Average Error: 0.2 → 0.0
Time: 9.6s
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 2019004 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 9.2s)Debug log

sample56.0ms

Algorithm
intervals

simplify75.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

75.0ms
(+ (+ (* 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)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

5.0ms
(* (+ d2 30) d1)

series26.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

26.0ms
(* (+ d2 30) d1)

simplify252.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

167.0ms
(* (- (* d2 d2) (* 30 30)) d1)
41.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
13.0ms
(+ (* d2 d1) (* 30 d1))

prune120.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

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))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

19.0ms
(* (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:

63.0ms
(* (sqrt (+ d2 30)) d1)
26.0ms
(* (sqrt (+ d2 30)) (* (sqrt (+ d2 30)) d1))
22.0ms
(sqrt (+ d2 30))
22.0ms
(sqrt (+ d2 30))

simplify2.2s

Counts
51 → 90
Calls

51 calls. Slowest were:

432.0ms
(* (* (* (sqrt (+ d2 30)) (sqrt (+ d2 30))) (sqrt (+ d2 30))) (* (* (* (sqrt (+ d2 30)) d1) (* (sqrt (+ d2 30)) d1)) (* (sqrt (+ d2 30)) d1)))
316.0ms
(* (sqrt (- (* d2 d2) (* 30 30))) (* (sqrt (- (* d2 d2) (* 30 30))) d1))
254.0ms
(- (+ (* (sqrt 30) d1) (* 1/2 (/ (* d2 d1) (sqrt 30)))) (* 1/8 (/ (* (pow d2 2) d1) (pow (sqrt 30) 3))))

prune777.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

17.1b
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
4.3b
(* (+ (pow d2 3) (pow 30 3)) d1)
0.0b
(+ (* d2 d2) (- (* 30 30) (* d2 30)))
0.0b
(- (* 30 30) (* d2 30))

rewrite37.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

23.0ms
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
7.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
5.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

series119.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

57.0ms
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
27.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
26.0ms
(- (* 30 30) (* d2 30))
9.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

simplify3.1s

Counts
43 → 90
Calls

43 calls. Slowest were:

356.0ms
(+ (* (* d2 d2) (* d2 d2)) (- (* (- (* 30 30) (* d2 30)) (- (* 30 30) (* d2 30))) (* (* d2 d2) (- (* 30 30) (* d2 30)))))
308.0ms
(* (+ (pow (pow d2 3) 3) (pow (pow 30 3) 3)) d1)
286.0ms
(* (+ (pow (pow d2 3) 3) (pow (pow 30 3) 3)) d1)

prune973.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes70.0ms

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