Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	45×	body	1280	valid
5.0ms	46×	body	640	valid
4.0ms	128×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	10×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

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: 29.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
2.0ms	(/ x (+ x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune173.0ms

Filtered

113 candidates to 76 candidates (32.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.1b

Counts

114 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(exp (/ x (+ x 1.0)))
2.2b	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
2.6b	(log (exp (/ x (+ x 1.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
5.0ms	(exp (/ x (+ x 1.0)))
33.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
6.0ms	(log (exp (/ x (+ x 1.0))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ x (+ x 1.0))
3.0ms	(exp (/ x (+ x 1.0)))
7.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
3.0ms	(log (exp (/ x (+ x 1.0))))

simplify126.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	340	707
1	1019	638
2	3884	627
3	5001	627

prune168.0ms

Filtered

120 candidates to 90 candidates (25.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Merged error: 0.1b

Counts

125 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
20.1b	(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-div`
32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
20×	`frac-times` `flip3-+` `flip-+`
17×	`frac-sub`
14×	`add-cube-cbrt` `associate-*l/`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3` `distribute-lft-out`
7×	`associate-r/` `associate-r` `associate-l*`
6×	`add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
9.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
12.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
7.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	685	1563
1	2436	1476
2	5001	1428

prune260.0ms

Filtered

122 candidates to 82 candidates (32.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	120	7	127

Merged error: 0.1b

Counts

127 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
15.7b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
32×	`frac-sub`
30×	`*-un-lft-identity` `flip3-+` `flip-+`
20×	`frac-times`
19×	`flip3--` `flip--`
18×	`add-sqr-sqrt` `associate-/l/`
16×	`add-cube-cbrt`
12×	`times-frac`
10×	`pow1` `associate-*l/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `distribute-lft-out`
5×	`add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `associate--l+` `associate-/r*` `difference-of-squares`
3×	`sub-neg` `associate-/l*`
2×	`associate-/r/` `associate--r+`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 126

Calls

3 calls:

8.0ms	(* (+ x 1.0) (+ x 1.0))
13.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
8.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series10.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify123.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	719	1640
1	4033	1538
2	5003	1533

prune219.0ms

Filtered

135 candidates to 92 candidates (31.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	3	1	4
Picked	1	0	1
Done	1	1	2
Total	139	3	142

Merged error: 0.0b

Counts

142 → 3

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch18.0ms

Steps

Iters	Range		Point
9	7423.9342200737565	94425228992.39874	97779899.39815049
2	-3787208771264.523	-3299728841212.5835	-3604403797495.046

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	15
1	44	15
2	44	15

end0.0ms

sample728.0ms

Algorithm

intervals

Results

252.0ms	1718×	body	1280	valid
149.0ms	1274×	body	640	valid
127.0ms	4099×	body	80	valid
50.0ms	585×	body	320	valid
19.0ms	324×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Details

sample25.0ms

simplify17.0ms

prune2.0ms

localize6.0ms

rewrite47.0ms

series12.0ms

simplify42.0ms

prune173.0ms

localize9.0ms

rewrite55.0ms

series15.0ms

simplify126.0ms

prune168.0ms

localize9.0ms

rewrite32.0ms

series25.0ms

simplify77.0ms

prune260.0ms

localize10.0ms

rewrite35.0ms

series10.0ms

simplify123.0ms

prune219.0ms

regimes36.0ms

bsearch18.0ms

simplify2.0ms

end0.0ms

sample728.0ms

Profiling

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6