Average Error: 28.2 → 28.2
Time: 56.3s
Precision: 64
Internal Precision: 128
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

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 28.2

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

  3. Applied div-inv28.2

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.2

    \[\leadsto \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(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: 48.6s)Debug log

start90.0ms

Algorithm
intervals

setup142.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize52.0ms

Local error

Found 4 expressions with local error:

32.5b
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
0.1b
(* (+ (* x y) z) y)
0.1b
(* (+ (* (+ (* (+ y a) y) b) y) c) y)

rewrite76.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

42.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
15.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
14.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)

series453.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

306.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
67.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
43.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
37.0ms
(* (+ (* x y) z) y)

simplify8.9s

Counts
53 → 90
Calls

53 calls. Slowest were:

499.0ms
(+ (pow (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) 3) (pow t 3))
450.0ms
(* (+ (pow (* (+ (* (+ y a) y) b) y) 3) (pow c 3)) y)
435.0ms
(* (- (* (* (+ (* (+ y a) y) b) y) (* (+ (* (+ y a) y) b) y)) (* c c)) y)

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.7b

localize15.0ms

Local error

Found 4 expressions with local error:

31.9b
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
0.7b
(/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
0.1b
(* (+ (* x y) z) y)

rewrite76.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

43.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
14.0ms
(/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
10.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)

series511.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

376.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
58.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
54.0ms
(/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
22.0ms
(* (+ (* x y) z) y)

simplify7.6s

Counts
46 → 91
Calls

46 calls. Slowest were:

602.0ms
(* (+ (pow (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) 3) (pow t 3)) 1)
517.0ms
(* (- (* (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)) (* t t)) 1)
469.0ms
(+ (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) (* (+ (* (+ (* (+ y a) y) b) y) c) y)) (- (* i i) (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 31.7b

localize17.0ms

Local error

Found 4 expressions with local error:

28.5b
(/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* 27464.7644705 y) 230661.510616) y)
0.1b
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
0.1b
(* (+ (* (+ y a) y) b) y)

rewrite66.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

27.0ms
(/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
22.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
9.0ms
(* (+ (* 27464.7644705 y) 230661.510616) y)

series267.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

144.0ms
(/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
57.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
43.0ms
(* (+ (* 27464.7644705 y) 230661.510616) y)
23.0ms
(* (+ (* (+ y a) y) b) y)

simplify9.3s

Counts
53 → 90
Calls

53 calls. Slowest were:

558.0ms
(- (* (* (+ (* 27464.7644705 y) 230661.510616) y) (* (+ (* 27464.7644705 y) 230661.510616) y)) (* t t))
467.0ms
(* (+ (pow (* (+ (* (+ y a) y) b) y) 3) (pow c 3)) y)
446.0ms
(* (- (* (* (+ (* (+ y a) y) b) y) (* (+ (* (+ y a) y) b) y)) (* c c)) y)

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 31.4b

localize31.0ms

Local error

Found 4 expressions with local error:

28.5b
(/ (+ (* (* (cbrt (fma y 27464.7644705 230661.510616)) (cbrt (fma y 27464.7644705 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
1.7b
(cbrt (+ (* 27464.7644705 y) 230661.510616))
1.7b
(cbrt (fma y 27464.7644705 230661.510616))
1.7b
(cbrt (fma y 27464.7644705 230661.510616))

rewrite74.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

71.0ms
(/ (+ (* (* (cbrt (fma y 27464.7644705 230661.510616)) (cbrt (fma y 27464.7644705 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
1.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))
0.0ms
(cbrt (fma y 27464.7644705 230661.510616))

series636.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

450.0ms
(/ (+ (* (* (cbrt (fma y 27464.7644705 230661.510616)) (cbrt (fma y 27464.7644705 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
71.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))
61.0ms
(cbrt (fma y 27464.7644705 230661.510616))
53.0ms
(cbrt (fma y 27464.7644705 230661.510616))

simplify9.4s

Counts
52 → 86
Calls

52 calls. Slowest were:

479.0ms
(+ (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) (* (+ (* (+ (* (+ y a) y) b) y) c) y)) (- (* i i) (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
377.0ms
(- (* (* (* (cbrt (fma y 27464.7644705 230661.510616)) (cbrt (fma y 27464.7644705 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) (* (* (cbrt (fma y 27464.7644705 230661.510616)) (cbrt (fma y 27464.7644705 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y))) (* t t))
339.0ms
(/ (+ (* (* (cbrt (fma y 27464.7644705 230661.510616)) (cbrt (fma y 27464.7644705 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (sqrt (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

prune2.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 31.4b

regimes2.2s

Accuracy

0% (1.0b remaining)

Error of 28.2b against oracle of 27.3b and baseline of 28.2b

bsearch8.0ms