Details

sample79.0ms

Algorithm

intervals

Results

22.0ms	54×	body	1280	valid
17.0ms	26×	body	320	valid
13.0ms	42×	body	640	valid
7.0ms	120×	body	80	valid
2.0ms	14×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

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)))
3.4b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite155.0ms

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:

11.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
9.0ms	(+ 1.0 (exp (* -2.0 x)))
129.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series193.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
35.0ms	(+ 1.0 (exp (* -2.0 x)))
116.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	1294
1	420
0	180

prune618.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* (* x x) 5.551115123125783e-17))
0.2b	(* 0.33333333333333337 (* x x))
0.9b	(* (* x x) 5.551115123125783e-17)
9.6b	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* x x) (* (* x x) 5.551115123125783e-17)))

rewrite144.0ms

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×	`prod-diff`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `*-commutative`
2×	`unswap-sqr`
1×	`flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 98

Calls

4 calls:

59.0ms	(* (* x x) (* (* x x) 5.551115123125783e-17))
14.0ms	(* 0.33333333333333337 (* x x))
16.0ms	(* (* x x) 5.551115123125783e-17)
50.0ms	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* x x) (* (* x x) 5.551115123125783e-17)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* x x) (* (* x x) 5.551115123125783e-17))
50.0ms	(* 0.33333333333333337 (* x x))
31.0ms	(* (* x x) 5.551115123125783e-17)
86.0ms	(- (* x (- 1.0 (* 0.33333333333333337 (* x x)))) (* (* x x) (* (* x x) 5.551115123125783e-17)))

simplify3.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	3058
1	410
0	138

prune545.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize41.0ms

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)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.4b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite611.0ms

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:

9.0ms	(+ 1.0 (exp (* -2.0 x)))
39.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
18.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
377.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series270.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ 1.0 (exp (* -2.0 x)))
52.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
102.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
94.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify1.6s

Counts

1120 → 1120

Iterations

Iter	Nodes
done	5000
1	1649
0	705

prune3.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (* (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0) (* (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0) (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0))))
3.4b	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)
3.4b	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)
3.4b	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

rewrite664.0ms

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
169×	`add-sqr-sqrt`
162×	`prod-diff`
154×	`add-cube-cbrt`
147×	`times-frac`
54×	`fma-neg`
36×	`distribute-lft-out`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
24×	`associate-/r/`
14×	`associate-*r/`
12×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
8×	`associate-*l/`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`cbrt-prod` `pow1/3` `cube-unmult` `rem-cbrt-cube`

Counts

4 → 305

Calls

4 calls:

366.0ms	(cbrt (* (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0) (* (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0) (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0))))
89.0ms	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)
100.0ms	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)
91.0ms	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

series406.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (* (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0) (* (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0) (- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0))))
101.0ms	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)
110.0ms	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)
88.0ms	(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

simplify1.8s

Counts

317 → 317

Iterations

Iter	Nodes
done	5000
2	1673
1	506
0	243

prune1.9s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes171.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	1764×	body	1280	valid
420.0ms	1180×	body	640	valid
239.0ms	4133×	body	80	valid
93.0ms	604×	body	320	valid
34.0ms	319×	body	160	valid