Details

sample413.0ms

Algorithm

intervals

Results

56.0ms	196×	body	10240	exit
12.0ms	406×	body	80	nan
9.0ms	229×	body	80	valid
3.0ms	35×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	181	12
6	489	12
7	1695	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.4b	(- (exp x) 1.0)

rewrite121.0ms

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-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

32.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
44.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
21.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series200.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

167 → 167

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1071	2471
3	3554	2362
done	5000	2356

prune381.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ (exp x) 1.0))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.2b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-prod` `flip--` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `hypot-def` `div-inv` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

13.0ms	(sqrt (+ (exp x) 1.0))
91.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
18.0ms	(- (exp (* 2.0 x)) 1.0)
66.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series237.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ (exp x) 1.0))
159.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
27.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify819.0ms

Counts

137 → 137

Iterations

Useful iterations: done (814.0ms)

Iter	Nodes	Cost
0	223	2351
1	508	2210
2	1366	1996
done	5000	1944

prune425.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.2b	(sqrt (exp x))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.2b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `flip--` `log1p-expm1-u`
3×	`exp-prod` `sqrt-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

93.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
3.0ms	(sqrt (exp x))
16.0ms	(- (exp (* 2.0 x)) 1.0)
65.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series220.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
12.0ms	(sqrt (exp x))
25.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.2s

Counts

136 → 136

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	209	2258
1	465	2125
2	1132	1916
3	4318	1819
done	5000	1817

prune488.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ (exp x) 1.0))
0.4b	(cbrt (+ (exp x) 1.0))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.2b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`prod-diff`
8×	`cbrt-prod` `add-log-exp`
7×	`fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `pow1/3` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

8.0ms	(cbrt (+ (exp x) 1.0))
7.0ms	(cbrt (+ (exp x) 1.0))
16.0ms	(- (exp (* 2.0 x)) 1.0)
66.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series280.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (+ (exp x) 1.0))
114.0ms	(cbrt (+ (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.5s

Counts

96 → 96

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	158	1205
1	344	1079
2	872	928
3	3229	853
done	5000	851

prune355.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes28.0ms

Accuracy

73.8% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.8b

bsearch54.0ms

Steps

Iters	Range		Point
8	-2.9262005697949513e-16	-6.905829970388517e-19	-5.5042063086886815e-17

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	47
1	34	47
done	34	47

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	6573×	body	10240	exit
386.0ms	12651×	body	80	nan
242.0ms	7430×	body	80	valid
56.0ms	708×	body	160	valid