Average Error: 0.3 → 0.3
Time: 7.5s
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. Initial simplification0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 4.6s)Debug log

start58.0ms

Algorithm
intervals

setup6.0ms

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)))

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify73.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

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

prune160.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (- (acos a)) a))
0.2b
(/ (- (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))

series37.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

22.0ms
(/ 1 (/ (- (acos a)) a))
15.0ms
(/ (- (acos a)) a)

simplify76.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

10.0ms
(* -1 (/ a (acos a)))
8.0ms
(* -1 (/ a (acos a)))
8.0ms
(* -1 (/ (acos a) a))

prune412.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 66
Calls

2 calls. Slowest were:

8.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
2.0ms
(/ 1 (- (acos a)))

series34.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

24.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.9s

Counts
58 → 72
Calls

58 calls. Slowest were:

1.1s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
102.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
93.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune652.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
2 → 50
Calls

2 calls. Slowest were:

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

series54.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

27.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
26.0ms
(* (- (acos a)) (/ 1 a))

simplify506.0ms

Counts
24 → 56
Calls

24 calls. Slowest were:

313.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
45.0ms
(* (- (acos a)) (/ 1 a))
17.0ms
(+ (log (- (acos a))) (log (/ 1 a)))

prune448.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms