Details

sample74.0ms

Algorithm

intervals

Results

36.0ms	58×	body	1280	valid
9.0ms	42×	body	640	valid
6.0ms	119×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	18×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize9.0ms

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))))
4.3b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite139.0ms

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:

8.0ms	(+ 1.0 (exp (* -2.0 x)))
15.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
108.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series209.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ 1.0 (exp (* -2.0 x)))
68.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
122.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.6s

Counts

150 → 150

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	180	3092
1	400	2501
2	856	2219
3	2401	1982
done	5001	1796

prune423.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
8.1b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

28.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(* 0.33333333333333337 (pow x 3))
142.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify2.0s

Counts

49 → 49

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	70	445
1	141	409
2	388	369
3	1882	369
done	5000	369

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
4.3b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

119×	`*-un-lft-identity`
92×	`times-frac`
71×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
27×	`distribute-lft-out`
24×	`swap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
12×	`associate-/r/`
11×	`pow1`
8×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 185

Calls

4 calls:

29.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
223.0ms	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
104.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
52.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series544.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
289.0ms	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
62.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
125.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify2.4s

Counts

197 → 197

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	262	5475
1	727	4963
2	2805	4101
done	5001	3739

prune704.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
4.3b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
6.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
6.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
33.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series702.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
169.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
194.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
142.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify1.6s

Counts

77 → 77

Iterations

Useful iterations: 3 (610.0ms)

Iter	Nodes	Cost
0	102	1318
1	253	1259
2	746	1095
3	2393	987
done	5001	987

prune365.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes360.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 31.9b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	103
1	51	99
done	51	99

end0.0ms

sample2.1s

Algorithm

intervals

Results

815.0ms	1208×	body	640	valid
627.0ms	1711×	body	1280	valid
176.0ms	4092×	body	80	valid
131.0ms	649×	body	320	valid
33.0ms	340×	body	160	valid