Average Error: 18.2 → 1.3
Time: 16.1s
Precision: 64
Internal Precision: 128
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{t1}{t1 + u} \cdot \frac{-v}{t1 + u}\]

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 18.2

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

  3. Applied times-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019007 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 15.6s)Debug log

sample135.0ms

Algorithm
intervals

simplify147.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

147.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize15.0ms

Local error

Found 2 expressions with local error:

16.6b
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
0.0b
(* (+ t1 u) (+ t1 u))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
2 → 56
Calls

2 calls. Slowest were:

23.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
7.0ms
(* (+ t1 u) (+ t1 u))

series77.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

63.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
14.0ms
(* (+ t1 u) (+ t1 u))

simplify3.6s

Counts
48 → 62
Calls

48 calls. Slowest were:

362.0ms
(* (- (* t1 t1) (* u u)) (+ t1 u))
324.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (- t1 u))
286.0ms
(/ (* (* (* (- t1) v) (* (- t1) v)) (* (- t1) v)) (* (* (* (+ t1 u) (+ t1 u)) (* (+ t1 u) (+ t1 u))) (* (+ t1 u) (+ t1 u))))

prune611.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 91
Calls

3 calls. Slowest were:

6.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
3.0ms
(/ (- t1) (+ t1 u))
1.0ms
(/ v (+ t1 u))

series127.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

82.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
25.0ms
(/ v (+ t1 u))
20.0ms
(/ (- t1) (+ t1 u))

simplify1.5s

Counts
82 → 100
Calls

82 calls. Slowest were:

270.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
264.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
140.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune944.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (/ (+ t1 u) v))
0.5b
(* (/ (- t1) (+ t1 u)) (/ 1 (/ (+ t1 u) v)))
0.0b
(/ (+ t1 u) v)
0.0b
(/ (- t1) (+ t1 u))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 111
Calls

4 calls. Slowest were:

6.0ms
(* (/ (- t1) (+ t1 u)) (/ 1 (/ (+ t1 u) v)))
3.0ms
(/ (- t1) (+ t1 u))
2.0ms
(/ (+ t1 u) v)

series188.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

84.0ms
(* (/ (- t1) (+ t1 u)) (/ 1 (/ (+ t1 u) v)))
47.0ms
(/ 1 (/ (+ t1 u) v))
34.0ms
(/ (- t1) (+ t1 u))
22.0ms
(/ (+ t1 u) v)

simplify3.1s

Counts
90 → 123
Calls

90 calls. Slowest were:

434.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ 1 (/ (+ t1 u) v))))
370.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
348.0ms
(* (/ (- t1) (+ t1 u)) (/ 1 (/ (+ t1 u) v)))

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

1.9b
(* (/ (- t1) (+ t1 u)) v)
1.0b
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
0.0b
(/ (- t1) (+ t1 u))

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
3 → 86
Calls

3 calls. Slowest were:

14.0ms
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
9.0ms
(* (/ (- t1) (+ t1 u)) v)
6.0ms
(/ (- t1) (+ t1 u))

series154.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

74.0ms
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
60.0ms
(* (/ (- t1) (+ t1 u)) v)
20.0ms
(/ (- t1) (+ t1 u))

simplify1.2s

Counts
79 → 95
Calls

79 calls. Slowest were:

304.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
144.0ms
(/ (* (* (* (/ (- t1) (+ t1 u)) v) (* (/ (- t1) (+ t1 u)) v)) (* (/ (- t1) (+ t1 u)) v)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
134.0ms
(- (log (* (/ (- t1) (+ t1 u)) v)) (log (+ t1 u)))

prune815.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes144.0ms

Accuracy

0% (1.3b remaining)

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

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm
intervals