Details

sample51.0ms

Algorithm

intervals

Results

21.0ms	67×	body	1280	valid
7.0ms	31×	body	640	valid
5.0ms	135×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3503
6	454
5	122
4	55
3	31
2	22
1	15
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize17.0ms

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))))
2.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite116.0ms

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:

5.0ms	(+ 1.0 (exp (* -2.0 x)))
17.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
87.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series202.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1.0 (exp (* -2.0 x)))
64.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
119.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1295
1	420
0	180

prune645.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize42.0ms

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))))
0.2b	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

551×	`sqrt-prod`
463×	`*-un-lft-identity`
378×	`prod-diff`
351×	`add-sqr-sqrt`
321×	`add-cube-cbrt`
256×	`times-frac`
128×	`distribute-rgt-in` `distribute-lft-in`
67×	`distribute-lft-out`
42×	`associate-/r/`
24×	`flip3-+` `flip-+`
21×	`fma-neg` `div-inv`
12×	`difference-of-squares`
11×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3--` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`sub-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-l/` `associate-r/`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 533

Calls

4 calls:

11.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
18.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
461.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
134.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series928.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
43.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
619.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
207.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify2.0s

Counts

545 → 545

Iterations

Iter	Nodes
done	5001
1	1662
0	503

prune2.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize116.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite898.0ms

Algorithm

rewrite-expression-head

Rules

596×	`sqrt-prod`
462×	`*-un-lft-identity`
378×	`prod-diff`
363×	`add-sqr-sqrt`
320×	`add-cube-cbrt`
258×	`times-frac`
65×	`distribute-lft-out`
63×	`fma-neg`
48×	`flip3-+` `flip-+`
42×	`associate-/r/`
28×	`frac-times`
23×	`pow1`
21×	`div-inv`
18×	`difference-of-squares`
14×	`associate-*l/`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-*r/`
6×	`pow-plus` `pow-prod-up` `distribute-lft-out--`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`pow2` `pow-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 567

Calls

4 calls:

519.0ms	(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
119.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
102.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
97.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series806.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
132.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
160.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
189.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify1.8s

Counts

579 → 579

Iterations

Iter	Nodes
done	5001
1	1031
0	360

prune3.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 5.551115123125783e-17 (* x x)) (* x x))
0.1b	(* 0.33333333333333337 (* x x))
1.3b	(* 5.551115123125783e-17 (* x x))
14.3b	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* 5.551115123125783e-17 (* x x)) (* x x)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1` `add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate--l+`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l` `prod-diff`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-r` `*-commutative`
2×	`unswap-sqr`
1×	`flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 98

Calls

4 calls:

75.0ms	(* (* 5.551115123125783e-17 (* x x)) (* x x))
21.0ms	(* 0.33333333333333337 (* x x))
13.0ms	(* 5.551115123125783e-17 (* x x))
52.0ms	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* 5.551115123125783e-17 (* x x)) (* x x)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* 5.551115123125783e-17 (* x x)) (* x x))
42.0ms	(* 0.33333333333333337 (* x x))
44.0ms	(* 5.551115123125783e-17 (* x x))
65.0ms	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* 5.551115123125783e-17 (* x x)) (* x x)))

simplify2.9s

Counts

110 → 110

Iterations

Iter	Nodes
done	5002
2	2862
1	394
0	134

prune346.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes321.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 29.3b

bsearch2.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	46
1	46
0	33

end0.0ms

sample1.9s

Algorithm

intervals

Results

602.0ms	1668×	body	1280	valid
512.0ms	4107×	body	80	valid
305.0ms	1307×	body	640	valid
142.0ms	617×	body	320	valid
115.0ms	301×	body	160	valid