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

simplify118.0ms

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	59	12
5	75	12
6	83	12
7	98	12
8	128	12
9	182	12
10	225	12
done	225	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize8.0ms

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)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

12.0ms	(/ (- x y) (- 1.0 y))
23.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
30.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- x y) (- 1.0 y))
89.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.1s

Counts

239 → 239

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	390	8619
1	1002	7647
2	3236	5746
done	5000	5731

prune471.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`associate-r`
17×	`times-frac`
15×	`prod-diff`
14×	`add-exp-log`
11×	`pow1`
9×	`add-cbrt-cube`
7×	`flip3--` `flip--` `add-log-exp`
6×	`log-prod` `fma-neg` `distribute-lft-out--`
5×	`associate-l` `log-pow` `difference-of-squares`
4×	`expm1-log1p-u` `log-div` `prod-exp` `log1p-expm1-u`
3×	`associate--r+` `unswap-sqr`
2×	`frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `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 → 125

Calls

4 calls:

5.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
27.0ms	(* (- x y) (/ 1 (- 1.0 y)))
2.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
43.0ms	(* (- x y) (/ 1 (- 1.0 y)))
87.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
51.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify916.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (204.0ms)

Iter	Nodes	Cost
0	249	3041
1	613	2196
2	2259	1846
done	5000	1846

prune310.0ms

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)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
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 → 248

Calls

4 calls:

22.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
12.0ms	(/ (- x y) (- 1.0 y))
43.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
26.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
42.0ms	(/ (- x y) (- 1.0 y))
127.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.2s

Counts

260 → 260

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	432	8789
1	1086	8133
2	3574	6363
done	5000	6348

prune567.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

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 (- 1.0 y))))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
6.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
96×	`prod-diff`
77×	`times-frac`
75×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`distribute-lft-out--`
15×	`log-prod`
9×	`cbrt-prod`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `fma-neg` `associate-/r/`
4×	`expm1-log1p-u` `log-div` `cbrt-div` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`div-inv`
2×	`sub-neg` `pow1/3` `diff-log` `rem-log-exp`
1×	`div-sub` `associate--r-`

Counts

4 → 177

Calls

4 calls:

24.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
2.0ms	(log (cbrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
26.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
115.0ms	(log (cbrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
52.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify943.0ms

Counts

189 → 189

Iterations

Useful iterations: done (935.0ms)

Iter	Nodes	Cost
0	378	7577
1	876	6858
2	2613	5012
done	5000	4997

prune522.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes63.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch133.0ms

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	27	58
1	33	41
done	33	41

end0.0ms

sample999.0ms

Algorithm

intervals

Results

216.0ms	5665×	body	80	valid
166.0ms	845×	body	1280	valid
107.0ms	771×	body	640	valid
101.0ms	3700×	body	80	nan
54.0ms	360×	body	1280	nan
44.0ms	386×	body	640	nan
43.0ms	449×	body	320	valid
18.0ms	270×	body	160	valid
17.0ms	202×	body	320	nan
6.0ms	113×	body	160	nan