Average Error: 0.2 → 0.2
Time: 14.1s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]

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 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019010 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))

Details

Time bar (total: 13.5s)Debug log

sample208.0ms

Algorithm
intervals

simplify186.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
185.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
3×fma-udef
3×add-cube-cbrt
3×associate-*r*
3×*-un-lft-identity
3×add-sqr-sqrt
2×add-log-exp
2×log1p-expm1-u
2×add-exp-log
2×add-cbrt-cube
2×pow1
2×expm1-log1p-u
1×*-commutative
1×distribute-lft-in
1×distribute-rgt-in
Counts
2 → 25
Calls
2 calls:
Slowest
5.0ms
(* m (fma (- 1 m) (/ m v) -1))
0.0ms
(fma (- 1 m) (/ m v) -1)

series39.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
27.0ms
(* m (fma (- 1 m) (/ m v) -1))
12.0ms
(fma (- 1 m) (/ m v) -1)

simplify725.0ms

Counts
11 → 31
Calls
11 calls:
Slowest
171.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
147.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
143.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
74.0ms
(- (/ m v) (+ (/ (pow m 2) v) 1))
72.0ms
(- (/ m v) (+ (/ (pow m 2) v) 1))

prune305.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt
7×*-un-lft-identity
5×add-exp-log
4×add-log-exp
4×flip--
4×log1p-expm1-u
4×associate-*r/
4×associate-*l*
4×fma-neg
4×add-cbrt-cube
4×flip3--
4×pow1
4×expm1-log1p-u
3×associate-*r*
3×sub-neg
2×associate-/l/
2×div-inv
2×*-commutative
2×associate-*l/
2×difference-of-sqr-1
2×distribute-lft-in
2×distribute-rgt-in
1×associate-/l*
1×frac-2neg
1×clear-num
1×expm1-def
Counts
4 → 69
Calls
4 calls:
Slowest
8.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
4.0ms
(- (/ (* m (- 1 m)) v) 1)
3.0ms
(/ (* m (- 1 m)) v)
1.0ms
(* m (- 1 m))

series72.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
22.0ms
(* m (- 1 m))
22.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
18.0ms
(/ (* m (- 1 m)) v)
11.0ms
(- (/ (* m (- 1 m)) v) 1)

simplify1.8s

Counts
33 → 81
Calls
33 calls:
Slowest
267.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
162.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
157.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
136.0ms
(sqrt (- (/ (* m (- 1 m)) v) 1))
136.0ms
(* (cbrt (- (/ (* m (- 1 m)) v) 1)) (cbrt (- (/ (* m (- 1 m)) v) 1)))

prune715.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ v (* m (- 1 m))))
0.1b
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
0.1b
(/ v (* m (- 1 m)))
0.0b
(* m (- 1 m))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt
7×*-un-lft-identity
7×associate-/r*
6×associate-*r/
5×associate-/r/
5×add-exp-log
5×pow1
4×add-log-exp
4×flip--
4×log1p-expm1-u
4×associate-*l*
4×add-cbrt-cube
4×flip3--
4×expm1-log1p-u
3×div-inv
3×associate-*r*
2×*-commutative
2×associate-*l/
2×distribute-lft-in
2×frac-2neg
2×sub-neg
2×clear-num
2×distribute-rgt-in
1×inv-pow
1×pow-flip
1×difference-of-sqr-1
1×rec-exp
Counts
4 → 72
Calls
4 calls:
Slowest
7.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
1.0ms
(/ 1 (/ v (* m (- 1 m))))
1.0ms
(* m (- 1 m))
1.0ms
(/ v (* m (- 1 m)))

series111.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
33.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
30.0ms
(/ v (* m (- 1 m)))
27.0ms
(/ 1 (/ v (* m (- 1 m))))
20.0ms
(* m (- 1 m))

simplify2.0s

Counts
37 → 84
Calls
37 calls:
Slowest
309.0ms
(* (- (pow (/ 1 (/ v (* m (- 1 m)))) 3) (pow 1 3)) m)
218.0ms
(sqrt (- (/ 1 (/ v (* m (- 1 m)))) 1))
196.0ms
(+ (sqrt (/ 1 (/ v (* m (- 1 m))))) 1)
177.0ms
(* (- (* (/ 1 (/ v (* m (- 1 m)))) (/ 1 (/ v (* m (- 1 m))))) (* 1 1)) m)
168.0ms
(* (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)) (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)))

prune753.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* v (/ 1 (* m (- 1 m)))))
0.2b
(* v (/ 1 (* m (- 1 m))))
0.1b
(* (- (/ 1 (* v (/ 1 (* m (- 1 m))))) 1) m)
0.1b
(/ 1 (* m (- 1 m)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×add-cube-cbrt
6×associate-/r/
6×add-exp-log
6×associate-*r/
6×associate-*r*
6×*-un-lft-identity
6×pow1
4×add-log-exp
4×log1p-expm1-u
4×associate-*l*
4×add-cbrt-cube
4×expm1-log1p-u
3×flip--
3×div-inv
3×flip3--
2×inv-pow
2×pow-flip
2×*-commutative
2×un-div-inv
2×associate-*l/
2×frac-2neg
2×associate-/r*
2×clear-num
2×rec-exp
1×difference-of-sqr-1
Counts
4 → 70
Calls
4 calls:
Slowest
14.0ms
(* (- (/ 1 (* v (/ 1 (* m (- 1 m))))) 1) m)
3.0ms
(/ 1 (* m (- 1 m)))
2.0ms
(* v (/ 1 (* m (- 1 m))))
1.0ms
(/ 1 (* v (/ 1 (* m (- 1 m)))))

series106.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
34.0ms
(* (- (/ 1 (* v (/ 1 (* m (- 1 m))))) 1) m)
33.0ms
(/ 1 (* v (/ 1 (* m (- 1 m)))))
24.0ms
(* v (/ 1 (* m (- 1 m))))
15.0ms
(/ 1 (* m (- 1 m)))

simplify3.2s

Counts
33 → 82
Calls
33 calls:
Slowest
648.0ms
(* (- (pow (/ 1 (* v (/ 1 (* m (- 1 m))))) 3) (pow 1 3)) m)
385.0ms
(+ (sqrt (/ 1 (* v (/ 1 (* m (- 1 m)))))) 1)
381.0ms
(* (cbrt (- (/ 1 (* v (/ 1 (* m (- 1 m))))) 1)) (cbrt (- (/ 1 (* v (/ 1 (* m (- 1 m))))) 1)))
374.0ms
(sqrt (- (/ 1 (* v (/ 1 (* m (- 1 m))))) 1))
328.0ms
(* (- (* (/ 1 (* v (/ 1 (* m (- 1 m))))) (/ 1 (* v (/ 1 (* m (- 1 m)))))) (* 1 1)) m)

prune720.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample2.3s

Algorithm
intervals