Average Error: 0.0 → 0.0
Time: 22.5s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(d2 + \left(d3 + 37\right)\right) \cdot d1\]

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

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(d3 + \left(d2 + 37\right)\right) \cdot d1}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{d3 \cdot d1 + \left(d2 \cdot d1 + 37 \cdot d1\right)}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(37 + d3\right)\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(d2 + \left(d3 + 37\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019002 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))

Details

Time bar (total: 22.0s)Debug log

sample57.0ms

Algorithm
intervals

simplify314.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

314.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d3 (+ d2 37)) d1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

3.0ms
(* (+ d3 (+ d2 37)) d1)

series18.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

18.0ms
(* (+ d3 (+ d2 37)) d1)

simplify894.0ms

Counts
7 → 16
Calls

7 calls. Slowest were:

639.0ms
(* (+ (pow d3 3) (pow (+ d2 37) 3)) d1)
124.0ms
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
49.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))

prune147.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ d2 (+ 37 d3)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* d1 (+ d2 (+ 37 d3)))

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

19.0ms
(* d1 (+ d2 (+ 37 d3)))

simplify364.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

191.0ms
(+ (* d2 d2) (- (* (+ 37 d3) (+ 37 d3)) (* d2 (+ 37 d3))))
40.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
38.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune181.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ d3 (+ d2 37)))
0.6b
(cbrt (+ d3 (+ d2 37)))
0.6b
(cbrt (+ d3 (+ d2 37)))
0.3b
(* (cbrt (+ d3 (+ d2 37))) (cbrt (+ d3 (+ d2 37))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

11.0ms
(* (cbrt (+ d3 (+ d2 37))) (cbrt (+ d3 (+ d2 37))))
2.0ms
(cbrt (+ d3 (+ d2 37)))
1.0ms
(cbrt (+ d3 (+ d2 37)))

series361.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

106.0ms
(cbrt (+ d3 (+ d2 37)))
100.0ms
(cbrt (+ d3 (+ d2 37)))
85.0ms
(cbrt (+ d3 (+ d2 37)))
70.0ms
(* (cbrt (+ d3 (+ d2 37))) (cbrt (+ d3 (+ d2 37))))

simplify7.5s

Counts
59 → 87
Calls

59 calls. Slowest were:

508.0ms
(cbrt (- (* d3 d3) (* (+ d2 37) (+ d2 37))))
504.0ms
(cbrt (- (* d3 d3) (* (+ d2 37) (+ d2 37))))
491.0ms
(* (cbrt (+ (pow d3 3) (pow (+ d2 37) 3))) (cbrt (- (* d3 d3) (* (+ d2 37) (+ d2 37)))))

prune989.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

17.0b
(/ (* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1) (- d3 (+ d2 37)))
9.0b
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
2.8b
(- (* d3 d3) (* (+ d2 37) (+ d2 37)))
0.0b
(* (+ d2 37) (+ d2 37))

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
4 → 82
Calls

4 calls. Slowest were:

13.0ms
(/ (* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1) (- d3 (+ d2 37)))
9.0ms
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
7.0ms
(* (+ d2 37) (+ d2 37))

series151.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

74.0ms
(/ (* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1) (- d3 (+ d2 37)))
38.0ms
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
30.0ms
(- (* d3 d3) (* (+ d2 37) (+ d2 37)))
8.0ms
(* (+ d2 37) (+ d2 37))

simplify8.5s

Counts
63 → 94
Calls

63 calls. Slowest were:

713.0ms
(* (- (pow (* d3 d3) 3) (pow (* (+ d2 37) (+ d2 37)) 3)) d1)
637.0ms
(* (- (pow (* d3 d3) 3) (pow (* (+ d2 37) (+ d2 37)) 3)) d1)
571.0ms
(* (- (* d2 d2) (* 37 37)) (+ d2 37))

prune662.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals