Details

sample281.0ms

Algorithm

intervals

Results

85.0ms	208×	body	10240	exit
53.0ms	399×	body	80	nan
15.0ms	238×	body	80	valid
3.0ms	23×	body	160	valid

simplify11.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4825
7	1216
6	342
5	135
4	66
3	38
2	27
1	19
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.9b	(- (exp x) 1.0)

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 159

Calls

4 calls:

124.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
68.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
52.0ms	(- (exp (* 2.0 x)) 1.0)
37.0ms	(- (exp x) 1.0)

series398.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
172.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(- (exp (* 2.0 x)) 1.0)
54.0ms	(- (exp x) 1.0)

simplify7.1s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
3	3946
2	1180
1	505
0	236

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize163.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.2b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
4.9b	(- (exp x) 1.0)
4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

624×	`*-un-lft-identity`
593×	`sqrt-prod`
554×	`add-sqr-sqrt`
528×	`times-frac`
184×	`difference-of-squares`
180×	`add-cube-cbrt`
120×	`distribute-lft-out--`
102×	`distribute-lft-out`
45×	`prod-diff`
13×	`associate-/r/`
9×	`associate-/r*` `flip3--` `fma-neg` `flip--`
8×	`add-log-exp`
7×	`div-inv`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 447

Calls

4 calls:

119.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
182.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
35.0ms	(- (exp x) 1.0)
65.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
705.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
32.0ms	(- (exp x) 1.0)
87.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify9.6s

Counts

459 → 459

Iterations

Iter	Nodes
done	5003
2	3870
1	1451
0	657

prune2.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize220.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.2b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (posit16->real (real->posit16 (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))))
4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.9b	(- (exp x) 1.0)

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
106×	`sqrt-prod`
62×	`add-cube-cbrt`
61×	`times-frac`
45×	`prod-diff`
39×	`difference-of-squares`
25×	`distribute-lft-out--`
9×	`associate-/r*` `fma-neg`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 205

Calls

4 calls:

161.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
86.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (posit16->real (real->posit16 (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))))
68.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
51.0ms	(- (exp x) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
617.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (posit16->real (real->posit16 (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))))
77.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
38.0ms	(- (exp x) 1.0)

simplify6.5s

Counts

217 → 217

Iterations

Iter	Nodes
done	5000
2	2420
1	861
0	369

prune3.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize286.0ms

Local error

Found 4 expressions with local error:

4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.9b	(- (exp x) 1.0)
4.9b	(- (exp x) 1.0)
4.9b	(- (exp x) 1.0)

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
63×	`prod-diff`
61×	`*-un-lft-identity`
51×	`add-cube-cbrt`
45×	`sqrt-prod`
15×	`fma-neg`
12×	`add-log-exp`
7×	`difference-of-squares`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

4 → 150

Calls

4 calls:

59.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
28.0ms	(- (exp x) 1.0)
26.0ms	(- (exp x) 1.0)
55.0ms	(- (exp x) 1.0)

series130.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)
21.0ms	(- (exp x) 1.0)
20.0ms	(- (exp x) 1.0)

simplify5.0s

Counts

162 → 162

Iterations

Iter	Nodes
done	5000
3	2198
2	753
1	349
0	158

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes127.0ms

Accuracy

72.4% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch65.0ms

Steps

Iters	Range		Point
6	-1.790535254998819e-16	-1.1589515176165432e-17	-1.6879468583117964e-16

simplify28.0ms

Iterations

Iter	Nodes
done	35
1	35
0	31

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.4s	6697×	body	10240	exit
1.7s	12419×	body	80	nan
834.0ms	7394×	body	80	valid
202.0ms	732×	body	160	valid