Average Error: 17.6 → 1.1
Time: 19.8s
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 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 18.8s)Debug log

sample162.0ms

Algorithm
intervals

simplify128.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

128.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

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))

series97.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

85.0ms
(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
12.0ms
(* (+ t1 u) (+ t1 u))

simplify4.4s

Counts
48 → 62
Calls

48 calls. Slowest were:

514.0ms
(- (log (* (- t1) v)) (+ (log (+ t1 u)) (log (+ t1 u))))
471.0ms
(* (- (* t1 t1) (* u u)) (+ t1 u))
320.0ms
(* (+ (* t1 t1) (- (* u u) (* t1 u))) (- t1 u))

prune594.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
3 → 91
Calls

3 calls. Slowest were:

12.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
7.0ms
(/ (- t1) (+ t1 u))
1.0ms
(/ v (+ t1 u))

series136.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

77.0ms
(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))
35.0ms
(/ (- t1) (+ t1 u))
24.0ms
(/ v (+ t1 u))

simplify1.7s

Counts
82 → 100
Calls

82 calls. Slowest were:

319.0ms
(/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u)))
300.0ms
(+ (- (log (- t1)) (log (+ t1 u))) (log (/ v (+ t1 u))))
181.0ms
(* (/ (* (* (- t1) (- t1)) (- t1)) (* (* (+ t1 u) (+ t1 u)) (+ t1 u))) (* (* (/ v (+ t1 u)) (/ v (+ t1 u))) (/ v (+ t1 u))))

prune867.0ms

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))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 86
Calls

4 calls. Slowest were:

21.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
8.0ms
(* (- t1) (/ 1 (+ t1 u)))
1.0ms
(/ 1 (+ t1 u))

series138.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

72.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
25.0ms
(/ v (+ t1 u))
25.0ms
(* (- t1) (/ 1 (+ t1 u)))
16.0ms
(/ 1 (+ t1 u))

simplify2.9s

Counts
60 → 98
Calls

60 calls. Slowest were:

440.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
414.0ms
(* (* (- t1) (/ 1 (+ t1 u))) (/ v (+ t1 u)))
345.0ms
(* (* (* (- t1) (- t1)) (- t1)) (* (* (/ 1 (+ t1 u)) (/ 1 (+ t1 u))) (/ 1 (+ t1 u))))

prune1.0s

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 → 79
Calls

2 calls. Slowest were:

8.0ms
(/ (/ (* (- t1) v) (+ t1 u)) (+ t1 u))
6.0ms
(/ (* (- t1) v) (+ t1 u))

series104.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

54.0ms
(/ (/ (* (- t1) v) (+ t1 u)) (+ t1 u))
50.0ms
(/ (* (- t1) v) (+ t1 u))

simplify4.3s

Counts
94 → 85
Calls

94 calls. Slowest were:

296.0ms
(/ (/ (* (- t1) v) (+ (pow t1 3) (pow u 3))) (* (cbrt (+ t1 u)) (cbrt (+ t1 u))))
285.0ms
(- (- (log (* (- t1) v)) (log (+ t1 u))) (log (+ t1 u)))
245.0ms
(/ (* (- t1) v) (- (* t1 t1) (* u u)))

prune684.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes145.0ms

Accuracy

0% (1.0b remaining)

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

bsearch4.0ms

end0.0ms

sample1.2s

Algorithm
intervals