Average Error: 18.2 → 1.3
Time: 24.4s
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 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 23.8s)Debug log

sample122.0ms

Algorithm
intervals

simplify181.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

181.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
2 → 60
Calls

2 calls. Slowest were:

17.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
8.0ms
(* (+ t1 u) (+ t1 u))

series82.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

60.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
23.0ms
(* (+ t1 u) (+ t1 u))

simplify4.3s

Counts
48 → 66
Calls

48 calls. Slowest were:

405.0ms
(* (- (* t1 t1) (* u u)) (+ (pow t1 3) (pow u 3)))
360.0ms
(/ (* (* (* (- t1) v) (* (- t1) v)) (* (- t1) v)) (* (* (* (+ t1 u) (+ t1 u)) (* (+ t1 u) (+ t1 u))) (* (+ t1 u) (+ t1 u))))
358.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (+ (* t1 t1) (- (* u u) (* t1 u))))

prune695.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
3 → 97
Calls

3 calls. Slowest were:

6.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
5.0ms
(/ (- t1) (+ t1 u))
1.0ms
(/ v (+ t1 u))

series121.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

77.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
27.0ms
(/ (- t1) (+ t1 u))
17.0ms
(/ v (+ t1 u))

simplify1.9s

Counts
82 → 106
Calls

82 calls. Slowest were:

477.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
277.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
179.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize11.0ms

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))

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
3 → 92
Calls

3 calls. Slowest were:

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

series155.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

76.0ms
(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))
59.0ms
(* (/ (- t1) (+ t1 u)) v)
20.0ms
(/ (- t1) (+ t1 u))

simplify1.5s

Counts
79 → 101
Calls

79 calls. Slowest were:

438.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
140.0ms
(/ (* (* (* (/ (- t1) (+ t1 u)) v) (* (/ (- t1) (+ t1 u)) v)) (* (/ (- t1) (+ t1 u)) v)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
139.0ms
(- (log (* (/ (- t1) (+ t1 u)) v)) (log (+ t1 u)))

prune968.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.8b
(/ (/ (- t1) (+ t1 u)) (/ (+ t1 u) v))
0.0b
(/ (+ t1 u) v)
0.0b
(/ (- t1) (+ t1 u))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
3 → 168
Calls

3 calls. Slowest were:

7.0ms
(/ (/ (- t1) (+ t1 u)) (/ (+ t1 u) v))
5.0ms
(/ (+ t1 u) v)
3.0ms
(/ (- t1) (+ t1 u))

series153.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

94.0ms
(/ (/ (- t1) (+ t1 u)) (/ (+ t1 u) v))
37.0ms
(/ (- t1) (+ t1 u))
22.0ms
(/ (+ t1 u) v)

simplify8.8s

Counts
220 → 177
Calls

220 calls. Slowest were:

431.0ms
(/ (/ (- t1) (- (* t1 t1) (* u u))) (* (cbrt (/ (+ t1 u) v)) (cbrt (/ (+ t1 u) v))))
424.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
372.0ms
(/ (/ (- t1) (- (* t1 t1) (* u u))) (+ t1 u))

prune2.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (1.3b remaining)

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

bsearch7.0ms

end0.0ms

sample1.2s

Algorithm
intervals