Details

sample92.0ms

Algorithm

intervals

Results

43.0ms	61×	body	10240	exit
17.0ms	260×	body	80	valid
8.0ms	9×	body	1280	valid
3.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	19
1	12
0	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`log-div` `fma-neg` `prod-diff` `associate--l+` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `add-cbrt-cube` `log-pow` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

3 → 62

Calls

3 calls:

11.0ms	(+ 1.0 (exp x))
20.0ms	(- (log (+ 1.0 (exp x))) (* x y))
9.0ms	(log (+ 1.0 (exp x)))

series593.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1.0 (exp x))
500.0ms	(- (log (+ 1.0 (exp x))) (* x y))
77.0ms	(log (+ 1.0 (exp x)))

simplify2.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	3790
2	755
1	242
0	105

prune385.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`fma-def` `add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 78

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
10.0ms	(+ 1.0 (exp x))
11.0ms	(log (sqrt (+ 1.0 (exp x))))
11.0ms	(log (sqrt (+ 1.0 (exp x))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp x))
16.0ms	(+ 1.0 (exp x))
170.0ms	(log (sqrt (+ 1.0 (exp x))))
174.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5002
3	2373
2	505
1	167
0	84

prune561.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (+ 1.0 (exp x))))
1.0b	(log1p (+ 1.0 (exp x)))
1.0b	(log (sqrt (+ 1.0 (exp x))))
16.7b	(log (sqrt (expm1 (log1p (+ 1.0 (exp x))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`log-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
7×	`sqrt-prod`
6×	`add-exp-log` `log-pow`
5×	`expm1-log1p-u`
4×	`add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `sqrt-pow1` `pow1/2` `sqrt-div` `rem-log-exp`
1×	`log1p-udef` `expm1-log1p` `flip3-+` `log1p-expm1` `flip-+` `distribute-lft-out` `expm1-udef`

Counts

4 → 63

Calls

4 calls:

0.0ms	(expm1 (log1p (+ 1.0 (exp x))))
1.0ms	(log1p (+ 1.0 (exp x)))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
2.0ms	(log (sqrt (expm1 (log1p (+ 1.0 (exp x))))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(expm1 (log1p (+ 1.0 (exp x))))
91.0ms	(log1p (+ 1.0 (exp x)))
141.0ms	(log (sqrt (+ 1.0 (exp x))))
382.0ms	(log (sqrt (expm1 (log1p (+ 1.0 (exp x))))))

simplify2.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	4284
2	853
1	287
0	148

prune426.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x))))))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-prod`
35×	`pow1`
30×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
23×	`log-pow`
21×	`log-prod`
18×	`add-cube-cbrt`
15×	`sqrt-pow1` `pow1/2`
13×	`swap-sqr`
9×	`associate-r` `associate-l` `add-exp-log`
6×	`log-div` `add-cbrt-cube` `sqrt-div`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `rem-log-exp` `pow-prod-down` `pow-sqr` `flip-+` `distribute-lft-out`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

25.0ms	(* (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x))))))
9.0ms	(log (sqrt (+ 1.0 (exp x))))
9.0ms	(log (sqrt (+ 1.0 (exp x))))
14.0ms	(log (sqrt (+ 1.0 (exp x))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x))))))
132.0ms	(log (sqrt (+ 1.0 (exp x))))
133.0ms	(log (sqrt (+ 1.0 (exp x))))
137.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.2s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	982
1	252
0	124

prune690.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes109.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	2501×	body	10240	exit
903.0ms	8406×	body	80	valid
132.0ms	264×	body	640	valid
99.0ms	139×	body	1280	valid
49.0ms	202×	body	320	valid
15.0ms	104×	body	160	valid