Average Error: 0.3 → 0.3
Time: 4.6s
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 0.3

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

  2. Final simplification0.3

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

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 4.2s)Debug log

sample41.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
13.0ms246×body80nan

simplify1.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
1.0ms
(/ a (- (acos a)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-/r*
4×add-cube-cbrt
4×*-un-lft-identity
4×add-sqr-sqrt
3×distribute-rgt-neg-in
3×distribute-lft-neg-in
1×add-log-exp
1×div-inv
1×log1p-expm1-u
1×add-exp-log
1×add-cbrt-cube
1×frac-2neg
1×neg-mul-1
1×clear-num
1×pow1
1×expm1-log1p-u
Counts
1 → 22
Calls
1 calls:
Slowest
1.0ms
(/ a (- (acos a)))

series16.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
16.0ms
(/ a (- (acos a)))

simplify59.0ms

Counts
13 → 25
Calls
13 calls:
Slowest
23.0ms
(* -1 (/ a (acos a)))
13.0ms
(* -1 (/ a (acos a)))
10.0ms
(* -1 (/ a (acos a)))
2.0ms
(- (sqrt (acos a)))
1.0ms
(cbrt (- (acos a)))

prune137.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-/r*
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
4×associate-*r*
3×add-exp-log
3×distribute-rgt-neg-in
3×pow1
3×distribute-lft-neg-in
2×add-log-exp
2×div-inv
2×log1p-expm1-u
2×add-cbrt-cube
2×expm1-log1p-u
1×inv-pow
1×pow-flip
1×*-commutative
1×un-div-inv
1×associate-*r/
1×frac-2neg
1×neg-mul-1
1×clear-num
1×rec-exp
Counts
2 → 41
Calls
2 calls:
Slowest
2.0ms
(* a (/ 1 (- (acos a))))
2.0ms
(/ 1 (- (acos a)))

series20.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
14.0ms
(* a (/ 1 (- (acos a))))
6.0ms
(/ 1 (- (acos a)))

simplify50.0ms

Counts
23 → 47
Calls
23 calls:
Slowest
10.0ms
(* -1 (/ a (acos a)))
10.0ms
(* -1 (/ a (acos a)))
8.0ms
(* -1 (/ a (acos a)))
4.0ms
(cbrt (/ 1 (- (acos a))))
2.0ms
(sqrt (/ 1 (- (acos a))))

prune242.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-/l*
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
4×associate-/r*
3×div-inv
3×add-exp-log
3×distribute-rgt-neg-in
3×pow1
3×distribute-lft-neg-in
2×add-log-exp
2×log1p-expm1-u
2×add-cbrt-cube
2×frac-2neg
2×clear-num
2×expm1-log1p-u
1×inv-pow
1×pow-flip
1×associate-/r/
1×distribute-frac-neg
1×div-sub
1×neg-mul-1
1×rec-exp
1×neg-sub0
Counts
2 → 44
Calls
2 calls:
Slowest
6.0ms
(/ (- (acos a)) a)
2.0ms
(/ 1 (/ (- (acos a)) a))

series38.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
21.0ms
(/ (- (acos a)) a)
17.0ms
(/ 1 (/ (- (acos a)) a))

simplify75.0ms

Counts
20 → 50
Calls
20 calls:
Slowest
14.0ms
(* -1 (/ (acos a) a))
12.0ms
(* -1 (/ (acos a) a))
8.0ms
(* -1 (/ (acos a) a))
7.0ms
(* -1 (/ a (acos a)))
7.0ms
(* -1 (/ a (acos a)))

prune301.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b
(/ 1 (- (acos a)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
16×times-frac
15×add-cube-cbrt
15×*-un-lft-identity
15×add-sqr-sqrt
14×associate-/r*
12×div-inv
7×add-exp-log
4×associate-/l*
4×add-cbrt-cube
3×distribute-rgt-neg-in
3×pow1
3×distribute-lft-neg-in
2×add-log-exp
2×log1p-expm1-u
2×div-exp
2×frac-2neg
2×clear-num
2×rec-exp
2×expm1-log1p-u
1×associate-/l/
1×inv-pow
1×pow-flip
1×associate-/r/
1×neg-mul-1
1×cbrt-undiv
Counts
2 → 66
Calls
2 calls:
Slowest
8.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
2.0ms
(/ 1 (- (acos a)))

series31.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
23.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
8.0ms
(/ 1 (- (acos a)))

simplify1.4s

Counts
58 → 72
Calls
58 calls:
Slowest
787.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
74.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
73.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
62.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
50.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune453.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
640.0ms8000×body80valid
384.0ms7987×body80nan