Details

sample74.0ms

Algorithm

intervals

Results

35.0ms	57×	body	1280	valid
13.0ms	52×	body	640	valid
5.0ms	29×	body	320	valid
5.0ms	106×	body	80	valid
1.0ms	12×	body	160	valid

simplify3.8s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize19.0ms

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

rewrite146.0ms

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:

15.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(+ 1.0 (exp (* -2.0 x)))
116.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series202.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
30.0ms	(+ 1.0 (exp (* -2.0 x)))
130.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.6s

Counts

150 → 150

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	180	3092
1	400	2501
2	858	2219
3	2411	1982
done	5001	1796

prune428.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
6.4b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite16.0ms

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:

14.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series212.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* 0.33333333333333337 (pow x 3))
164.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify1.8s

Counts

49 → 49

Iterations

Useful iterations: 2 (89.0ms)

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

prune170.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 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)))) 1.0))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
4.2b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite669.0ms

Algorithm

rewrite-expression-head

Rules

579×	`*-un-lft-identity`
504×	`prod-diff`
436×	`add-sqr-sqrt`
396×	`unpow-prod-down` `cube-prod`
385×	`add-cube-cbrt`
369×	`times-frac`
92×	`distribute-lft-out`
66×	`sqr-pow`
60×	`associate-/r/`
56×	`cube-mult` `unpow3`
42×	`fma-neg`
33×	`flip3-+` `flip-+`
30×	`div-inv`
24×	`difference-of-squares`
18×	`fma-def` `associate-l`
12×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
1×	`difference-cubes` `+-commutative` `cube-div` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip--`

Counts

4 → 726

Calls

4 calls:

92.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
207.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
26.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
272.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series448.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
117.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
74.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
179.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify3.4s

Counts

738 → 738

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	479	30443
1	1288	20259
2	4460	15747
done	5000	15746

prune952.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
4.2b	(log (exp (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))))
4.2b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1049×	`*-un-lft-identity`
1008×	`prod-diff`
806×	`add-sqr-sqrt`
756×	`unpow-prod-down` `cube-prod`
709×	`add-cube-cbrt`
653×	`times-frac`
509×	`log-prod`
506×	`exp-sum`
160×	`distribute-lft-out`
130×	`sqr-pow`
110×	`cube-mult` `unpow3`
106×	`associate-/r/`
55×	`flip3-+` `flip-+`
53×	`div-inv`
48×	`difference-of-squares`
42×	`fma-neg`
34×	`log-pow`
33×	`exp-prod`
18×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow`
2×	`difference-cubes` `cbrt-undiv` `frac-times` `sub-neg` `associate-*r/` `div-exp` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-div` `distribute-rgt-in` `pow-to-exp` `log-div` `flip3--` `pow-pow` `distribute-lft-in` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 1248

Calls

4 calls:

259.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
19.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
594.0ms	(log (exp (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))))
299.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series469.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
64.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
147.0ms	(log (exp (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))))
145.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify1.2s

Counts

1260 → 1260

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	918	59566
1	1742	37292
done	5000	30590

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes365.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch2.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	117
1	52	117
done	52	117

end0.0ms

sample1.9s

Algorithm

intervals

Results

666.0ms	1207×	body	640	valid
655.0ms	1680×	body	1280	valid
214.0ms	4117×	body	80	valid
93.0ms	642×	body	320	valid
32.0ms	354×	body	160	valid