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

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 6.4s)Debug log

sample26.0ms

Algorithm
intervals

simplify60.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

59.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune6.0ms

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
(* (+ d2 30) d1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

3.0ms
(* (+ d2 30) d1)

series14.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

14.0ms
(* (+ d2 30) d1)

simplify200.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

158.0ms
(* (- (* d2 d2) (* 30 30)) d1)
18.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
10.0ms
(+ (* d2 d1) (* 30 d1))

prune115.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

12.1b
(/ (* (fma d2 d2 -900) d1) (- d2 30))
4.2b
(* (fma d2 d2 -900) d1)

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

5.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
4.0ms
(* (fma d2 d2 -900) d1)

series86.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

48.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
38.0ms
(* (fma d2 d2 -900) d1)

simplify284.0ms

Counts
22 → 42
Calls

22 calls. Slowest were:

107.0ms
(/ (* (* (* (fma d2 d2 -900) d1) (* (fma d2 d2 -900) d1)) (* (fma d2 d2 -900) d1)) (* (* (- d2 30) (- d2 30)) (- d2 30)))
31.0ms
(- (log (* (fma d2 d2 -900) d1)) (log (- d2 30)))
21.0ms
(+ (* d2 d2) (+ (* 30 30) (* d2 30)))

prune301.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

18.5b
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
2.4b
(* (+ (pow d2 3) (pow 30 3)) d1)
0.0b
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
3 → 61
Calls

3 calls. Slowest were:

27.0ms
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
13.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
9.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

series82.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

46.0ms
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
27.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
9.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

simplify3.0s

Counts
36 → 70
Calls

36 calls. Slowest were:

309.0ms
(* (+ (pow (pow d2 3) 3) (pow (pow 30 3) 3)) d1)
308.0ms
(+ (* (* d2 d2) (* d2 d2)) (- (* (- (* 30 30) (* d2 30)) (- (* 30 30) (* d2 30))) (* (* d2 d2) (- (* 30 30) (* d2 30)))))
303.0ms
(* (+ (pow (pow d2 3) 3) (pow (pow 30 3) 3)) d1)

prune776.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals