Details

sample314.0ms

Algorithm

intervals

Results

165.0ms	224×	body	10240	exit
26.0ms	353×	body	80	nan
17.0ms	230×	body	80	valid
6.0ms	32×	body	160	valid

simplify3.3s

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: 7.0b

localize16.0ms

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))
6.9b	(- (exp (* 2.0 x)) 1.0)
7.1b	(- (exp x) 1.0)

rewrite152.0ms

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:

58.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series343.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
106.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
46.0ms	(- (exp (* 2.0 x)) 1.0)
53.0ms	(- (exp x) 1.0)

simplify1.8s

Counts

135 → 135

Iterations

Useful iterations: done (1.7s)

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

prune563.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
6.9b	(- (exp (* 2.0 x)) 1.0)
6.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
230×	`*-un-lft-identity`
188×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
88×	`difference-of-squares`
36×	`distribute-lft-out`
30×	`exp-sum` `associate-/r*`
28×	`distribute-lft-out--`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 253

Calls

4 calls:

129.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
183.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
26.0ms	(- (exp (* 2.0 x)) 1.0)
106.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series296.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
168.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
46.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.0s

Counts

265 → 265

Iterations

Useful iterations: 2 (834.0ms)

Iter	Nodes	Cost
0	362	8009
1	1020	7743
2	3664	7375
done	5000	7375

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) 3)
0.4b	(cbrt (pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) 3))
6.9b	(- (exp (* 2.0 x)) 1.0)
6.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
80×	`times-frac`
65×	`add-sqr-sqrt`
58×	`cbrt-prod`
52×	`unpow-prod-down` `cube-prod`
46×	`add-cube-cbrt`
35×	`difference-of-squares`
20×	`distribute-lft-out`
17×	`exp-sum`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `flip-+` `div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `flip--` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

113.0ms	(pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) 3)
121.0ms	(cbrt (pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) 3))
29.0ms	(- (exp (* 2.0 x)) 1.0)
92.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series293.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) 3)
81.0ms	(cbrt (pow (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) 3))
53.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.7s

Counts

180 → 180

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	260	4501
1	704	3921
2	2073	3540
done	5000	3494

prune700.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 2.0 (* x (+ (* 0.5 x) 1.0)))
0.0b	(* x (+ (* 0.5 x) 1.0))
22.4b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

20.0ms	(+ 2.0 (* x (+ (* 0.5 x) 1.0)))
28.0ms	(* x (+ (* 0.5 x) 1.0))
8.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series260.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ 2.0 (* x (+ (* 0.5 x) 1.0)))
88.0ms	(* x (+ (* 0.5 x) 1.0))
137.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify3.4s

Counts

59 → 59

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	116	826
1	308	754
2	1027	702
3	4405	693
done	5000	693

prune127.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

77.2% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.1b

bsearch50.0ms

Steps

Iters	Range		Point
7	-6.966399513907256e-05	-2.622143780401686e-06	-1.6397092074611636e-05

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	38
1	33	38
done	33	38

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.8s	6510×	body	10240	exit
1.1s	12470×	body	80	nan
509.0ms	7358×	body	80	valid
113.0ms	772×	body	160	valid