Average Error: 17.9 → 1.4
Time: 27.8s
Precision: 64
Internal Precision: 128
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-1}{\frac{t1 + u}{t1}}\]

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 neg-mul-11.3

    \[\leadsto \frac{\color{blue}{-1 \cdot t1}}{t1 + u} \cdot \frac{v}{t1 + u}\]

  6. Applied associate-/l*1.4

    \[\leadsto \color{blue}{\frac{-1}{\frac{t1 + u}{t1}}} \cdot \frac{v}{t1 + u}\]

  7. Final simplification1.4

    \[\leadsto \frac{v}{t1 + u} \cdot \frac{-1}{\frac{t1 + u}{t1}}\]

Reproduce

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

Details

Time bar (total: 27.1s)Debug log

sample177.0ms

Algorithm
intervals

simplify166.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

166.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
2 → 60
Calls

2 calls. Slowest were:

18.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
8.0ms
(* (+ t1 u) (+ t1 u))

series77.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

62.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
15.0ms
(* (+ t1 u) (+ t1 u))

simplify4.3s

Counts
48 → 66
Calls

48 calls. Slowest were:

384.0ms
(* (- (* t1 t1) (* u u)) (+ (pow t1 3) (pow u 3)))
371.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (+ (* t1 t1) (- (* u u) (* t1 u))))
350.0ms
(/ (* (* (* (- t1) v) (* (- t1) v)) (* (- t1) v)) (* (* (* (+ t1 u) (+ t1 u)) (* (+ t1 u) (+ t1 u))) (* (+ t1 u) (+ t1 u))))

prune595.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 97
Calls

3 calls. Slowest were:

6.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
3.0ms
(/ (- t1) (+ t1 u))
0.0ms
(/ v (+ t1 u))

series121.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

78.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
25.0ms
(/ (- t1) (+ t1 u))
17.0ms
(/ v (+ t1 u))

simplify2.0s

Counts
82 → 106
Calls

82 calls. Slowest were:

447.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
341.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
140.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune988.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 105
Calls

4 calls. Slowest were:

28.0ms
(* (/ (* (cbrt (- t1)) (cbrt (- t1))) (* (cbrt (+ t1 u)) (cbrt (+ t1 u)))) (* (/ (cbrt (- t1)) (cbrt (+ t1 u))) (/ v (+ t1 u))))
1.0ms
(cbrt (- t1))
0.0ms
(cbrt (- t1))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

302.0ms
(cbrt (- t1))
299.0ms
(cbrt (- t1))
299.0ms
(cbrt (- t1))
234.0ms
(* (/ (* (cbrt (- t1)) (cbrt (- t1))) (* (cbrt (+ t1 u)) (cbrt (+ t1 u)))) (* (/ (cbrt (- t1)) (cbrt (+ t1 u))) (/ v (+ t1 u))))

simplify12.6s

Counts
79 → 117
Calls

79 calls. Slowest were:

535.0ms
(* (/ (* (* (* (cbrt (- t1)) (cbrt (- t1))) (* (cbrt (- t1)) (cbrt (- t1)))) (* (cbrt (- t1)) (cbrt (- t1)))) (* (+ t1 u) (+ t1 u))) (* (* (* (/ (cbrt (- t1)) (cbrt (+ t1 u))) (/ v (+ t1 u))) (* (/ (cbrt (- t1)) (cbrt (+ t1 u))) (/ v (+ t1 u)))) (* (/ (cbrt (- t1)) (cbrt (+ t1 u))) (/ v (+ t1 u)))))
535.0ms
(+ (- (+ (log (cbrt (- t1))) (log (cbrt (- t1)))) (+ (log (cbrt (+ t1 u))) (log (cbrt (+ t1 u))))) (+ (- (log (cbrt (- t1))) (log (cbrt (+ t1 u)))) (log (/ v (+ t1 u)))))
527.0ms
(* (* (cbrt (- t1)) (cbrt (- t1))) (* (/ (cbrt (- t1)) (cbrt (+ t1 u))) (/ v (+ t1 u))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize8.0ms

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)

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

6.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
2.0ms
(/ (+ t1 u) t1)
0.0ms
(/ -1 (/ (+ t1 u) t1))

series180.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

104.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
35.0ms
(/ -1 (/ (+ t1 u) t1))
29.0ms
(/ v (+ t1 u))
12.0ms
(/ (+ t1 u) t1)

simplify1.2s

Counts
41 → 90
Calls

41 calls. Slowest were:

276.0ms
(* (/ (+ t1 u) t1) (+ t1 u))
255.0ms
(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))
150.0ms
(+ (log (/ -1 (/ (+ t1 u) t1))) (log (/ v (+ t1 u))))

prune718.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes187.0ms

Accuracy

0% (1.4b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 1.4b

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals