Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	55×	body	1280	valid
9.0ms	140×	body	80	valid
7.0ms	32×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	13×	body	160	valid

simplify186.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
3.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 117

Calls

3 calls:

8.0ms	(/ x (+ x 1))
28.0ms	(/ (+ x 1) (- x 1))
66.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ x (+ x 1))
31.0ms	(/ (+ x 1) (- x 1))
107.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5008
3	3663
2	1074
1	399
0	180

prune473.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) x)
0.0b	(/ (+ x 1) (- x 1))
0.1b	(/ 1 (/ (+ x 1) x))
3.7b	(- (/ 1 (/ (+ x 1) x)) (/ (+ x 1) (- x 1)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
161×	`times-frac`
128×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
26×	`associate-/r*` `distribute-lft-out`
20×	`difference-of-squares`
19×	`add-exp-log`
13×	`add-cbrt-cube` `distribute-lft-out--`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv` `difference-of-sqr-1`
4×	`insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`rec-exp` `flip3-+` `flip3--` `1-exp` `flip-+` `flip--`
1×	`sub-neg` `diff-log` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 209

Calls

4 calls:

25.0ms	(/ (+ x 1) x)
35.0ms	(/ (+ x 1) (- x 1))
12.0ms	(/ 1 (/ (+ x 1) x))
71.0ms	(- (/ 1 (/ (+ x 1) x)) (/ (+ x 1) (- x 1)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (+ x 1) x)
49.0ms	(/ (+ x 1) (- x 1))
43.0ms	(/ 1 (/ (+ x 1) x))
150.0ms	(- (/ 1 (/ (+ x 1) x)) (/ (+ x 1) (- x 1)))

simplify1.6s

Counts

221 → 221

Iterations

Iter	Nodes
done	5028
2	2066
1	701
0	285

prune722.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.0b	(/ (+ x 1) (- x 1))
3.7b	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
3.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
88×	`times-frac`
76×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod` `distribute-lft-out`
22×	`difference-of-squares`
20×	`add-cube-cbrt`
17×	`log-pow`
9×	`add-log-exp`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `log-prod` `difference-of-sqr-1`
4×	`exp-sum` `insert-posit16` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `frac-sub` `flip-+` `div-inv`

Counts

4 → 144

Calls

4 calls:

175.0ms	(exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
34.0ms	(/ (+ x 1) (- x 1))
196.0ms	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
78.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
29.0ms	(/ (+ x 1) (- x 1))
103.0ms	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
135.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.2s

Counts

156 → 156

Iterations

Iter	Nodes
done	5007
3	3138
2	1117
1	436
0	193

prune563.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ (+ x 1) (- x 1))))
0.0b	(/ (+ x 1) (- x 1))
0.0b	(* (exp (/ x (+ x 1))) (exp (- (/ (+ x 1) (- x 1)))))
3.7b	(log (* (exp (/ x (+ x 1))) (exp (- (/ (+ x 1) (- x 1))))))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

223×	`*-un-lft-identity`
116×	`times-frac`
112×	`exp-prod`
98×	`add-sqr-sqrt`
52×	`distribute-rgt-neg-in`
44×	`add-cube-cbrt`
38×	`distribute-lft-out`
34×	`distribute-lft-neg-in`
26×	`difference-of-squares`
21×	`distribute-lft-out--`
20×	`pow-prod-up`
13×	`difference-of-sqr-1`
12×	`log-pow`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`associate-/r*` `add-exp-log`
6×	`associate-/r/` `add-log-exp`
5×	`exp-neg`
4×	`associate-r/` `insert-posit16` `associate-/l`
3×	`neg-sub0` `log-div` `flip3--` `exp-diff` `associate-r` `associate-l` `div-inv` `flip--`
2×	`rem-log-exp` `pow-prod-down` `prod-exp` `un-div-inv` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-prod` `clear-num` `neg-mul-1` `frac-2neg` `flip3-+` `div-exp` `neg-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

46.0ms	(exp (- (/ (+ x 1) (- x 1))))
28.0ms	(/ (+ x 1) (- x 1))
207.0ms	(* (exp (/ x (+ x 1))) (exp (- (/ (+ x 1) (- x 1)))))
184.0ms	(log (* (exp (/ x (+ x 1))) (exp (- (/ (+ x 1) (- x 1))))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(exp (- (/ (+ x 1) (- x 1))))
35.0ms	(/ (+ x 1) (- x 1))
142.0ms	(* (exp (/ x (+ x 1))) (exp (- (/ (+ x 1) (- x 1)))))
225.0ms	(log (* (exp (/ x (+ x 1))) (exp (- (/ (+ x 1) (- x 1))))))

simplify2.4s

Counts

210 → 210

Iterations

Iter	Nodes
done	5003
3	3631
2	1257
1	551
0	251

prune815.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes106.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch136.0ms

Steps

Iters	Range		Point
9	2842.495256040047	513310621636.50653	11473.666639898413
8	-29345360.474346694	-7508.589471958369	-13116.810079769337

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

474.0ms	1762×	body	1280	valid
456.0ms	593×	body	320	valid
299.0ms	4063×	body	80	valid
279.0ms	1269×	body	640	valid
28.0ms	313×	body	160	valid