Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify121.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	9
1	51	9
2	69	9
3	86	9
4	94	9
5	105	9
6	139	9
7	177	9
8	202	9
9	246	9
10	416	9
11	615	9
12	992	9
13	1948	9
14	2240	9
15	3154	9
16	5001	9

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.0b	(+ 2.30753 (* x 0.27061))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
14.0b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

30.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
9.0ms	(+ 2.30753 (* x 0.27061))
9.0ms	(* x (+ 0.99229 (* x 0.04481)))
19.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
33.0ms	(+ 2.30753 (* x 0.27061))
67.0ms	(* x (+ 0.99229 (* x 0.04481)))
63.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	502	1098
1	2145	1031
2	5001	1031

prune187.0ms

Filtered

129 candidates to 75 candidates (41.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	2	130

Merged error: 0b

Counts

130 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
0.1b	(/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
13.9b	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
13.9b	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

454×	`*-un-lft-identity`
280×	`associate-/r*`
252×	`frac-times`
251×	`sqrt-prod`
207×	`add-sqr-sqrt`
159×	`add-cube-cbrt`
144×	`distribute-lft-out`
138×	`associate-/l*`
110×	`times-frac`
102×	`associate-l`
46×	`associate-r`
36×	`clear-num`
35×	`frac-2neg`
30×	`add-exp-log` `associate-/l/`
20×	`flip3-+` `flip-+`
18×	`associate-*r/` `add-cbrt-cube`
15×	`unswap-sqr`
14×	`associate-*l/`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r/`
5×	`cbrt-undiv`
4×	`un-div-inv` `cbrt-unprod` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 489

Calls

4 calls:

71.0ms	(* (/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
16.0ms	(/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
11.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
11.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
104.0ms	(/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
81.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
88.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

501 → 501

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1518	7877
1	5001	7028

prune570.0ms

Filtered

501 candidates to 169 candidates (66.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	501	0	501
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	501	2	503

Merged error: 0b

Counts

503 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ 0.99229 (* x 0.04481)))
0.1b	(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.1b	(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
14.0b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

12.0ms	(* x (+ 0.99229 (* x 0.04481)))
31.0ms	(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
43.0ms	(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
19.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (+ 0.99229 (* x 0.04481)))
131.0ms	(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
167.0ms	(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
59.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	640	1912
1	2964	1730
2	5003	1726

prune273.0ms

Filtered

175 candidates to 99 candidates (43.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	175	2	177

Merged error: 0b

Counts

177 → 2

regimes27.0ms

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	30	17
1	30	17

end0.0ms

sample352.0ms

Algorithm

intervals

Results

263.0ms

8000×

body

valid