Average Error: 0.3 → 0.3
Time: 6.2s
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 2019010 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 5.7s)Debug log

sample54.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
2.0ms
(/ a (- (acos a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

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)))

series15.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
15.0ms
(/ a (- (acos a)))

simplify69.0ms

Counts
13 → 25
Calls
13 calls:
Slowest
27.0ms
(* -1 (/ a (acos a)))
17.0ms
(* -1 (/ a (acos a)))
17.0ms
(* -1 (/ a (acos a)))
1.0ms
(cbrt (- (acos a)))
1.0ms
(sqrt (- (acos a)))

prune161.0ms

Pruning

5 alts after pruning (4 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
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
7.0ms
(/ (- (acos a)) a)
2.0ms
(/ 1 (/ (- (acos a)) a))

series49.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
25.0ms
(/ (- (acos a)) a)
24.0ms
(/ 1 (/ (- (acos a)) a))

simplify105.0ms

Counts
20 → 50
Calls
20 calls:
Slowest
16.0ms
(* -1 (/ a (acos a)))
14.0ms
(* -1 (/ a (acos a)))
9.0ms
(* -1 (/ (acos a) a))
9.0ms
(* -1 (/ a (acos a)))
9.0ms
(* -1 (/ (acos a) a))

prune366.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*l*
7×add-exp-log
7×pow1
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
4×associate-*r*
4×add-cbrt-cube
3×distribute-rgt-neg-in
3×distribute-lft-neg-in
2×add-log-exp
2×pow-flip
2×div-inv
2×log1p-expm1-u
2×un-div-inv
2×associate-/r/
2×associate-*r/
2×prod-exp
2×pow-prod-down
2×rec-exp
2×expm1-log1p-u
1×inv-pow
1×cbrt-unprod
1×*-commutative
1×frac-2neg
1×neg-mul-1
1×associate-/r*
1×clear-num
1×distribute-lft-neg-out
Counts
2 → 50
Calls
2 calls:
Slowest
9.0ms
(* (- (acos a)) (/ 1 a))
7.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

series32.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
17.0ms
(* (- (acos a)) (/ 1 a))
15.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify514.0ms

Counts
24 → 56
Calls
24 calls:
Slowest
369.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
27.0ms
(* (- (acos a)) (/ 1 a))
20.0ms
(+ (log (- (acos a))) (log (/ 1 a)))
11.0ms
(* -1 (/ (acos a) a))
9.0ms
(* -1 (/ a (acos a)))

prune433.0ms

Pruning

12 alts after pruning (10 fresh and 2 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)))

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

series27.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
21.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.7s

Counts
58 → 72
Calls
58 calls:
Slowest
938.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
101.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
71.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
71.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
64.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune454.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals