Average Error: 0.1 → 0.1
Time: 36.0s
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 2019008 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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

Details

Time bar (total: 35.3s)Debug log

sample71.0ms

Algorithm
intervals

simplify31.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

31.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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)))

series18.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify385.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

205.0ms
(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
47.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
40.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune216.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

10.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))
2.0ms
(+ (* d1 3) (* d1 d2))

series47.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

28.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))
18.0ms
(+ (* d1 3) (* d1 d2))

simplify627.0ms

Counts
12 → 32
Calls

12 calls. Slowest were:

252.0ms
(* (* (exp (* d1 3)) (exp (* d1 d2))) (exp (* d1 d3)))
155.0ms
(* (exp (+ (* d1 3) (* d1 d2))) (exp (* d1 d3)))
49.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune325.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

9.0ms
(* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))
1.0ms
(cbrt (+ d2 (+ 3 d3)))
1.0ms
(cbrt (+ d2 (+ 3 d3)))

series320.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

89.0ms
(cbrt (+ d2 (+ 3 d3)))
86.0ms
(cbrt (+ d2 (+ 3 d3)))
77.0ms
(cbrt (+ d2 (+ 3 d3)))
67.0ms
(* (cbrt (+ d2 (+ 3 d3))) (cbrt (+ d2 (+ 3 d3))))

simplify6.6s

Counts
59 → 87
Calls

59 calls. Slowest were:

503.0ms
(* (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (+ d2 (+ 3 d3))))
480.0ms
(* (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))))
413.0ms
(* (cbrt (+ (pow d2 3) (pow (+ 3 d3) 3))) (cbrt (+ d2 (+ 3 d3))))

prune882.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

19.0b
(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
2.0b
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
0.7b
(/ (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (- d2 (+ 3 d3))))
0.4b
(cbrt (- d2 (+ 3 d3)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 113
Calls

4 calls. Slowest were:

11.0ms
(/ (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (- d2 (+ 3 d3))))
4.0ms
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
3.0ms
(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))

series332.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

133.0ms
(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
106.0ms
(/ (cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (cbrt (- d2 (+ 3 d3))))
74.0ms
(cbrt (- d2 (+ 3 d3)))
18.0ms
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))

simplify21.2s

Counts
130 → 125
Calls

130 calls. Slowest were:

679.0ms
(cbrt (- (pow (* d2 d2) 3) (pow (* (+ 3 d3) (+ 3 d3)) 3)))
628.0ms
(cbrt (- (* (* d2 d2) (* d2 d2)) (* (* (+ 3 d3) (+ 3 d3)) (* (+ 3 d3) (+ 3 d3)))))
521.0ms
(cbrt (- (pow (* d2 d2) 3) (pow (* (+ 3 d3) (+ 3 d3)) 3)))

prune1.9s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes206.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm
intervals