Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	61×	body	640	valid
4.0ms	131×	body	80	valid
2.0ms	18×	body	1280	valid
2.0ms	27×	body	320	valid
1.0ms	19×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 9.9b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
19.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
30.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (+ x 1.0))
27.0ms	(/ 1.0 (- x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
268.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5001	816

prune203.0ms

Filtered

126 candidates to 92 candidates (73.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	3	127

Merged error: 0.1b

Counts

127 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ 1.0 (+ x 1.0)))
0.3b	(cbrt (/ 1.0 (+ x 1.0)))
0.3b	(cbrt (/ 1.0 (+ x 1.0)))
15.9b	(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
48×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`cbrt-div`
10×	`distribute-lft-out`
9×	`frac-add` `add-log-exp`
7×	`frac-sub`
6×	`associate-/r/`
5×	`frac-times` `associate-*l/`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`pow1/3` `associate-*r/` `div-inv`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 106

Calls

4 calls:

4.0ms	(cbrt (/ 1.0 (+ x 1.0)))
4.0ms	(cbrt (/ 1.0 (+ x 1.0)))
4.0ms	(cbrt (/ 1.0 (+ x 1.0)))
31.0ms	(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (/ 1.0 (+ x 1.0)))
150.0ms	(cbrt (/ 1.0 (+ x 1.0)))
149.0ms	(cbrt (/ 1.0 (+ x 1.0)))
245.0ms	(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	583	1569
1	1917	1428
2	5001	1297

prune338.0ms

Filtered

118 candidates to 94 candidates (79.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Merged error: 0.1b

Counts

121 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
18.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-*l/`
36×	`flip3--` `flip--`
32×	`frac-add`
28×	`frac-times`
24×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
15×	`add-sqr-sqrt`
14×	`associate-*r/`
13×	`*-un-lft-identity`
11×	`pow1`
10×	`associate-r`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
4×	`associate-+l+` `associate-l` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

8.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
21.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
10.0ms	(* (* (+ x 1.0) x) (- x 1.0))
11.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series226.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
88.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
98.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1037	2507
1	5001	2360

prune427.0ms

Filtered

156 candidates to 121 candidates (77.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	156	3	159

Merged error: 0.0b

Counts

159 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.1b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*l/`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`pow1`
8×	`frac-times` `add-cube-cbrt` `associate-r` `associate-/r/`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`flip3--` `flip--`
5×	`associate-l`
4×	`associate-*r/` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

6.0ms	(* (+ x 1.0) x)
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
10.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (+ x 1.0) x)
98.0ms	(* (* (+ x 1.0) x) (- x 1.0))
91.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	430	600
1	2219	516
2	5002	515

prune122.0ms

Filtered

93 candidates to 62 candidates (66.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	91	5	96

Merged error: 0.0b

Counts

96 → 5

regimes20.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample591.0ms

Algorithm

intervals

Results

200.0ms	1881×	body	640	valid
123.0ms	4179×	body	80	valid
75.0ms	893×	body	320	valid
74.0ms	555×	body	1280	valid
26.0ms	493×	body	160	valid