Details

sample70.0ms

Algorithm

intervals

Results

21.0ms	58×	body	1280	valid
16.0ms	59×	body	640	valid
5.0ms	95×	body	80	valid
5.0ms	90×	body	80	overflowed
5.0ms	29×	body	320	valid
2.0ms	16×	body	160	valid

simplify936.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	172	12
6	494	12
7	1677	12
done	5001	12

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.0b

Counts

2 → 1

localize12.0ms

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)))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
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 → 123

Calls

4 calls:

10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series37.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
3.0ms	(- (exp (* 2.0 x)) 1.0)
11.0ms	(- (exp x) 1.0)

simplify687.0ms

Counts

135 → 135

Iterations

Useful iterations: done (676.0ms)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	968	2169
3	2667	2156
done	5001	2154

prune261.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0.2b

Counts

136 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))) (sqrt 2.0))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`frac-times` `pow-to-exp` `flip3--` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

16.0ms	(+ (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))) (sqrt 2.0))
23.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))

series34.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))) (sqrt 2.0))
8.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))

simplify582.0ms

Counts

233 → 233

Iterations

Useful iterations: done (575.0ms)

Iter	Nodes	Cost
0	268	3262
1	614	3051
2	2330	2750
done	5001	2730

prune521.0ms

Filtered

151 candidates to 233 candidates (-54.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	232	3	235

Merged error: 0.2b

Counts

235 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

253×	`times-frac`
208×	`*-un-lft-identity`
178×	`add-sqr-sqrt`
135×	`sqrt-prod`
92×	`add-cube-cbrt`
79×	`difference-of-squares`
31×	`distribute-lft-out`
27×	`distribute-lft-out--`
26×	`exp-sum`
13×	`associate-/r/`
8×	`add-log-exp`
7×	`div-inv`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`pow1` `associate-/l*`
4×	`associate-/r*`
3×	`rem-sqrt-square` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 222

Calls

4 calls:

13.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
27.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
4.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
19.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
3.0ms	(- (exp (* 2.0 x)) 1.0)
3.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify727.0ms

Counts

234 → 234

Iterations

Useful iterations: done (710.0ms)

Iter	Nodes	Cost
0	510	7530
1	1088	7263
2	3312	6945
done	5001	6943

prune563.0ms

Filtered

160 candidates to 234 candidates (-46.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	233	4	237

Merged error: 0.2b

Counts

237 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) 3))))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

534×	`times-frac`
423×	`*-un-lft-identity`
373×	`add-sqr-sqrt`
310×	`sqrt-prod`
296×	`cbrt-prod`
187×	`add-cube-cbrt`
154×	`difference-of-squares`
132×	`unpow-prod-down` `cube-prod`
62×	`distribute-lft-out--`
56×	`distribute-lft-out`
46×	`exp-sum`
23×	`associate-/r/`
12×	`div-inv`
11×	`flip3-+` `flip-+`
8×	`rem-sqrt-square` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
5×	`pow1` `cube-mult` `unpow3` `associate-/l*`
4×	`associate-/r*`
3×	`flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `cube-div` `cbrt-div` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 402

Calls

4 calls:

14.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
53.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) 3))))
4.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
19.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) 3))))
2.0ms	(- (exp (* 2.0 x)) 1.0)
3.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify889.0ms

Counts

414 → 414

Iterations

Useful iterations: done (862.0ms)

Iter	Nodes	Cost
0	713	17190
1	1414	14986
2	4013	14210
done	5000	14162

prune700.0ms

Filtered

179 candidates to 414 candidates (-131.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	414	4	418

Merged error: 0.2b

Counts

418 → 4

regimes48.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.0b

bsearch20.0ms

Steps

Iters	Range		Point
9	-0.0001616040529746431	-1.1951251334293225e-11	-1.2211091000924002e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	50
1	41	50
done	41	50

end0.0ms

sample1.7s

Algorithm

intervals

Results

732.0ms	2297×	body	1280	valid
350.0ms	1663×	body	640	valid
134.0ms	2864×	body	80	valid
115.0ms	802×	body	320	valid
109.0ms	2519×	body	80	overflowed
43.0ms	423×	body	160	valid

Details

sample70.0ms

simplify936.0ms

prune5.0ms

localize12.0ms

rewrite38.0ms

series37.0ms

simplify687.0ms

prune261.0ms

localize14.0ms

rewrite64.0ms

series34.0ms

simplify582.0ms

prune521.0ms

localize15.0ms

rewrite71.0ms

series33.0ms

simplify727.0ms

prune563.0ms

localize18.0ms

rewrite123.0ms

series33.0ms

simplify889.0ms

prune700.0ms

regimes48.0ms

bsearch20.0ms

simplify3.0ms

end0.0ms

sample1.7s

Profiling