Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	47×	body	1280	valid
4.0ms	30×	body	640	valid
4.0ms	141×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1646	5
7	5001	5
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 141

Calls

3 calls:

7.0ms	(+ 1.0 (exp (* -2.0 x)))
14.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
84.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series130.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify53.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	1645
1	1287	1235
2	5001	1212
done	5001	1212

prune248.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite520.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
205×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `prod-diff`
151×	`times-frac`
54×	`fma-neg`
36×	`distribute-lft-out`
32×	`cbrt-prod`
24×	`associate-/r/`
14×	`difference-of-squares`
12×	`cbrt-div` `flip3-+` `flip-+` `div-inv`
11×	`pow1` `swap-sqr`
10×	`add-log-exp`
9×	`flip3--` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 328

Calls

4 calls:

253.0ms	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
82.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series455.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
76.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify76.0ms

Counts

340 → 340

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	472	4999
1	1486	3759
2	5001	3576
done	5001	3576

prune631.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

296×	`*-un-lft-identity`
218×	`add-sqr-sqrt`
216×	`prod-diff`
198×	`add-cube-cbrt`
184×	`times-frac`
59×	`log-prod`
56×	`exp-sum`
54×	`fma-neg`
45×	`distribute-lft-out`
30×	`associate-/r/`
15×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
8×	`difference-of-squares`
7×	`log-pow`
6×	`exp-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 344

Calls

4 calls:

82.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
80.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
158.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
76.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
80.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

simplify182.0ms

Counts

356 → 356

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	463	5176
1	1135	3600
2	4481	2775
3	5001	2775
done	5001	2775

prune651.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
0.1b	(* 0.33333333333333337 (pow x 3))
7.8b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
12.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
39.0ms	(* 0.33333333333333337 (pow x 3))
98.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify193.0ms

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	170	298
1	655	262
2	4021	262
3	5002	262
done	5002	262

prune150.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes185.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.2b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30
done	39	30

end0.0ms

sample874.0ms

Algorithm

intervals

Results

344.0ms	1695×	body	1280	valid
162.0ms	1270×	body	640	valid
108.0ms	4109×	body	80	valid
51.0ms	610×	body	320	valid
17.0ms	316×	body	160	valid