Details

sample46.0ms

Algorithm

intervals

Results

8.0ms	170×	body	80	valid
6.0ms	27×	body	1280	valid
6.0ms	33×	body	640	valid
3.0ms	99×	body	80	nan
2.0ms	19×	body	320	valid
2.0ms	14×	body	640	nan
1.0ms	11×	body	320	nan
1.0ms	5×	body	1280	nan
1.0ms	7×	body	160	valid
0.0ms	3×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	2335
8	741
7	343
6	223
5	123
4	75
3	41
2	29
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize19.0ms

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))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.4b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite201.0ms

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×	`add-cbrt-cube` `fma-neg` `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` `clear-num` `frac-2neg` `div-exp` `rem-log-exp`

Counts

4 → 227

Calls

4 calls:

31.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
59.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
55.0ms	(/ (- x y) (- 1.0 y))
71.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
134.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.4s

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
2	4243
1	1025
0	389

prune878.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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))))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite157.0ms

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` `clear-num` `frac-2neg` `div-sub` `rem-log-exp` `associate-/l/`
1×	`log-div` `sub-neg` `diff-log` `log-pow` `associate--r-`

Counts

4 → 248

Calls

4 calls:

28.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
19.0ms	(/ (- x y) (- 1.0 y))
55.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
43.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
57.0ms	(/ (- x y) (- 1.0 y))
144.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
62.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.8s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
2	4483
1	1124
0	433

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (* 1.0 (exp 1.0)) (fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y))))
0.0b	(+ (* 1.0 (exp 1.0)) (fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y)))
0.1b	(fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y))
0.3b	(* (- (* 1.0 (exp 1.0))) y)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
6×	`add-cbrt-cube` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-r`
2×	`log-div` `flip3-+` `flip-+` `fma-udef`
1×	`distribute-lft-neg-out` `distribute-lft-neg-in` `+-commutative` `associate-+r+` `neg-mul-1` `sum-log` `fma-def` `distribute-rgt-neg-in` `rem-log-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

14.0ms	(log (+ (* 1.0 (exp 1.0)) (fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y))))
15.0ms	(+ (* 1.0 (exp 1.0)) (fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y)))
0.0ms	(fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y))
18.0ms	(* (- (* 1.0 (exp 1.0))) y)

series661.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(log (+ (* 1.0 (exp 1.0)) (fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y))))
133.0ms	(+ (* 1.0 (exp 1.0)) (fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y)))
156.0ms	(fma (* 1.0 (exp 1.0)) x (* (- (* 1.0 (exp 1.0))) y))
105.0ms	(* (- (* 1.0 (exp 1.0))) y)

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1547
1	298
0	121

prune505.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0)))
0.0b	(log1p (expm1 (log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0)))))
0.2b	(fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0))
2.3b	(expm1 (log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`log-prod`
1×	`log1p-udef` `expm1-log1p` `rem-log-exp` `log1p-expm1` `log-pow` `fma-udef` `expm1-udef`

Counts

4 → 46

Calls

4 calls:

1.0ms	(log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0)))
0.0ms	(log1p (expm1 (log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0)))))
0.0ms	(fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0))
1.0ms	(expm1 (log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0))))

series2.6s

Counts

4 → 12

Calls

4 calls:

244.0ms	(log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0)))
431.0ms	(log1p (expm1 (log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0)))))
111.0ms	(fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0))
1.8s	(expm1 (log (fma (* (exp 1.0) 1.0) (- x y) (* (exp 1.0) 1.0))))

simplify3.0s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	4593
2	759
1	232
0	101

prune392.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes275.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.4b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
0	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	5677×	body	80	valid
325.0ms	817×	body	1280	valid
294.0ms	3924×	body	80	nan
233.0ms	803×	body	640	valid
112.0ms	383×	body	1280	nan
84.0ms	461×	body	320	valid
79.0ms	363×	body	640	nan
72.0ms	201×	body	320	nan
34.0ms	242×	body	160	valid
10.0ms	99×	body	160	nan