Average Error: 0.1 → 0.1
Time: 38.9s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d2 + \left(d3 + 3\right)\right) \cdot d1\]

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019002 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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

Details

Time bar (total: 38.4s)Debug log

sample66.0ms

Algorithm
intervals

simplify48.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

47.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

18.0ms
(* d1 (+ d2 (+ 3 d3)))

simplify367.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

169.0ms
(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
54.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
51.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune160.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))
1.0ms
(cbrt (+ d2 (+ 3 d3)))
1.0ms
(cbrt (+ d2 (+ 3 d3)))

series266.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

74.0ms
(* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))
65.0ms
(cbrt (+ d2 (+ 3 d3)))
65.0ms
(cbrt (+ d2 (+ 3 d3)))
63.0ms
(cbrt (+ d2 (+ 3 d3)))

simplify7.5s

Counts
59 → 87
Calls

59 calls. Slowest were:

625.0ms
(* (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (+ d2 (+ 3 d3))))
472.0ms
(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
468.0ms
(* (cbrt (+ (pow d2 3) (pow (+ 3 d3) 3))) (cbrt (+ (pow d2 3) (pow (+ 3 d3) 3))))

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

17.0b
(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
9.0b
(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
3.0b
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
3 → 56
Calls

3 calls. Slowest were:

11.0ms
(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
6.0ms
(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
4.0ms
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))

series187.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

101.0ms
(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
62.0ms
(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
23.0ms
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))

simplify5.5s

Counts
39 → 65
Calls

39 calls. Slowest were:

472.0ms
(sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
454.0ms
(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
380.0ms
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))

prune521.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

29.5b
(/ (* d1 (+ (pow d2 3) (pow (+ 3 d3) 3))) (- (* (+ d3 3) (+ d3 3)) (* (+ (- 3 d2) d3) d2)))
5.0b
(* d1 (+ (pow d2 3) (pow (+ 3 d3) 3)))
2.4b
(+ (pow d2 3) (pow (+ 3 d3) 3))
2.0b
(- (* (+ d3 3) (+ d3 3)) (* (+ (- 3 d2) d3) d2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 99
Calls

4 calls. Slowest were:

14.0ms
(/ (* d1 (+ (pow d2 3) (pow (+ 3 d3) 3))) (- (* (+ d3 3) (+ d3 3)) (* (+ (- 3 d2) d3) d2)))
7.0ms
(- (* (+ d3 3) (+ d3 3)) (* (+ (- 3 d2) d3) d2))
6.0ms
(* d1 (+ (pow d2 3) (pow (+ 3 d3) 3)))

series336.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

158.0ms
(/ (* d1 (+ (pow d2 3) (pow (+ 3 d3) 3))) (- (* (+ d3 3) (+ d3 3)) (* (+ (- 3 d2) d3) d2)))
96.0ms
(* d1 (+ (pow d2 3) (pow (+ 3 d3) 3)))
52.0ms
(+ (pow d2 3) (pow (+ 3 d3) 3))
30.0ms
(- (* (+ d3 3) (+ d3 3)) (* (+ (- 3 d2) d3) d2))

simplify18.8s

Counts
91 → 111
Calls

91 calls. Slowest were:

832.0ms
(* (exp (pow d2 3)) (exp (pow (+ 3 d3) 3)))
626.0ms
(* (* (+ (* d3 d3) (- (* 3 3) (* d3 3))) (- d3 3)) (- (- 3 d2) d3))
555.0ms
(* (* (- d3 3) (- d3 3)) (+ (* (- 3 d2) (- 3 d2)) (- (* d3 d3) (* (- 3 d2) d3))))

prune1.6s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals