Details

sample427.0ms

Algorithm

intervals

Results

144.0ms	213×	body	10240	exit
130.0ms	424×	body	80	nan
20.0ms	235×	body	80	valid
5.0ms	26×	body	160	valid

simplify4.9s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite115.0ms

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/` `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 → 155

Calls

4 calls:

36.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
39.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series268.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
49.0ms	(- (exp (* 2.0 x)) 1.0)
41.0ms	(- (exp x) 1.0)

simplify2.5s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4025
2	1183
1	501
0	232

prune867.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
5.4b	(- (exp x) 1.0)
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt` `sqrt-prod`
45×	`*-un-lft-identity` `prod-diff`
39×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
6×	`pow1` `sqrt-pow1`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`rem-sqrt-square` `exp-prod` `sub-neg` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 124

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
3.0ms	(sqrt (exp (* 2.0 x)))
11.0ms	(- (exp x) 1.0)
29.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series159.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (exp (* 2.0 x)))
39.0ms	(sqrt (exp (* 2.0 x)))
26.0ms	(- (exp x) 1.0)
70.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify2.7s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
3	2160
2	771
1	352
0	162

prune649.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp 2.0) (/ x 2))
0.0b	(sqrt (exp (* 2.0 x)))
5.4b	(- (exp x) 1.0)
5.4b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
51×	`prod-diff`
49×	`add-cube-cbrt`
27×	`sqrt-prod`
26×	`unpow-prod-down`
13×	`pow-unpow`
10×	`fma-neg` `sqr-pow`
9×	`times-frac` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `pow-pow` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `exp-to-pow` `pow1/2` `pow-exp` `div-inv`

Counts

4 → 147

Calls

4 calls:

5.0ms	(pow (exp 2.0) (/ x 2))
3.0ms	(sqrt (exp (* 2.0 x)))
13.0ms	(- (exp x) 1.0)
43.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series173.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (exp 2.0) (/ x 2))
25.0ms	(sqrt (exp (* 2.0 x)))
25.0ms	(- (exp x) 1.0)
74.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify2.7s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
3	3452
2	1239
1	555
0	237

prune979.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (exp x) 1.0)
5.4b	(- (exp x) 1.0)
5.4b	(- (exp x) 1.0)
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite111.0ms

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` `log1p-expm1-u` `flip--`

Counts

4 → 146

Calls

4 calls:

19.0ms	(- (exp x) 1.0)
19.0ms	(- (exp x) 1.0)
17.0ms	(- (exp x) 1.0)
44.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series154.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (exp x) 1.0)
32.0ms	(- (exp x) 1.0)
20.0ms	(- (exp x) 1.0)
78.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify2.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
3	2149
2	760
1	347
0	156

prune808.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.9b

bsearch141.0ms

Steps

Iters	Range		Point
8	1.1912796939881877e-06	0.0022991053059264813	1.5780242412218974e-06
10	-945.2327765630807	-4.034181863829644e-08	-9.813313662631737e-06

simplify7.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	6574×	body	10240	exit
1.4s	12433×	body	80	nan
526.0ms	7385×	body	80	valid
137.0ms	733×	body	160	valid