Average Error: 0.1 → 0.1
Time: 29.9s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

  2. Final simplification0.1

    \[\leadsto \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))

Details

Time bar (total: 29.4s)Debug log

sample205.0ms

Algorithm
intervals

simplify501.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

501.0ms
(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (- 1 m) (/ m v) -1)
0.1b
(* (fma (- 1 m) (/ m v) -1) (- 1 m))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
2 → 35
Calls

2 calls. Slowest were:

4.0ms
(* (fma (- 1 m) (/ m v) -1) (- 1 m))
2.0ms
(fma (- 1 m) (/ m v) -1)

series45.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

26.0ms
(* (fma (- 1 m) (/ m v) -1) (- 1 m))
19.0ms
(fma (- 1 m) (/ m v) -1)

simplify4.8s

Counts
20 → 41
Calls

20 calls. Slowest were:

954.0ms
(* (- m) (fma (- 1 m) (/ m v) -1))
903.0ms
(* (- m) (fma (- 1 m) (/ m v) -1))
639.0ms
(* (* (* (fma (- 1 m) (/ m v) -1) (fma (- 1 m) (/ m v) -1)) (fma (- 1 m) (/ m v) -1)) (* (* (- 1 m) (- 1 m)) (- 1 m)))

prune342.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (/ m v) (* m (+ -1 m)) m)
0.1b
(fma (- 1 m) (/ m v) -1)
0.0b
(+ (* 1 (fma (- 1 m) (/ m v) -1)) (fma (/ m v) (* m (+ -1 m)) m))
0.0b
(* m (+ -1 m))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 55
Calls

4 calls. Slowest were:

7.0ms
(+ (* 1 (fma (- 1 m) (/ m v) -1)) (fma (/ m v) (* m (+ -1 m)) m))
2.0ms
(* m (+ -1 m))
0.0ms
(fma (/ m v) (* m (+ -1 m)) m)

series87.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

27.0ms
(+ (* 1 (fma (- 1 m) (/ m v) -1)) (fma (/ m v) (* m (+ -1 m)) m))
25.0ms
(fma (/ m v) (* m (+ -1 m)) m)
18.0ms
(fma (- 1 m) (/ m v) -1)
17.0ms
(* m (+ -1 m))

simplify3.9s

Counts
23 → 67
Calls

23 calls. Slowest were:

2.1s
(+ (fma (- 1 m) (/ m v) -1) (fma (/ m v) (* m (+ -1 m)) m))
283.0ms
(* 1 (* (- 1 m) (/ m v)))
276.0ms
(- (+ m (/ (pow m 3) v)) (* 2 (/ (pow m 2) v)))

prune736.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (/ m v) (* m (+ -1 m)) m)
0.1b
(fma m (/ m v) 1)
0.0b
(+ (* 1 (- (/ m v) (fma m (/ m v) 1))) (fma (/ m v) (* m (+ -1 m)) m))
0.0b
(* m (+ -1 m))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 81
Calls

4 calls. Slowest were:

13.0ms
(+ (* 1 (- (/ m v) (fma m (/ m v) 1))) (fma (/ m v) (* m (+ -1 m)) m))
2.0ms
(* m (+ -1 m))
0.0ms
(fma (/ m v) (* m (+ -1 m)) m)

series102.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

37.0ms
(+ (* 1 (- (/ m v) (fma m (/ m v) 1))) (fma (/ m v) (* m (+ -1 m)) m))
25.0ms
(fma (/ m v) (* m (+ -1 m)) m)
21.0ms
(fma m (/ m v) 1)
19.0ms
(* m (+ -1 m))

simplify7.1s

Counts
49 → 93
Calls

49 calls. Slowest were:

347.0ms
(* (fma (sqrt (/ m v)) (sqrt (/ m v)) (- (* (fma m (/ m v) 1) 1))) 1)
324.0ms
(* (fma m (/ 1 v) (- (* (fma m (/ m v) 1) 1))) 1)
319.0ms
(* 1 (fma (sqrt (/ m v)) (sqrt (/ m v)) (- (* (fma m (/ m v) 1) 1))))

prune913.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* m (- 1 m)) v)
0.1b
(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))
0.0b
(* m (- 1 m))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
3 → 66
Calls

3 calls. Slowest were:

10.0ms
(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))
3.0ms
(/ (* m (- 1 m)) v)
1.0ms
(* m (- 1 m))

series82.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

38.0ms
(* m (- 1 m))
27.0ms
(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))
17.0ms
(/ (* m (- 1 m)) v)

simplify7.7s

Counts
45 → 75
Calls

45 calls. Slowest were:

776.0ms
(* (- m) (- (/ (* m (- 1 m)) v) 1))
695.0ms
(* (- m) (- (/ (* m (- 1 m)) v) 1))
655.0ms
(* (+ (/ (* m (- 1 m)) v) 1) (+ 1 m))

prune599.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes176.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm
intervals