Details

sample342.0ms

Algorithm

intervals

Results

76.0ms	204×	body	10240	exit
72.0ms	388×	body	80	nan
51.0ms	242×	body	80	valid
3.0ms	20×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	175	12
6	479	12
7	1665	12
done	5000	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

53.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
43.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
21.0ms	(- (exp (* 2.0 x)) 1.0)
18.0ms	(- (exp x) 1.0)

series306.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
148.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
43.0ms	(- (exp (* 2.0 x)) 1.0)
41.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	903	2169
3	2294	2156
done	5001	2154

prune444.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.2b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
25×	`times-frac`
21×	`difference-of-squares`
16×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`pow1` `exp-sum` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sqrt-div` `associate-/r` `associate-/l`
4×	`flip3--` `flip--`
2×	`frac-times` `sub-neg` `sqrt-pow1` `flip3-+` `diff-log` `associate-*r/` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 96

Calls

4 calls:

164.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
69.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
29.0ms	(- (exp (* 2.0 x)) 1.0)
115.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series494.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
195.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
31.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	196	2198
1	477	2130
2	1418	1971
done	5001	1882

prune598.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0)))) (+ (exp x) 1.0)))
0.3b	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0))))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite732.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`associate-r`
20×	`frac-times` `sqrt-div`
19×	`*-un-lft-identity`
17×	`times-frac`
14×	`add-cube-cbrt` `associate-*l/`
13×	`add-exp-log`
12×	`pow1`
11×	`flip3--` `flip--`
10×	`difference-of-squares`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3-+` `flip-+`
6×	`associate-*r/`
5×	`associate-l`
4×	`exp-sum` `pow-prod-down` `prod-exp` `un-div-inv`
3×	`sqrt-pow1` `unswap-sqr`
2×	`sub-neg` `diff-log` `div-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `sqrt-prod` `*-commutative` `div-inv`

Counts

4 → 110

Calls

4 calls:

347.0ms	(sqrt (* (* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0)))) (+ (exp x) 1.0)))
276.0ms	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0))))
18.0ms	(- (exp (* 2.0 x)) 1.0)
79.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series676.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt (* (* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0)))) (+ (exp x) 1.0)))
366.0ms	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0))))
45.0ms	(- (exp (* 2.0 x)) 1.0)
35.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.1s

Counts

122 → 122

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	262	2756
1	673	2474
2	2413	2251
done	5000	2193

prune679.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))
4.5b	(- (exp (+ x x)) (* 1.0 1.0))
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
9×	`add-sqr-sqrt`
7×	`difference-of-squares`
6×	`*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`
3×	`exp-sum`
1×	`distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

27.0ms	(- (exp (* 2.0 x)) 1.0)
110.0ms	(- (exp (+ x x)) (* 1.0 1.0))
102.0ms	(- (exp (+ x x)) (* 1.0 1.0))
89.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series128.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp (+ x x)) (* 1.0 1.0))
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))
38.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.8s

Counts

68 → 68

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	78	840
1	171	808
2	433	696
3	1150	682
4	3602	674
done	5001	674

prune823.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes29.0ms

Accuracy

74.3% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch67.0ms

Steps

Iters	Range		Point
6	-4.509995249856902e-05	-5.9023817294571485e-06	-1.3083797218550047e-05

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	37
1	36	37
done	36	37

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.6s	6588×	body	10240	exit
1.5s	12585×	body	80	nan
1.1s	7352×	body	80	valid
216.0ms	757×	body	160	valid