Average Error: 0.2 → 0.0
Time: 7.7s
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 2019005 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 7.3s)Debug log

sample42.0ms

Algorithm
intervals

simplify39.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

39.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)

simplify230.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

175.0ms
(* (- (* d2 d2) (* 30 30)) d1)
18.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
11.0ms
(+ (* d2 d1) (* 30 d1))

prune120.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

11.0ms
(* (sqrt (+ d2 30)) (* (sqrt (+ d2 30)) d1))
6.0ms
(* (sqrt (+ d2 30)) d1)
1.0ms
(sqrt (+ d2 30))

series133.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

62.0ms
(* (sqrt (+ d2 30)) d1)
25.0ms
(sqrt (+ d2 30))
24.0ms
(* (sqrt (+ d2 30)) (* (sqrt (+ d2 30)) d1))
22.0ms
(sqrt (+ d2 30))

simplify2.3s

Counts
51 → 90
Calls

51 calls. Slowest were:

486.0ms
(* (* (* (sqrt (+ d2 30)) (sqrt (+ d2 30))) (sqrt (+ d2 30))) (* (* (* (sqrt (+ d2 30)) d1) (* (sqrt (+ d2 30)) d1)) (* (sqrt (+ d2 30)) d1)))
377.0ms
(* (sqrt (- (* d2 d2) (* 30 30))) (* (sqrt (- (* d2 d2) (* 30 30))) d1))
314.0ms
(- (+ (* (sqrt 30) d1) (* 1/2 (/ (* d2 d1) (sqrt 30)))) (* 1/8 (/ (* (pow d2 2) d1) (pow (sqrt 30) 3))))

prune814.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b
(expm1 (log1p (sqrt (+ d2 30))))
0.2b
(* (expm1 (log1p (sqrt (+ d2 30)))) (* (sqrt (+ d2 30)) d1))
0.1b
(* (sqrt (+ d2 30)) d1)
0.0b
(log1p (sqrt (+ d2 30)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

17.0ms
(* (expm1 (log1p (sqrt (+ d2 30)))) (* (sqrt (+ d2 30)) d1))
6.0ms
(* (sqrt (+ d2 30)) d1)
1.0ms
(log1p (sqrt (+ d2 30)))

series531.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

332.0ms
(* (expm1 (log1p (sqrt (+ d2 30)))) (* (sqrt (+ d2 30)) d1))
88.0ms
(expm1 (log1p (sqrt (+ d2 30))))
65.0ms
(log1p (sqrt (+ d2 30)))
46.0ms
(* (sqrt (+ d2 30)) d1)

simplify1.1s

Counts
28 → 71
Calls

28 calls. Slowest were:

315.0ms
(* (* (* (expm1 (log1p (sqrt (+ d2 30)))) (expm1 (log1p (sqrt (+ d2 30))))) (expm1 (log1p (sqrt (+ d2 30))))) (* (* (* (sqrt (+ d2 30)) d1) (* (sqrt (+ d2 30)) d1)) (* (sqrt (+ d2 30)) d1)))
261.0ms
(- (+ (* (sqrt 30) d1) (* 1/2 (/ (* d2 d1) (sqrt 30)))) (* 1/8 (/ (* (pow d2 2) d1) (pow (sqrt 30) 3))))
134.0ms
(- (+ (* 1/2 (/ d2 (* (+ (sqrt 30) 1) (sqrt 30)))) (log (+ (sqrt 30) 1))) (+ (* 1/8 (/ (pow d2 2) (* (+ (sqrt 30) 1) (pow (sqrt 30) 3)))) (* 1/8 (/ (pow d2 2) (* (pow (+ (sqrt 30) 1) 2) (pow (sqrt 30) 2))))))

prune651.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm
intervals