Average Error: 18.0 → 1.3
Time: 15.2s
Precision: 64
Internal Precision: 128
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{t1}{t1 + u} \cdot \left(-v\right)}{t1 + u}\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.0

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.3

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]

  6. Final simplification1.3

    \[\leadsto \frac{\frac{t1}{t1 + u} \cdot \left(-v\right)}{t1 + u}\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 14.6s)Debug log

sample118.0ms

Algorithm
intervals

simplify195.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

195.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize21.0ms

Local error

Found 2 expressions with local error:

15.0b
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
0.0b
(* (+ t1 u) (+ t1 u))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
2 → 60
Calls

2 calls. Slowest were:

9.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
4.0ms
(* (+ t1 u) (+ t1 u))

series69.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

59.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
10.0ms
(* (+ t1 u) (+ t1 u))

simplify4.3s

Counts
48 → 66
Calls

48 calls. Slowest were:

338.0ms
(* (- (* t1 t1) (* u u)) (+ (pow t1 3) (pow u 3)))
337.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (+ (* t1 t1) (- (* u u) (* t1 u))))
327.0ms
(/ (* (* (* (- t1) v) (* (- t1) v)) (* (- t1) v)) (* (* (* (+ t1 u) (+ t1 u)) (* (+ t1 u) (+ t1 u))) (* (+ t1 u) (+ t1 u))))

prune598.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.7b
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
0.0b
(/ v (+ t1 u))
0.0b
(/ (- t1) (+ t1 u))

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
3 → 97
Calls

3 calls. Slowest were:

17.0ms
(/ (- t1) (+ t1 u))
16.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
1.0ms
(/ v (+ t1 u))

series144.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

92.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
29.0ms
(/ v (+ t1 u))
23.0ms
(/ (- t1) (+ t1 u))

simplify1.9s

Counts
82 → 106
Calls

82 calls. Slowest were:

374.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
307.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
236.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune768.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

2.7b
(* (/ (- t1) (+ t1 u)) v)
0.5b
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
0.0b
(/ (- t1) (+ t1 u))

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
3 → 92
Calls

3 calls. Slowest were:

14.0ms
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
8.0ms
(* (/ (- t1) (+ t1 u)) v)
6.0ms
(/ (- t1) (+ t1 u))

series191.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

87.0ms
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
70.0ms
(* (/ (- t1) (+ t1 u)) v)
33.0ms
(/ (- t1) (+ t1 u))

simplify1.5s

Counts
79 → 101
Calls

79 calls. Slowest were:

464.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
178.0ms
(- (log (* (/ (- t1) (+ t1 u)) v)) (log (+ t1 u)))
146.0ms
(/ (* (* (* (/ (- t1) (+ t1 u)) v) (* (/ (- t1) (+ t1 u)) v)) (* (/ (- t1) (+ t1 u)) v)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))

prune843.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
0.4b
(/ -1 (/ (+ t1 u) t1))
0.0b
(/ (+ t1 u) t1)
0.0b
(/ v (+ t1 u))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

7.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
5.0ms
(/ (+ t1 u) t1)
1.0ms
(/ -1 (/ (+ t1 u) t1))

series129.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

66.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
30.0ms
(/ v (+ t1 u))
20.0ms
(/ -1 (/ (+ t1 u) t1))
14.0ms
(/ (+ t1 u) t1)

simplify1.1s

Counts
41 → 90
Calls

41 calls. Slowest were:

289.0ms
(* (/ (+ t1 u) t1) (+ t1 u))
228.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
187.0ms
(+ (log (/ -1 (/ (+ t1 u) t1))) (log (/ v (+ t1 u))))

prune810.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes168.0ms

Accuracy

0% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 1.3b

bsearch7.0ms

end0.0ms

sample1.7s

Algorithm
intervals