Average Error: 0.2 → 0.0
Time: 11.8s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(30 + d2\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(30 + d2\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(30 + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2019005 
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))

Details

Time bar (total: 11.4s)Debug log

sample31.0ms

Algorithm
intervals

simplify48.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

48.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ 30 d2))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

1.0ms
(* d1 (+ 30 d2))

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

18.0ms
(* d1 (+ 30 d2))

simplify127.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

82.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
10.0ms
(+ (* d2 d1) (* 30 d1))
10.0ms
(+ (* d2 d1) (* 30 d1))

prune98.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* d1 (sqrt (+ 30 d2))) (sqrt (+ 30 d2)))
0.1b
(* d1 (sqrt (+ 30 d2)))
0.0b
(sqrt (+ 30 d2))
0.0b
(sqrt (+ 30 d2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

9.0ms
(* (* d1 (sqrt (+ 30 d2))) (sqrt (+ 30 d2)))
2.0ms
(* d1 (sqrt (+ 30 d2)))
1.0ms
(sqrt (+ 30 d2))

series105.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

47.0ms
(* d1 (sqrt (+ 30 d2)))
21.0ms
(sqrt (+ 30 d2))
19.0ms
(* (* d1 (sqrt (+ 30 d2))) (sqrt (+ 30 d2)))
17.0ms
(sqrt (+ 30 d2))

simplify2.6s

Counts
53 → 82
Calls

53 calls. Slowest were:

732.0ms
(* (* (* (* d1 (sqrt (+ 30 d2))) (* d1 (sqrt (+ 30 d2)))) (* d1 (sqrt (+ 30 d2)))) (* (* (sqrt (+ 30 d2)) (sqrt (+ 30 d2))) (sqrt (+ 30 d2))))
298.0ms
(- (+ (* (sqrt 30) d1) (* 1/2 (/ (* d2 d1) (sqrt 30)))) (* 1/8 (/ (* (pow d2 2) d1) (pow (sqrt 30) 3))))
269.0ms
(- (+ (* 1/2 (/ d2 (sqrt 30))) (sqrt 30)) (* 1/8 (/ (pow d2 2) (pow (sqrt 30) 3))))

prune622.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (sqrt (- 900 (* d2 d2))) (* (sqrt (+ 30 d2)) d1)) (sqrt (- 30 d2)))
0.1b
(* (sqrt (- 900 (* d2 d2))) (* (sqrt (+ 30 d2)) d1))
0.1b
(* (sqrt (+ 30 d2)) d1)
0.0b
(- 900 (* d2 d2))

rewrite46.0ms

Algorithm
rewrite-expression-head
Counts
4 → 90
Calls

4 calls. Slowest were:

24.0ms
(/ (* (sqrt (- 900 (* d2 d2))) (* (sqrt (+ 30 d2)) d1)) (sqrt (- 30 d2)))
17.0ms
(* (sqrt (- 900 (* d2 d2))) (* (sqrt (+ 30 d2)) d1))
3.0ms
(* (sqrt (+ 30 d2)) d1)

series232.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

85.0ms
(* (sqrt (- 900 (* d2 d2))) (* (sqrt (+ 30 d2)) d1))
65.0ms
(/ (* (sqrt (- 900 (* d2 d2))) (* (sqrt (+ 30 d2)) d1)) (sqrt (- 30 d2)))
54.0ms
(* (sqrt (+ 30 d2)) d1)
29.0ms
(- 900 (* d2 d2))

simplify4.6s

Counts
72 → 102
Calls

72 calls. Slowest were:

382.0ms
(* (sqrt (- (* 900 900) (* (* d2 d2) (* d2 d2)))) (* (sqrt (- (* 30 30) (* d2 d2))) d1))
370.0ms
(* (* (* (sqrt (- 900 (* d2 d2))) (sqrt (- 900 (* d2 d2)))) (sqrt (- 900 (* d2 d2)))) (* (* (* (sqrt (+ 30 d2)) d1) (* (sqrt (+ 30 d2)) d1)) (* (sqrt (+ 30 d2)) d1)))
364.0ms
(- (+ (* (sqrt 27000) d1) (* 450 (/ (* d2 d1) (sqrt 27000)))) (+ (* 101250 (/ (* (pow d2 2) d1) (pow (sqrt 27000) 3))) (* 15 (/ (* (pow d2 2) d1) (sqrt 27000)))))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals