Details

sample417.0ms

Algorithm

intervals

Results

102.0ms	198×	body	10240	exit
79.0ms	241×	body	80	valid
63.0ms	369×	body	80	nan
3.0ms	17×	body	160	valid

simplify2.8s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp x) 1.0)

rewrite154.0ms

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:

52.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
19.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series279.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
76.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
43.0ms	(- (exp (* 2.0 x)) 1.0)
37.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

135 → 135

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	904	2169
3	2293	2156
done	5001	2154

prune461.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
4.5b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.5b	(- (exp x) 1.0)

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/r*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

128.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
77.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
19.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series569.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
273.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
71.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

117 → 117

Iterations

Useful iterations: 2 (319.0ms)

Iter	Nodes	Cost
0	180	2590
1	473	1851
2	2004	1667
done	5002	1667

prune411.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 0.5 x) 1.0))
23.2b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

33.0ms	(* x (+ (* 0.5 x) 1.0))
5.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series189.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(* x (+ (* 0.5 x) 1.0))
86.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify2.2s

Counts

43 → 43

Iterations

Useful iterations: 3 (798.0ms)

Iter	Nodes	Cost
0	106	598
1	280	541
2	885	507
3	3334	498
done	5002	498

prune121.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* 0.5 x) 1.0))
0.0b	(* x (+ (* 0.5 x) 1.0))
0.1b	(/ (sqrt (- (* 2.0 2.0) (* (* x (+ (* 0.5 x) 1.0)) (* x (+ (* 0.5 x) 1.0))))) (sqrt (- 2.0 (* x (+ (* 0.5 x) 1.0)))))
0.2b	(* (* x (+ (* 0.5 x) 1.0)) (* x (+ (* 0.5 x) 1.0)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-prod`
47×	`pow1`
42×	`add-sqr-sqrt` `times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
18×	`associate-*r/`
10×	`prod-exp` `cbrt-unprod`
8×	`flip3-+` `flip-+`
7×	`associate-r` `associate-l` `associate-/l*` `difference-of-squares`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`frac-times` `sqrt-div` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`*-commutative`
2×	`flip3--` `pow-plus` `associate-*l/` `associate-/r/` `flip--` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `sqrt-undiv` `frac-2neg` `swap-sqr` `div-exp` `clear-num` `div-inv`

Counts

4 → 162

Calls

4 calls:

47.0ms	(* x (+ (* 0.5 x) 1.0))
26.0ms	(* x (+ (* 0.5 x) 1.0))
45.0ms	(/ (sqrt (- (* 2.0 2.0) (* (* x (+ (* 0.5 x) 1.0)) (* x (+ (* 0.5 x) 1.0))))) (sqrt (- 2.0 (* x (+ (* 0.5 x) 1.0)))))
106.0ms	(* (* x (+ (* 0.5 x) 1.0)) (* x (+ (* 0.5 x) 1.0)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* x (+ (* 0.5 x) 1.0))
93.0ms	(* x (+ (* 0.5 x) 1.0))
221.0ms	(/ (sqrt (- (* 2.0 2.0) (* (* x (+ (* 0.5 x) 1.0)) (* x (+ (* 0.5 x) 1.0))))) (sqrt (- 2.0 (* x (+ (* 0.5 x) 1.0)))))
68.0ms	(* (* x (+ (* 0.5 x) 1.0)) (* x (+ (* 0.5 x) 1.0)))

simplify1.4s

Counts

174 → 174

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	242	5365
1	588	4728
2	2118	4482
done	5002	4456

prune528.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

79.9% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 3.3b

bsearch77.0ms

Steps

Iters	Range		Point
8	-9.640722949014248e-05	-2.3145164395556077e-08	-3.356135868947112e-05

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	37
1	30	37
done	30	37

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.4s	6799×	body	10240	exit
1.7s	12844×	body	80	nan
665.0ms	7436×	body	80	valid
99.0ms	687×	body	160	valid