Average Error: 0.1 → 0.1
Time: 22.1s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d2 \cdot d1 + \left(3 + d3\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(3 + d3\right)\right)}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in0.1

    \[\leadsto \color{blue}{d2 \cdot d1 + \left(3 + d3\right) \cdot d1}\]

  5. Final simplification0.1

    \[\leadsto d2 \cdot d1 + \left(3 + d3\right) \cdot d1\]

Reproduce

herbie shell --seed 2019005 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))

Details

Time bar (total: 21.6s)Debug log

sample71.0ms

Algorithm
intervals

simplify48.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

48.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ d2 (+ 3 d3)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* d1 (+ d2 (+ 3 d3)))

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

28.0ms
(* d1 (+ d2 (+ 3 d3)))

simplify307.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

153.0ms
(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
29.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
28.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune136.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* d2 d1) (* (+ 3 d3) d1))
0.0b
(* (+ 3 d3) d1)

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

5.0ms
(+ (* d2 d1) (* (+ 3 d3) d1))
4.0ms
(* (+ 3 d3) d1)

series38.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

23.0ms
(+ (* d2 d1) (* (+ 3 d3) d1))
16.0ms
(* (+ 3 d3) d1)

simplify417.0ms

Counts
12 → 31
Calls

12 calls. Slowest were:

150.0ms
(* (- (* 3 3) (* d3 d3)) d1)
98.0ms
(* (exp (* d2 d1)) (exp (* (+ 3 d3) d1)))
43.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune232.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (+ d2 (+ 3 d3)))
0.4b
(cbrt (+ d2 (+ 3 d3)))
0.4b
(cbrt (+ d2 (+ 3 d3)))
0.3b
(* (* d1 (* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))) (cbrt (+ d2 (+ 3 d3))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
4 → 83
Calls

4 calls. Slowest were:

22.0ms
(* (* d1 (* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))) (cbrt (+ d2 (+ 3 d3))))
1.0ms
(cbrt (+ d2 (+ 3 d3)))
1.0ms
(cbrt (+ d2 (+ 3 d3)))

series318.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

102.0ms
(cbrt (+ d2 (+ 3 d3)))
95.0ms
(cbrt (+ d2 (+ 3 d3)))
88.0ms
(cbrt (+ d2 (+ 3 d3)))
33.0ms
(* (* d1 (* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))) (cbrt (+ d2 (+ 3 d3))))

simplify14.1s

Counts
78 → 95
Calls

78 calls. Slowest were:

586.0ms
(* (* d1 (* (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (+ d2 (+ 3 d3))))) (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))))
512.0ms
(* (* d1 (* (cbrt (+ d2 (+ 3 d3))) (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))))) (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))))
498.0ms
(* (* d1 (* (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))))) (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

10.1b
(/ (* (- 9 (* d3 d3)) d1) (- 3 d3))
5.2b
(* (- 9 (* d3 d3)) d1)
0.0b
(+ (* d2 d1) (/ (* (- 9 (* d3 d3)) d1) (- 3 d3)))
0.0b
(- 9 (* d3 d3))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
4 → 58
Calls

4 calls. Slowest were:

5.0ms
(+ (* d2 d1) (/ (* (- 9 (* d3 d3)) d1) (- 3 d3)))
5.0ms
(/ (* (- 9 (* d3 d3)) d1) (- 3 d3))
2.0ms
(* (- 9 (* d3 d3)) d1)

series187.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

83.0ms
(+ (* d2 d1) (/ (* (- 9 (* d3 d3)) d1) (- 3 d3)))
49.0ms
(/ (* (- 9 (* d3 d3)) d1) (- 3 d3))
34.0ms
(* (- 9 (* d3 d3)) d1)
21.0ms
(- 9 (* d3 d3))

simplify1.7s

Counts
33 → 70
Calls

33 calls. Slowest were:

293.0ms
(* (- (pow 9 3) (pow (* d3 d3) 3)) d1)
274.0ms
(* (- (pow 9 3) (pow (* d3 d3) 3)) d1)
203.0ms
(* (- (* 9 9) (* (* d3 d3) (* d3 d3))) d1)

prune614.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm
intervals