Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	179×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	104×	body	80	nan
2.0ms	14×	body	1280	nan
2.0ms	15×	body	640	nan
1.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	6×	body	160	nan
0.0ms	3×	body	320	nan

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	58	12
5	63	12
6	71	12
7	86	12
8	114	12
9	137	12
10	144	12
done	144	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
2.7b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite82.0ms

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:

11.0ms	(/ (- x y) (- 1.0 y))
26.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- x y) (- 1.0 y))
98.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
89.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify662.0ms

Counts

120 → 120

Iterations

Useful iterations: done (658.0ms)

Iter	Nodes	Cost
0	205	1894
1	488	1792
2	1255	1680
done	5000	1671

prune297.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
2.7b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
6.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
16×	`add-cube-cbrt`
14×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`flip3--` `flip--` `add-log-exp`
6×	`log-prod` `distribute-lft-out--`
5×	`associate-l` `difference-of-squares`
4×	`log-div` `prod-exp`
3×	`associate--r+` `unswap-sqr`
2×	`frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `log-pow` `cbrt-unprod` `associate--r-`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 96

Calls

4 calls:

4.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
24.0ms	(* (- x y) (/ 1 (- 1.0 y)))
2.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
2.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
37.0ms	(* (- x y) (/ 1 (- 1.0 y)))
90.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
58.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify729.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	212	1817
1	515	1465
2	1619	1319
done	5001	1319

prune258.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

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))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite308.0ms

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:

23.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms	(/ (- x y) (- 1.0 y))
245.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
130.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify623.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	267	2917
1	619	2789
2	1635	2645
done	5000	2645

prune381.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.7b	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
2.7b	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`log-prod`
16×	`*-un-lft-identity`
12×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp` `difference-of-squares`
6×	`pow1` `add-exp-log`
4×	`log-div` `cbrt-div` `flip3--` `times-frac` `log-pow` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`sub-neg` `pow1/3` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 74

Calls

4 calls:

23.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
21.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
22.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
116.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify759.0ms

Counts

86 → 86

Iterations

Useful iterations: 3 (190.0ms)

Iter	Nodes	Cost
0	119	1594
1	240	1540
2	506	1412
3	1561	1360
done	5000	1360

prune277.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes101.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.1b

bsearch132.0ms

Steps

Iters	Range		Point
11	9.143643357499823e-08	2.0559595175552502e+22	25589815.688386947
8	-64880754058.88788	-1357526.7243520434	-119577009.99898484

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	28	60
1	36	42
done	36	42

end0.0ms

sample992.0ms

Algorithm

intervals

Results

217.0ms	5665×	body	80	valid
164.0ms	845×	body	1280	valid
105.0ms	771×	body	640	valid
98.0ms	3700×	body	80	nan
53.0ms	360×	body	1280	nan
45.0ms	386×	body	640	nan
43.0ms	449×	body	320	valid
19.0ms	270×	body	160	valid
16.0ms	202×	body	320	nan
6.0ms	113×	body	160	nan