Average Error: 0.2 → 0.0
Time: 6.7s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot 30 + d2 \cdot d1\]

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. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{d1 \cdot 30 + d1 \cdot d2}\]

  5. Final simplification0.0

    \[\leadsto d1 \cdot 30 + d2 \cdot d1\]

Reproduce

herbie shell --seed 2019008 
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 6.2s)Debug log

sample26.0ms

Algorithm
intervals

simplify27.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

27.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

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))

series17.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

17.0ms
(* d1 (+ 30 d2))

simplify99.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

56.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
11.0ms
(+ (* d2 d1) (* 30 d1))
10.0ms
(+ (* d2 d1) (* 30 d1))

prune132.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (* d1 30) (* d1 d2))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

2.0ms
(+ (* d1 30) (* d1 d2))

series30.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

30.0ms
(+ (* d1 30) (* d1 d2))

simplify54.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

20.0ms
(* (exp (* d1 30)) (exp (* d1 d2)))
10.0ms
(+ (* d2 d1) (* 30 d1))
10.0ms
(+ (* d2 d1) (* 30 d1))

prune121.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 2 expressions with local error:

7.4b
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
3.3b
(* d1 (- (* 30 30) (* d2 d2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

11.0ms
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
7.0ms
(* d1 (- (* 30 30) (* d2 d2)))

series80.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

47.0ms
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
34.0ms
(* d1 (- (* 30 30) (* d2 d2)))

simplify2.4s

Counts
31 → 47
Calls

31 calls. Slowest were:

586.0ms
(/ (- (* 30 30) (* d2 d2)) (- 30 d2))
347.0ms
(* d1 (- (pow (* 30 30) 3) (pow (* d2 d2) 3)))
239.0ms
(* d1 (- (* (* 30 30) (* 30 30)) (* (* d2 d2) (* d2 d2))))

prune390.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

7.4b
(/ (* d1 (- 900 (* d2 d2))) (- 30 d2))
3.3b
(* d1 (- 900 (* d2 d2)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 40
Calls

2 calls. Slowest were:

4.0ms
(/ (* d1 (- 900 (* d2 d2))) (- 30 d2))
1.0ms
(* d1 (- 900 (* d2 d2)))

series106.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

55.0ms
(/ (* d1 (- 900 (* d2 d2))) (- 30 d2))
51.0ms
(* d1 (- 900 (* d2 d2)))

simplify1.1s

Counts
30 → 46
Calls

30 calls. Slowest were:

312.0ms
(* d1 (- (pow 900 3) (pow (* d2 d2) 3)))
272.0ms
(* d1 (- (* 900 900) (* (* d2 d2) (* d2 d2))))
104.0ms
(/ (* (* (* d1 (- 900 (* d2 d2))) (* d1 (- 900 (* d2 d2)))) (* d1 (- 900 (* d2 d2)))) (* (* (- 30 d2) (- 30 d2)) (- 30 d2)))

prune390.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes97.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm
intervals