Details

sample46.0ms

Algorithm

intervals

Results

14.0ms	53×	body	1280	valid
6.0ms	37×	body	640	valid
5.0ms	126×	body	80	valid
4.0ms	31×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	15	10
2	22	10
3	31	10
4	55	10
5	120	10
6	278	10
7	819	10
8	3019	10
done	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `times-frac`
54×	`prod-diff`
18×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
5×	`flip3-+` `flip-+` `div-inv`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

2 → 124

Calls

2 calls:

16.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
146.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series177.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
117.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.8s

Counts

130 → 130

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	169	2922
1	378	2340
2	809	2072
3	2311	1837
done	5002	1651

prune339.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b	(log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
2.8b	(- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
108×	`exp-prod`
96×	`log-pow`
91×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
84×	`times-frac`
66×	`prod-diff`
22×	`fma-neg` `distribute-lft-out`
14×	`associate-/r/`
10×	`pow1`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`associate--l+` `associate-/l*`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip--` `rem-exp-log` `difference-of-squares`

Counts

4 → 203

Calls

4 calls:

30.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
54.0ms	(exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
63.0ms	(log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
392.0ms	(- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

series245.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
55.0ms	(exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
38.0ms	(log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
113.0ms	(- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

simplify3.0s

Counts

215 → 215

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	240	4360
1	480	3358
2	941	2918
3	2494	2639
done	5001	2313

prune518.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
30.7b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
36×	`sqrt-prod`
14×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`sqrt-div` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `flip3-+` `div-exp` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`rem-sqrt-square` `rec-exp` `1-exp` `fma-udef` `hypot-def` `inv-pow`

Counts

4 → 129

Calls

4 calls:

15.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
37.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
35.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series554.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
104.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
80.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
302.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify2.0s

Counts

141 → 141

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	198	2223
1	383	1968
2	840	1733
3	2166	1728
done	5000	1718

prune475.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
0.1b	(* 0.33333333333333337 (pow x 3))
9.2b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`associate-r`
8×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 62

Calls

3 calls:

18.0ms	(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
23.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
40.0ms	(* 0.33333333333333337 (pow x 3))
121.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify3.5s

Counts

71 → 71

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	112	1058
1	246	875
2	755	818
3	3941	781
done	5000	780

prune257.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes402.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.0b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	50
1	34	39
done	34	39

end0.0ms

sample1.4s

Algorithm

intervals

Results

511.0ms	1659×	body	1280	valid
269.0ms	1275×	body	640	valid
159.0ms	4134×	body	80	valid
85.0ms	621×	body	320	valid
28.0ms	311×	body	160	valid