Details

sample68.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
11.0ms	32×	body	640	valid
8.0ms	144×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	15×	body	160	valid

simplify3.5s

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: 26.3b

localize26.0ms

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)

rewrite164.0ms

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:

6.0ms	(+ 1.0 (exp (* -2.0 x)))
22.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
131.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series163.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ 1.0 (exp (* -2.0 x)))
40.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
98.0ms	(- (/ 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

prune650.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
4.1b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite556.0ms

Algorithm

rewrite-expression-head

Rules

1732×	`times-frac`
1496×	`*-un-lft-identity`
1020×	`add-sqr-sqrt`
997×	`sqrt-prod`
996×	`add-cube-cbrt`
585×	`prod-diff`
249×	`distribute-lft-out`
195×	`fma-neg`
84×	`sqrt-div` `associate-/r/`
43×	`flip3-+` `flip-+`
42×	`div-inv`
30×	`associate-/l*`
14×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 1108

Calls

4 calls:

5.0ms	(+ 1.0 (exp (* -2.0 x)))
66.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
20.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
332.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series287.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ 1.0 (exp (* -2.0 x)))
47.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
110.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
112.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify1.9s

Counts

1120 → 1120

Iterations

Iter	Nodes
done	5000
1	1649
0	705

prune3.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.4b	(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
26.9b	(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite5.9s

Algorithm

rewrite-expression-head

Rules

37358×	`times-frac`
34329×	`sqrt-prod`
26280×	`*-un-lft-identity`
17838×	`add-sqr-sqrt`
17716×	`add-cube-cbrt`
7704×	`prod-diff`
4281×	`distribute-lft-out`
2568×	`fma-neg`
1646×	`sqrt-div`
828×	`associate-/r/`
414×	`flip3-+` `flip-+` `div-inv`
405×	`associate-/l*`
27×	`associate-/r*` `difference-of-squares`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 13754

Calls

4 calls:

258.0ms	(/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
46.0ms	(/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
14.0ms	(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
2.8s	(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series428.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
94.0ms	(/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
181.0ms	(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
98.0ms	(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify10.5s

Counts

13766 → 13766

Iterations

Iter	Nodes
done	5000
0	4958

prune1.1m

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.33333333333333337 (* x x))
0.1b	(* (* 5.551115123125783e-17 (* x x)) (* x x))
1.5b	(* 5.551115123125783e-17 (* x x))
13.3b	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* 5.551115123125783e-17 (* x x)) (* x x)))

rewrite135.0ms

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:

18.0ms	(* 0.33333333333333337 (* x x))
50.0ms	(* (* 5.551115123125783e-17 (* x x)) (* x x))
15.0ms	(* 5.551115123125783e-17 (* x x))
46.0ms	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* 5.551115123125783e-17 (* x x)) (* x x)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 0.33333333333333337 (* x x))
45.0ms	(* (* 5.551115123125783e-17 (* x x)) (* x x))
44.0ms	(* 5.551115123125783e-17 (* x x))
69.0ms	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* 5.551115123125783e-17 (* x x)) (* x x)))

simplify3.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5002
2	2920
1	407
0	134

prune385.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes323.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.6b

bsearch3.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

588.0ms	1709×	body	1280	valid
348.0ms	1268×	body	640	valid
343.0ms	4070×	body	80	valid
98.0ms	637×	body	320	valid
31.0ms	316×	body	160	valid