Average Error: 17.6 → 1.1
Time: 21.4s
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 17.6

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

  3. Applied times-frac1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 20.8s)Debug log

sample326.0ms

Algorithm
intervals

simplify367.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

367.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize31.0ms

Local error

Found 2 expressions with local error:

15.8b
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
0.0b
(* (+ t1 u) (+ t1 u))

rewrite26.0ms

Algorithm
rewrite-expression-head
Counts
2 → 60
Calls

2 calls. Slowest were:

17.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
6.0ms
(* (+ t1 u) (+ t1 u))

series72.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

55.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
16.0ms
(* (+ t1 u) (+ t1 u))

simplify4.4s

Counts
48 → 66
Calls

48 calls. Slowest were:

361.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (+ (* t1 t1) (- (* u u) (* t1 u))))
350.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (+ (* t1 t1) (- (* u u) (* t1 u))))
348.0ms
(/ (* (* (* (- t1) v) (* (- t1) v)) (* (- t1) v)) (* (* (* (+ t1 u) (+ t1 u)) (* (+ t1 u) (+ t1 u))) (* (+ t1 u) (+ t1 u))))

prune716.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

1.6b
(* (/ (- 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))

series113.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

70.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
26.0ms
(/ (- t1) (+ t1 u))
17.0ms
(/ v (+ t1 u))

simplify2.1s

Counts
82 → 106
Calls

82 calls. Slowest were:

450.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
317.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
228.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune875.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
0.2b
(* (- t1) (/ 1 (+ t1 u)))
0.0b
(/ 1 (+ t1 u))
0.0b
(/ v (+ t1 u))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 94
Calls

4 calls. Slowest were:

21.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
8.0ms
(* (- t1) (/ 1 (+ t1 u)))
2.0ms
(/ 1 (+ t1 u))

series193.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

102.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
34.0ms
(* (- t1) (/ 1 (+ t1 u)))
29.0ms
(/ v (+ t1 u))
27.0ms
(/ 1 (+ t1 u))

simplify3.0s

Counts
60 → 106
Calls

60 calls. Slowest were:

452.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
446.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
304.0ms
(* (* (* (- t1) (- t1)) (- t1)) (* (* (/ 1 (+ t1 u)) (/ 1 (+ t1 u))) (/ 1 (+ t1 u))))

prune978.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

8.6b
(/ (* (- t1) v) (+ t1 u))
0.8b
(/ (/ (* (- t1) v) (+ t1 u)) (+ t1 u))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 83
Calls

2 calls. Slowest were:

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

series84.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

52.0ms
(/ (/ (* (- t1) v) (+ t1 u)) (+ t1 u))
32.0ms
(/ (* (- t1) v) (+ t1 u))

simplify5.1s

Counts
94 → 89
Calls

94 calls. Slowest were:

292.0ms
(/ (/ (* (- t1) v) (+ (pow t1 3) (pow u 3))) (* (cbrt (+ t1 u)) (cbrt (+ t1 u))))
273.0ms
(/ (* (- t1) v) (- (* t1 t1) (* u u)))
253.0ms
(- (log (/ (* (- t1) v) (+ t1 u))) (log (+ t1 u)))

prune827.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch3.0ms

end0.0ms

sample1.4s

Algorithm
intervals