Average Error: 28.3 → 28.3
Time: 55.8s
Precision: 64
Internal Precision: 128
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(\left(\left(y \cdot y\right) \cdot \left(y + a\right) + y \cdot b\right) + c\right)}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Taylor expanded around -inf 28.3

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(a \cdot {y}^{2} + \left({y}^{3} + y \cdot b\right)\right)} + c\right) \cdot y + i}\]

  3. Simplified28.3

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left(y \cdot y\right) \cdot \left(y + a\right)\right)} + c\right) \cdot y + i}\]

  4. Final simplification28.3

    \[\leadsto \frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(\left(\left(y \cdot y\right) \cdot \left(y + a\right) + y \cdot b\right) + c\right)}\]

Reproduce

herbie shell --seed 2019004 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

Details

Time bar (total: 53.7s)Debug log

sample68.0ms

Algorithm
intervals

simplify146.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

145.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize66.0ms

Local error

Found 4 expressions with local error:

30.2b
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* (+ y a) y) b) y)
0.1b
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
0.1b
(* (+ (* (+ (* (+ y a) y) b) y) c) y)

rewrite96.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

45.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
29.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
13.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)

series510.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

346.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
74.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
53.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
37.0ms
(* (+ (* (+ y a) y) b) y)

simplify8.3s

Counts
53 → 82
Calls

53 calls. Slowest were:

443.0ms
(+ (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) (* (+ (* (+ (* (+ y a) y) b) y) c) y)) (- (* i i) (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
385.0ms
(* (+ (pow (* (+ (* (+ y a) y) b) y) 3) (pow c 3)) y)
331.0ms
(+ (pow (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) 3) (pow t 3))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 29.6b

localize22.0ms

Local error

Found 4 expressions with local error:

30.2b
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (+ (* y b) (* (* y y) (+ y a))) c) y) i))
3.9b
(+ (* y b) (* (* y y) (+ y a)))
3.7b
(* (* y y) (+ y a))
0.1b
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)

rewrite96.0ms

Algorithm
rewrite-expression-head
Counts
4 → 76
Calls

4 calls. Slowest were:

63.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (+ (* y b) (* (* y y) (+ y a))) c) y) i))
19.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
7.0ms
(* (* y y) (+ y a))

series465.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

360.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (+ (* y b) (* (* y y) (+ y a))) c) y) i))
57.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
25.0ms
(* (* y y) (+ y a))
23.0ms
(+ (* y b) (* (* y y) (+ y a)))

simplify8.8s

Counts
58 → 88
Calls

58 calls. Slowest were:

849.0ms
(sqrt (+ (* (+ (+ (* y b) (* (* y y) (+ y a))) c) y) i))
430.0ms
(cbrt (+ (* (+ (+ (* y b) (* (* y y) (+ y a))) c) y) i))
392.0ms
(* (+ (pow (* (+ (* x y) z) y) 3) (pow 27464.7644705 3)) y)

prune2.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 29.6b

localize52.0ms

Local error

Found 4 expressions with local error:

30.2b
(/ (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
18.6b
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))
18.6b
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))
18.6b
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))

rewrite177.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

159.0ms
(/ (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
6.0ms
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))
6.0ms
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))

series876.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

350.0ms
(/ (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
202.0ms
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))
164.0ms
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))
159.0ms
(cbrt (+ (* (+ (* x y) z) y) 27464.7644705))

simplify12.0s

Counts
56 → 82
Calls

56 calls. Slowest were:

420.0ms
(+ (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) (* (+ (* (+ (* (+ y a) y) b) y) c) y)) (- (* i i) (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
396.0ms
(/ (* (cbrt (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t)) (cbrt (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t))) (sqrt (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
388.0ms
(/ (sqrt (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t)) (sqrt (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

prune2.0s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 29.6b

localize33.0ms

Local error

Found 4 expressions with local error:

30.2b
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) (cbrt (+ (* (+ (* (+ y a) y) b) y) c))) (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) y)) i))
24.1b
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))
24.1b
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))
24.1b
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))

rewrite145.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

118.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) (cbrt (+ (* (+ (* (+ y a) y) b) y) c))) (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) y)) i))
9.0ms
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))
9.0ms
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))

series675.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

311.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) (cbrt (+ (* (+ (* (+ y a) y) b) y) c))) (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) y)) i))
129.0ms
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))
126.0ms
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))
110.0ms
(cbrt (+ (* (+ (* (+ y a) y) b) y) c))

simplify9.3s

Counts
56 → 82
Calls

56 calls. Slowest were:

801.0ms
(exp (* 1/3 (- (log -1) (* 3 (log (/ -1 y))))))
776.0ms
(exp (* 1/3 (- (log -1) (* 3 (log (/ -1 y))))))
673.0ms
(exp (* 1/3 (- (log -1) (* 3 (log (/ -1 y))))))

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 29.6b

regimes1.6s

Accuracy

0% (0.7b remaining)

Error of 28.3b against oracle of 27.6b and baseline of 28.3b

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm
intervals