Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	49×	body	1280	valid
10.0ms	55×	body	640	valid
4.0ms	126×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5012
8	2654
7	760
6	224
5	98
4	49
3	28
2	20
1	15
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.1b	(- (/ 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-cbrt-cube` `add-exp-log` `div-inv`
4×	`associate-/r*`
3×	`expm1-log1p-u` `pow1` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

3 → 141

Calls

3 calls:

23.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
9.0ms	(+ 1.0 (exp (* -2.0 x)))
96.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series202.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
21.0ms	(+ 1.0 (exp (* -2.0 x)))
135.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
3	3707
2	1131
1	419
0	180

prune589.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

235×	`*-un-lft-identity`
175×	`add-sqr-sqrt`
162×	`prod-diff`
155×	`add-cube-cbrt`
148×	`times-frac`
54×	`fma-neg`
36×	`distribute-lft-out`
24×	`associate-/r/`
12×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 285

Calls

4 calls:

31.0ms	(cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
133.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
129.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
90.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series623.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
124.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
102.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
102.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.6s

Counts

297 → 297

Iterations

Iter	Nodes
done	5001
3	2766
2	900
1	407
0	183

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.1b	(- (/ (* (* (cbrt 2.0) (cbrt 2.0)) (cbrt 2.0)) (+ (exp (* -2.0 x)) 1.0)) 1.0)

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
138×	`prod-diff`
135×	`add-sqr-sqrt`
123×	`add-cube-cbrt`
114×	`times-frac`
46×	`fma-neg`
28×	`distribute-lft-out`
24×	`associate-/r/`
12×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-prod` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow1/3`

Counts

4 → 247

Calls

4 calls:

1.0ms	(cbrt 2.0)
99.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
171.0ms	(- (/ (* (* (cbrt 2.0) (cbrt 2.0)) (cbrt 2.0)) (+ (exp (* -2.0 x)) 1.0)) 1.0)

series409.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 2.0)
114.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
111.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
184.0ms	(- (/ (* (* (cbrt 2.0) (cbrt 2.0)) (cbrt 2.0)) (+ (exp (* -2.0 x)) 1.0)) 1.0)

simplify3.1s

Counts

257 → 257

Iterations

Iter	Nodes
done	5005
3	3334
2	1184
1	531
0	233

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x x) (* x x))
0.2b	(* 5.551115123125783e-17 (* (* x x) (* x x)))
7.9b	(fma (* x (* x x)) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

147×	`pow1`
41×	`pow-prod-up`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
24×	`prod-exp` `cbrt-unprod`
23×	`pow-sqr`
19×	`pow-plus`
14×	`pow2`
8×	`add-sqr-sqrt`
7×	`associate-l`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
1×	`cube-unmult` `swap-sqr` `fma-udef`

Counts

4 → 131

Calls

4 calls:

25.0ms	(* x (* x x))
39.0ms	(* (* x x) (* x x))
69.0ms	(* 5.551115123125783e-17 (* (* x x) (* x x)))
0.0ms	(fma (* x (* x x)) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* x (* x x))
59.0ms	(* (* x x) (* x x))
49.0ms	(* 5.551115123125783e-17 (* (* x x) (* x x)))
128.0ms	(fma (* x (* x x)) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

simplify2.3s

Counts

143 → 143

Iterations

Iter	Nodes
done	5017
3	2349
2	608
1	263
0	113

prune383.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes508.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.2b

bsearch2.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	48
1	48
0	39

end0.0ms

sample1.6s

Algorithm

intervals

Results

614.0ms	1731×	body	1280	valid
294.0ms	1234×	body	640	valid
230.0ms	4102×	body	80	valid
161.0ms	618×	body	320	valid
65.0ms	315×	body	160	valid