Details

sample60.0ms

Algorithm

intervals

Results

9.0ms	99×	body	80	nan
9.0ms	170×	body	80	valid
7.0ms	27×	body	1280	valid
6.0ms	33×	body	640	valid
3.0ms	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

simplify888.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize20.0ms

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))))

rewrite179.0ms

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:

48.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
20.0ms	(/ (- x y) (- 1.0 y))
40.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
55.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
40.0ms	(/ (- x y) (- 1.0 y))
72.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
116.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.0s

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
2	4243
1	1025
0	389

prune903.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite169.0ms

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:

34.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
24.0ms	(/ (- x y) (- 1.0 y))
59.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
36.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
44.0ms	(/ (- x y) (- 1.0 y))
154.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
79.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.9s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
2	4483
1	1124
0	433

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
0.3b	(expm1 (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.7b	(log1p (expm1 (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt`
150×	`*-un-lft-identity`
98×	`times-frac`
93×	`prod-diff`
80×	`add-cube-cbrt`
40×	`difference-of-squares`
35×	`distribute-lft-out--`
8×	`associate-/r/`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `add-exp-log` `log1p-expm1-u` `flip--`
4×	`expm1-log1p-u` `pow1` `div-inv`
3×	`fma-neg` `associate-/l*`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `log1p-expm1` `expm1-udef` `associate--r-`

Counts

4 → 179

Calls

4 calls:

56.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
0.0ms	(expm1 (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0ms	(log1p (expm1 (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))))
57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series3.0s

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
1.6s	(expm1 (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
1.2s	(log1p (expm1 (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))))
78.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.4s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	3982
1	998
0	387

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- x y))
0.5b	(cbrt (- x y))
4.4b	(log (+ (fma (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (/ (- (cbrt (- x y))) (/ (sqrt (- 1.0 y)) (cbrt (- x y)))) 1.0) (* (* (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (cbrt (- x y))) (+ (- (/ (cbrt (- x y)) (sqrt (- 1.0 y)))) (/ (cbrt (- x y)) (sqrt (- 1.0 y)))))))
17.9b	(fma (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (/ (- (cbrt (- x y))) (/ (sqrt (- 1.0 y)) (cbrt (- x y)))) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
7×	`add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`log-div` `flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `fma-udef`

Counts

4 → 60

Calls

4 calls:

6.0ms	(cbrt (- x y))
6.0ms	(cbrt (- x y))
6.0ms	(log (+ (fma (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (/ (- (cbrt (- x y))) (/ (sqrt (- 1.0 y)) (cbrt (- x y)))) 1.0) (* (* (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (cbrt (- x y))) (+ (- (/ (cbrt (- x y)) (sqrt (- 1.0 y)))) (/ (cbrt (- x y)) (sqrt (- 1.0 y)))))))
1.0ms	(fma (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (/ (- (cbrt (- x y))) (/ (sqrt (- 1.0 y)) (cbrt (- x y)))) 1.0)

series685.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt (- x y))
173.0ms	(cbrt (- x y))
202.0ms	(log (+ (fma (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (/ (- (cbrt (- x y))) (/ (sqrt (- 1.0 y)) (cbrt (- x y)))) 1.0) (* (* (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (cbrt (- x y))) (+ (- (/ (cbrt (- x y)) (sqrt (- 1.0 y)))) (/ (cbrt (- x y)) (sqrt (- 1.0 y)))))))
138.0ms	(fma (/ (cbrt (- x y)) (sqrt (- 1.0 y))) (/ (- (cbrt (- x y))) (/ (sqrt (- 1.0 y)) (cbrt (- x y)))) 1.0)

simplify685.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1149
1	350
0	150

prune645.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes241.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 19.0b

bsearch208.0ms

Steps

Iters	Range		Point
7	0.06034539567166679	10.445105708742691	0.9964180550553196
9	-33326255562.233612	-27495.286585169673	-47727873.56991197

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	31

end0.0ms

sample3.0s

Algorithm

intervals

Results

628.0ms	383×	body	1280	nan
495.0ms	5677×	body	80	valid
388.0ms	817×	body	1280	valid
268.0ms	3924×	body	80	nan
256.0ms	803×	body	640	valid
175.0ms	461×	body	320	valid
127.0ms	363×	body	640	nan
35.0ms	242×	body	160	valid
34.0ms	201×	body	320	nan
11.0ms	99×	body	160	nan