Average Error: 0.2 → 0.0
Time: 7.6s
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 2019008 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 7.2s)Debug log

sample60.0ms

Algorithm
intervals

simplify81.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

81.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)

series23.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

23.0ms
(* (+ d2 30) d1)

simplify252.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

174.0ms
(* (- (* d2 d2) (* 30 30)) d1)
36.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
11.0ms
(+ (* d2 d1) (* 30 d1))

prune104.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

6.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
2.0ms
(* (fma d2 d2 -900) d1)

series70.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

36.0ms
(* (fma d2 d2 -900) d1)
34.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))

simplify278.0ms

Counts
22 → 42
Calls

22 calls. Slowest were:

67.0ms
(/ (* (* (* (fma d2 d2 -900) d1) (* (fma d2 d2 -900) d1)) (* (fma d2 d2 -900) d1)) (* (* (- d2 30) (- d2 30)) (- d2 30)))
55.0ms
(- (log (* (fma d2 d2 -900) d1)) (log (- d2 30)))
34.0ms
(+ (* d2 d2) (+ (* 30 30) (* d2 30)))

prune354.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

7.5b
(* (* (fma d2 d2 -900) d1) (/ 1 (- d2 30)))
3.3b
(* (fma d2 d2 -900) d1)
0.0b
(/ 1 (- d2 30))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 56
Calls

3 calls. Slowest were:

8.0ms
(* (* (fma d2 d2 -900) d1) (/ 1 (- d2 30)))
2.0ms
(* (fma d2 d2 -900) d1)
1.0ms
(/ 1 (- d2 30))

series64.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

34.0ms
(* (* (fma d2 d2 -900) d1) (/ 1 (- d2 30)))
24.0ms
(* (fma d2 d2 -900) d1)
7.0ms
(/ 1 (- d2 30))

simplify1.2s

Counts
30 → 65
Calls

30 calls. Slowest were:

340.0ms
(* (* (fma d2 d2 -900) d1) (/ 1 (- d2 30)))
191.0ms
(- (+ (* 1/900 d2) (+ (* 1/27000 (pow d2 2)) 1/30)))
114.0ms
(+ (/ 1 d2) (+ (* 30 (/ 1 (pow d2 2))) (* 900 (/ 1 (pow d2 3)))))

prune652.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

10.9b
(* (fma d2 d2 -900) (* d1 (/ 1 (- d2 30))))
0.1b
(* d1 (/ 1 (- d2 30)))
0.0b
(/ 1 (- d2 30))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
3 → 57
Calls

3 calls. Slowest were:

9.0ms
(* (fma d2 d2 -900) (* d1 (/ 1 (- d2 30))))
2.0ms
(* d1 (/ 1 (- d2 30)))
2.0ms
(/ 1 (- d2 30))

series85.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

49.0ms
(* (fma d2 d2 -900) (* d1 (/ 1 (- d2 30))))
29.0ms
(* d1 (/ 1 (- d2 30)))
7.0ms
(/ 1 (- d2 30))

simplify2.1s

Counts
31 → 66
Calls

31 calls. Slowest were:

709.0ms
(* (* (* (fma d2 d2 -900) (fma d2 d2 -900)) (fma d2 d2 -900)) (* (* (* d1 (/ 1 (- d2 30))) (* d1 (/ 1 (- d2 30)))) (* d1 (/ 1 (- d2 30)))))
240.0ms
(- (+ (* 1/900 d2) (+ (* 1/27000 (pow d2 2)) 1/30)))
207.0ms
(+ (/ d1 d2) (+ (* 30 (/ d1 (pow d2 2))) (* 900 (/ d1 (pow d2 3)))))

prune692.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals