Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	189×	body	80	valid
3.0ms	27×	body	640	valid
2.0ms	17×	body	1280	valid
1.0ms	16×	body	320	valid
0.0ms	7×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5002	5

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: 22.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.1b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `times-frac` `associate-/r*` `add-log-exp`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `associate-*l/` `associate-/r/` `flip--` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

7.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series115.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
44.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	287	314
1	1151	281
2	5001	280

prune100.0ms

Filtered

47 candidates to 35 candidates (74.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	5	48

Merged error: 0.2b

Counts

48 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.4b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

5.0ms	(/ y (+ y 1.0))
12.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series151.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ y (+ y 1.0))
42.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
69.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	400	572
1	1790	526
2	5001	526

prune148.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
4.6b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
18.6b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

18.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
10.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series333.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
159.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
92.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	517	940
1	2749	822
2	5001	822

prune158.0ms

Filtered

92 candidates to 66 candidates (71.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Merged error: 0.2b

Counts

97 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

6.1b	(/ (* (- 1.0 x) y) (+ y 1.0))
6.1b	(/ (* (- 1.0 x) y) (+ y 1.0))
6.1b	(/ (* (- 1.0 x) y) (+ y 1.0))
12.2b	(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
87×	`times-frac`
64×	`difference-of-squares`
48×	`unpow-prod-down` `cube-prod`
40×	`add-cube-cbrt`
32×	`sqr-pow`
28×	`associate-/l*`
21×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--`
15×	`associate-/r*`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
6×	`associate-*l/` `distribute-lft-out`
4×	`pow1` `difference-cubes` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 201

Calls

4 calls:

9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
12.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
45.0ms	(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

series807.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
47.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
676.0ms	(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

simplify119.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	660	4788
1	2954	4635
2	5001	4633

prune449.0ms

Filtered

213 candidates to 135 candidates (63.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	214	4	218

Merged error: 0.2b

Counts

218 → 4

regimes173.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 24.8b

bsearch82.0ms

Steps

Iters	Range		Point
10	58344.181109934616	6083383802802402.0	66324553.14053678
8	-1.1084991128726907e+17	-7221686071369.7705	-7341054639220.949

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	33	14

end0.0ms

sample504.0ms

Algorithm

intervals

Results

174.0ms	6058×	body	80	valid
84.0ms	773×	body	640	valid
49.0ms	369×	body	1280	valid
42.0ms	482×	body	320	valid
17.0ms	318×	body	160	valid

Details

sample20.0ms

simplify70.0ms

prune2.0ms

localize10.0ms

rewrite17.0ms

series115.0ms

simplify39.0ms

prune100.0ms

localize6.0ms

rewrite23.0ms

series151.0ms

simplify53.0ms

prune148.0ms

localize10.0ms

rewrite34.0ms

series333.0ms

simplify77.0ms

prune158.0ms

localize15.0ms

rewrite84.0ms

series807.0ms

simplify119.0ms

prune449.0ms

regimes173.0ms

bsearch82.0ms

simplify1.0ms

end0.0ms

sample504.0ms

Profiling