Average Error: 0.2 → 0.0
Time: 9.7s
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 2019007 
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 9.3s)Debug log

sample27.0ms

Algorithm
intervals

simplify32.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

32.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune7.0ms

Pruning

1 alts after pruning (1 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))

series21.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

21.0ms
(* d1 (+ 30 d2))

simplify107.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

77.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
5.0ms
(+ (* d2 d1) (* 30 d1))
5.0ms
(+ (* d2 d1) (* 30 d1))

prune124.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 2 expressions with local error:

12.1b
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
4.2b
(* d1 (- (* 30 30) (* d2 d2)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

12.0ms
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
4.0ms
(* d1 (- (* 30 30) (* d2 d2)))

series85.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

44.0ms
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
40.0ms
(* d1 (- (* 30 30) (* d2 d2)))

simplify2.2s

Counts
31 → 47
Calls

31 calls. Slowest were:

539.0ms
(/ (- (* 30 30) (* d2 d2)) (- 30 d2))
385.0ms
(* d1 (- (pow (* 30 30) 3) (pow (* d2 d2) 3)))
204.0ms
(* d1 (- (* (* 30 30) (* 30 30)) (* (* d2 d2) (* d2 d2))))

prune420.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

12.6b
(/ (- 30 d2) (- (* 30 30) (* d2 d2)))
0.2b
(/ d1 (/ (- 30 d2) (- (* 30 30) (* d2 d2))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
2 → 65
Calls

2 calls. Slowest were:

8.0ms
(/ (- 30 d2) (- (* 30 30) (* d2 d2)))
3.0ms
(/ d1 (/ (- 30 d2) (- (* 30 30) (* d2 d2))))

series89.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

68.0ms
(/ d1 (/ (- 30 d2) (- (* 30 30) (* d2 d2))))
21.0ms
(/ (- 30 d2) (- (* 30 30) (* d2 d2)))

simplify4.3s

Counts
62 → 71
Calls

62 calls. Slowest were:

173.0ms
(+ (* (* 30 30) (* 30 30)) (+ (* (* d2 d2) (* d2 d2)) (* (* 30 30) (* d2 d2))))
170.0ms
(sqrt (/ (- 30 d2) (- (* 30 30) (* d2 d2))))
167.0ms
(/ (* (cbrt (- 30 d2)) (cbrt (- 30 d2))) (* (cbrt (- (* 30 30) (* d2 d2))) (cbrt (- (* 30 30) (* d2 d2)))))

prune592.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals