Details

sample21.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify126.0ms

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 (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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 2.30753 (* x 0.27061))
0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
15.3b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

3.0ms	(+ 2.30753 (* x 0.27061))
17.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 2.30753 (* x 0.27061))
98.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
262.0ms	(* x (+ 0.99229 (* x 0.04481)))
56.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	516	893
1	2218	827
2	5001	827

prune196.0ms

Filtered

103 candidates to 74 candidates (71.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	2	104

Merged error: 0b

Counts

104 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
0.1b	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
15.2b	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
15.2b	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

15.0ms	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
7.0ms	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
2.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
161.0ms	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
80.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
80.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	929	6227
1	3540	5694
2	5002	5620

prune538.0ms

Filtered

276 candidates to 150 candidates (54.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	276	2	278

Merged error: 0b

Counts

278 → 2

localize13.0ms

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))
0.2b	(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
15.3b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

5.0ms	(* x (+ 0.99229 (* x 0.04481)))
14.0ms	(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
15.0ms	(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (+ 0.99229 (* x 0.04481)))
126.0ms	(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
155.0ms	(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
62.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	606	1382
1	2775	1233
2	5003	1233

prune255.0ms

Filtered

127 candidates to 86 candidates (67.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0b

Counts

129 → 2

regimes29.0ms

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	25	16
1	25	16

end0.0ms

sample462.0ms

Algorithm

intervals

Results

365.0ms

8000×

body

valid

Details

sample21.0ms

simplify126.0ms

prune2.0ms

localize11.0ms

rewrite34.0ms

series454.0ms

simplify65.0ms

prune196.0ms

localize13.0ms

rewrite45.0ms

series377.0ms

simplify123.0ms

prune538.0ms

localize13.0ms

rewrite44.0ms

series414.0ms

simplify84.0ms

prune255.0ms

regimes29.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample462.0ms

Profiling