Average Error: 17.9 → 1.3
Time: 14.1s
Precision: 64
Internal Precision: 128
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-v}{u + t1} \cdot \frac{t1}{u + t1}\]

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 17.9

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

  3. Applied times-frac1.3

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

  5. Applied distribute-frac-neg1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019002 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 13.4s)Debug log

sample163.0ms

Algorithm
intervals

simplify172.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

172.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize32.0ms

Local error

Found 2 expressions with local error:

17.8b
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
0.0b
(* (+ t1 u) (+ t1 u))

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
2 → 56
Calls

2 calls. Slowest were:

26.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
8.0ms
(* (+ t1 u) (+ t1 u))

series74.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

57.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
16.0ms
(* (+ t1 u) (+ t1 u))

simplify4.3s

Counts
48 → 62
Calls

48 calls. Slowest were:

450.0ms
(* (- (* t1 t1) (* u u)) (+ t1 u))
385.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (- t1 u))
377.0ms
(/ (* (* (* (- t1) v) (* (- t1) v)) (* (- t1) v)) (* (* (* (+ t1 u) (+ t1 u)) (* (+ t1 u) (+ t1 u))) (* (+ t1 u) (+ t1 u))))

prune575.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.9b
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
0.0b
(/ (- t1) (+ t1 u))
0.0b
(/ v (+ t1 u))

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
3 → 91
Calls

3 calls. Slowest were:

12.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
6.0ms
(/ (- t1) (+ t1 u))
1.0ms
(/ v (+ t1 u))

series122.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

84.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
21.0ms
(/ (- t1) (+ t1 u))
17.0ms
(/ v (+ t1 u))

simplify1.7s

Counts
82 → 100
Calls

82 calls. Slowest were:

418.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
288.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
170.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune918.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.9b
(* (- (/ t1 (+ t1 u))) (/ v (+ t1 u)))
0.0b
(/ t1 (+ t1 u))
0.0b
(/ v (+ t1 u))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
3 → 67
Calls

3 calls. Slowest were:

11.0ms
(* (- (/ t1 (+ t1 u))) (/ v (+ t1 u)))
1.0ms
(/ t1 (+ t1 u))
1.0ms
(/ v (+ t1 u))

series147.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

87.0ms
(* (- (/ t1 (+ t1 u))) (/ v (+ t1 u)))
32.0ms
(/ t1 (+ t1 u))
28.0ms
(/ v (+ t1 u))

simplify834.0ms

Counts
45 → 76
Calls

45 calls. Slowest were:

108.0ms
(* (* (* (- (/ t1 (+ t1 u))) (- (/ t1 (+ t1 u)))) (- (/ t1 (+ t1 u)))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))
103.0ms
(/ t1 (- (* t1 t1) (* u u)))
90.0ms
(- (/ t1 (- (* t1 t1) (* u u))))

prune721.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
0.3b
(/ -1 (/ (+ t1 u) t1))
0.0b
(/ v (+ t1 u))
0.0b
(/ (+ t1 u) t1)

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

10.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
5.0ms
(/ (+ t1 u) t1)
1.0ms
(/ -1 (/ (+ t1 u) t1))

series153.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

73.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
34.0ms
(/ -1 (/ (+ t1 u) t1))
31.0ms
(/ v (+ t1 u))
15.0ms
(/ (+ t1 u) t1)

simplify906.0ms

Counts
41 → 82
Calls

41 calls. Slowest were:

223.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
191.0ms
(+ (log (/ -1 (/ (+ t1 u) t1))) (log (/ v (+ t1 u))))
116.0ms
(* (/ (+ t1 u) t1) (+ t1 u))

prune772.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes234.0ms

Accuracy

0% (1.2b remaining)

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

bsearch3.0ms

end0.0ms

sample1.3s

Algorithm
intervals