Average Error: 0.2 → 0.0
Time: 12.7s
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 2019002 
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 12.3s)Debug log

sample47.0ms

Algorithm
intervals

simplify31.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

31.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))

series20.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

20.0ms
(* d1 (+ 30 d2))

simplify107.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

63.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
10.0ms
(+ (* d2 d1) (* 30 d1))
10.0ms
(+ (* d2 d1) (* 30 d1))

prune114.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2))))
0.4b
(* (* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))) (cbrt (+ 30 d2)))
0.2b
(* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))
0.2b
(cbrt (+ 30 d2))

rewrite37.0ms

Algorithm
rewrite-expression-head
Counts
4 → 110
Calls

4 calls. Slowest were:

15.0ms
(* (* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))) (cbrt (+ 30 d2)))
14.0ms
(* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2))))
5.0ms
(* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))

series206.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

100.0ms
(* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2))))
52.0ms
(* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))
37.0ms
(cbrt (+ 30 d2))
17.0ms
(* (* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))) (cbrt (+ 30 d2)))

simplify6.7s

Counts
109 → 122
Calls

109 calls. Slowest were:

738.0ms
(* (* (* (* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2)))) (* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2))))) (* d1 (* (cbrt (+ 30 d2)) (cbrt (+ 30 d2))))) (+ 30 d2))
269.0ms
(- (+ (* 1/90 (* (pow 30 1/3) d2)) (pow 30 1/3)) (* 1/8100 (* (pow 30 1/3) (pow d2 2))))
215.0ms
(- (+ (* 1/45 (* d2 (pow 900 1/3))) (pow 900 1/3)) (* 1/8100 (* (pow d2 2) (pow 900 1/3))))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

7.2b
(/ (* (- 900 (* d2 d2)) d1) (- 30 d2))
6.6b
(* (- 900 (* d2 d2)) d1)

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

5.0ms
(/ (* (- 900 (* d2 d2)) d1) (- 30 d2))
2.0ms
(* (- 900 (* d2 d2)) d1)

series52.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

33.0ms
(/ (* (- 900 (* d2 d2)) d1) (- 30 d2))
20.0ms
(* (- 900 (* d2 d2)) d1)

simplify1.7s

Counts
26 → 42
Calls

26 calls. Slowest were:

405.0ms
(* (- (pow 900 3) (pow (* d2 d2) 3)) d1)
371.0ms
(* (- (pow 900 3) (pow (* d2 d2) 3)) d1)
256.0ms
(* (- (* 900 900) (* (* d2 d2) (* d2 d2))) d1)

prune281.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes67.0ms

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