Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	187×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	15×	body	320	valid
3.0ms	107×	body	80	nan
2.0ms	17×	body	640	valid
2.0ms	13×	body	1280	nan
2.0ms	12×	body	640	nan
1.0ms	12×	body	160	valid
0.0ms	4×	body	320	nan
0.0ms	5×	body	160	nan

simplify90.0ms

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: 17.1b

localize11.0ms

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))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.2b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite112.0ms

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:

25.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
15.0ms	(/ (- x y) (- 1.0 y))
28.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
31.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
89.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.0s

Counts

239 → 239

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	390	8619
1	974	7647
2	2815	5742
done	5000	5727

prune479.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(cbrt (- 1.0 y))
5.2b	(log (- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)))))
12.1b	(- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

25556×	`times-frac`
20709×	`add-sqr-sqrt`
20585×	`*-un-lft-identity`
15974×	`cbrt-prod`
11133×	`add-cube-cbrt`
8994×	`prod-diff`
4754×	`difference-of-squares`
4726×	`distribute-lft-out--`
442×	`cbrt-div`
438×	`associate-/r/`
223×	`flip3--` `flip--`
219×	`div-inv`
19×	`log-prod`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `div-sub`
2×	`log-div` `pow1/3`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 9094

Calls

4 calls:

2.0ms	(cbrt (- 1.0 y))
2.0ms	(cbrt (- 1.0 y))
1.5s	(log (- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)))))
1.5s	(- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (- 1.0 y))
91.0ms	(cbrt (- 1.0 y))
86.0ms	(log (- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)))))
64.0ms	(- 1.0 (/ (/ (/ (- x y) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))) (cbrt (- 1.0 y))))

simplify6.8s

Counts

9106 → 9106

Iterations

Useful iterations: 0 (2.4s)

Iter	Nodes	Cost
0	13837	1265809
done	13837	1265809

prune35.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite125.0ms

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:

13.0ms	(/ (- x y) (- 1.0 y))
25.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
42.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- x y) (- 1.0 y))
161.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
126.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.0s

Counts

260 → 260

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	432	8789
1	1064	8133
2	3075	6363
done	5001	6348

prune575.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y)))
0.0b	(log (fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y))))
0.3b	(* (* 1.0 (exp 1.0)) (- x y))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
5×	`associate-r`
3×	`expm1-log1p-u` `log-prod` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `rem-log-exp` `associate-l` `log-pow` `*-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 70

Calls

3 calls:

0.0ms	(fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y)))
1.0ms	(log (fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y))))
21.0ms	(* (* 1.0 (exp 1.0)) (- x y))

series350.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y)))
165.0ms	(log (fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y))))
96.0ms	(* (* 1.0 (exp 1.0)) (- x y))

simplify734.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (229.0ms)

Iter	Nodes	Cost
0	161	1503
1	397	1314
2	1391	1010
done	5000	1010

prune154.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes142.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.7b

bsearch135.0ms

Steps

Iters	Range		Point
11	3.382151548740658e-10	12169712469967.395	53143023.87049463
8	-542359391.39979	-925426.909356872	-69178602.40543562

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	67
1	31	50
done	31	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

238.0ms	5713×	body	80	valid
182.0ms	825×	body	1280	valid
116.0ms	788×	body	640	valid
111.0ms	3682×	body	80	nan
57.0ms	344×	body	1280	nan
55.0ms	403×	body	640	nan
49.0ms	434×	body	320	valid
20.0ms	213×	body	320	nan
17.0ms	240×	body	160	valid
6.0ms	101×	body	160	nan