Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

328×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (13.0ms)

Iter	Nodes	Cost
0	26	6
1	55	6
2	122	6
3	205	6
4	253	5
5	307	5
6	363	5
7	498	5
8	911	5
9	1187	5
10	1188	5
11	1188	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x 3.0) 4.0)
0.1b	(* 3.0 (+ 1.0 (* x (- (* x 3.0) 4.0))))
0.1b	(* x (- (* x 3.0) 4.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`associate-*r/`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`flip3-+` `diff-log` `flip-+`

Counts

3 → 58

Calls

3 calls:

8.0ms	(- (* x 3.0) 4.0)
15.0ms	(* 3.0 (+ 1.0 (* x (- (* x 3.0) 4.0))))
33.0ms	(* x (- (* x 3.0) 4.0))

series140.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(- (* x 3.0) 4.0)
31.0ms	(* 3.0 (+ 1.0 (* x (- (* x 3.0) 4.0))))
66.0ms	(* x (- (* x 3.0) 4.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	267	361
1	1213	324
2	5002	323

prune114.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (* 9.0 (pow x 2)) 3.0) (* 12.0 x))
0.2b	(* 9.0 (pow x 2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 41

Calls

2 calls:

53.0ms	(- (+ (* 9.0 (pow x 2)) 3.0) (* 12.0 x))
11.0ms	(* 9.0 (pow x 2))

series53.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (+ (* 9.0 (pow x 2)) 3.0) (* 12.0 x))
25.0ms	(* 9.0 (pow x 2))

simplify135.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	193	239
1	761	207
2	3883	201
3	5001	200

prune84.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* 9.0 x) 12.0)
0.1b	(* x (- (* 9.0 x) 12.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`sub-neg` `associate-r` `associate-l`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 36

Calls

2 calls:

8.0ms	(- (* 9.0 x) 12.0)
27.0ms	(* x (- (* 9.0 x) 12.0))

series105.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* 9.0 x) 12.0)
66.0ms	(* x (- (* 9.0 x) 12.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	135	189
1	536	167
2	2705	166
3	5001	166

prune73.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 9.0 x) 12.0)
0.1b	(* x (/ (- (* (* 9.0 x) (* 9.0 x)) (* 12.0 12.0)) (+ (* 9.0 x) 12.0)))
0.2b	(/ (- (* (* 9.0 x) (* 9.0 x)) (* 12.0 12.0)) (+ (* 9.0 x) 12.0))
0.3b	(* (* 9.0 x) (* 9.0 x))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
27×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-exp-log` `add-cbrt-cube`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`pow-prod-down`
10×	`prod-exp` `cbrt-unprod`
7×	`difference-of-squares`
6×	`add-log-exp`
4×	`associate-l` `associate-/r/` `pow-sqr` `pow-prod-up` `associate-/l*`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `pow-plus` `div-exp` `*-commutative` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `pow2` `flip3--` `frac-2neg` `div-sub` `associate-*r/` `swap-sqr` `clear-num` `sum-log` `flip--`

Counts

4 → 118

Calls

4 calls:

7.0ms	(+ (* 9.0 x) 12.0)
93.0ms	(* x (/ (- (* (* 9.0 x) (* 9.0 x)) (* 12.0 12.0)) (+ (* 9.0 x) 12.0)))
77.0ms	(/ (- (* (* 9.0 x) (* 9.0 x)) (* 12.0 12.0)) (+ (* 9.0 x) 12.0))
26.0ms	(* (* 9.0 x) (* 9.0 x))

series363.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* 9.0 x) 12.0)
172.0ms	(* x (/ (- (* (* 9.0 x) (* 9.0 x)) (* 12.0 12.0)) (+ (* 9.0 x) 12.0)))
122.0ms	(/ (- (* (* 9.0 x) (* 9.0 x)) (* 12.0 12.0)) (+ (* 9.0 x) 12.0))
29.0ms	(* (* 9.0 x) (* 9.0 x))

simplify83.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	433	1065
1	2422	940
2	5001	940

prune221.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample402.0ms

Algorithm

intervals

Results

256.0ms

10686×

body

valid