos a)))
17.0ms
(* -1 (/ a (acos a)))
17.0ms
(* -1 (/ a (acos a)))

prune221.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 44
Calls

2 calls. Slowest were:

7.0ms
(/ (- (acos a)) a)
3.0ms
(/ 1 (/ (- (acos a)) a))

series51.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

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

simplify90.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

16.0ms
(* -1 (/ (acos a) a))
14.0ms
(* -1 (/ (acos a) a))
10.0ms
(* -1 (/ a (acos a)))

prune446.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 66
Calls

2 calls. Slowest were:

8.0ms
(/ (/ 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)))

simplify1.2s

Counts
58 → 72
Calls

58 calls. Slowest were:

494.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
97.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
72.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune678.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
2 → 48
Calls

2 calls. Slowest were:

9.0ms
(* (/ 1 a) (- (acos a)))
7.0ms
(/ 1 (* (/ 1 a) (- (acos a))))

series44.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

26.0ms
(* (/ 1 a) (- (acos a)))
17.0ms
(/ 1 (* (/ 1 a) (- (acos a))))

simplify422.0ms

Counts
25 → 54
Calls

25 calls. Slowest were:

234.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
24.0ms
(* (/ 1 a) (- (acos a)))
18.0ms
(+ (log (/ 1 a)) (log (- (acos a))))

prune394.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms