Details

sample45.0ms

Algorithm

intervals

Results

8.0ms	168×	body	80	valid
7.0ms	33×	body	1280	valid
4.0ms	24×	body	640	valid
3.0ms	97×	body	80	nan
3.0ms	14×	body	1280	nan
2.0ms	20×	body	320	valid
2.0ms	15×	body	640	nan
1.0ms	11×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	7×	body	160	nan

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

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: 21.9b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.6b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms	(/ (- x y) (- 1.0 y))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
48.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
80.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify43.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune293.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 0.2b

Counts

121 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`times-frac`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
24×	`log-prod`
20×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
3×	`div-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 144

Calls

4 calls:

16.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
39.0ms	(/ (- x y) (- 1.0 y))
122.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	621	1546
1	1974	1467
2	5001	1448

prune378.0ms

Filtered

156 candidates to 117 candidates (75.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	156	6	162

Merged error: 0.1b

Counts

162 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1.0 y))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
0.2b	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
5.9b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
41×	`times-frac`
32×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`flip3--` `associate-/r/` `flip--` `associate-/l*` `add-log-exp`
5×	`div-exp` `associate-l`
4×	`prod-exp`
3×	`cbrt-undiv` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ 1 (- 1.0 y))
13.0ms	(* (- x y) (/ 1 (- 1.0 y)))
5.0ms	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (- 1.0 y))
36.0ms	(* (- x y) (/ 1 (- 1.0 y)))
125.0ms	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
50.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify67.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	540	1043
1	2358	932
2	5001	885

prune320.0ms

Filtered

144 candidates to 94 candidates (65.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	144	6	150

Merged error: 0.1b

Counts

150 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
46×	`*-un-lft-identity` `times-frac`
26×	`add-cube-cbrt`
20×	`difference-of-squares`
12×	`associate-/r*`
10×	`distribute-lft-out--`
8×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `associate-/l*`
4×	`pow1` `flip3--` `associate-/r/` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv` `associate--r-`

Counts

4 → 114

Calls

4 calls:

18.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
120.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify114.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	269	1308
1	826	1224
2	4007	1210
3	5001	1210

prune427.0ms

Filtered

126 candidates to 98 candidates (77.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	126	6	132

Merged error: 0.1b

Counts

132 → 6

regimes173.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.3b

bsearch128.0ms

Steps

Iters	Range		Point
9	4436625.583370406	1.11049414308367e+15	36362977.00338186
9	-21514814691.886383	-205992.06318510068	-411945099.21176857

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	27
1	36	27

end0.0ms

sample994.0ms

Algorithm

intervals

Results

217.0ms	5700×	body	80	valid
157.0ms	822×	body	1280	valid
109.0ms	781×	body	640	valid
100.0ms	3769×	body	80	nan
55.0ms	359×	body	1280	nan
46.0ms	362×	body	640	nan
45.0ms	470×	body	320	valid
16.0ms	197×	body	320	nan
15.0ms	227×	body	160	valid
6.0ms	114×	body	160	nan