Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	51×	body	1280	valid
7.0ms	41×	body	640	valid
5.0ms	132×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4085
11	1745
10	535
9	183
8	79
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
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 → 104

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
24.0ms	(/ (+ x 1.0) (- x 1.0))
120.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ x (+ x 1.0))
50.0ms	(/ (+ x 1.0) (- x 1.0))
206.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1794
1	408
0	176

prune477.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite846.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`log-pow` `difference-of-squares`
9×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum` `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 → 130

Calls

4 calls:

387.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
20.0ms	(/ (+ x 1.0) (- x 1.0))
319.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
107.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
53.0ms	(/ (+ x 1.0) (- x 1.0))
189.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
200.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.2s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	1652
1	429
0	185

prune575.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
8.9b	(log (exp (- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))))
8.9b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

10.0ms	(/ 1 (- x 1.0))
63.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
144.0ms	(log (exp (- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))))
65.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (- x 1.0))
58.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
179.0ms	(log (exp (- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))))
177.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify733.0ms

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
1	571
0	215

prune655.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
8.9b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
44×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `frac-sub` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp`
3×	`cbrt-undiv` `flip3--` `div-inv` `flip--` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-*r/` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

9.0ms	(/ x (+ x 1.0))
12.0ms	(/ 1 (- x 1.0))
45.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
65.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ x (+ x 1.0))
38.0ms	(/ 1 (- x 1.0))
42.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
176.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify707.0ms

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
1	618
0	234

prune481.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch134.0ms

Steps

Iters	Range		Point
8	160.65039477392645	261980.93535209994	16309.13855706637
10	-83422883652835.42	-0.9341403346610884	-10110.886514379905

simplify13.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

755.0ms	1667×	body	1280	valid
343.0ms	4096×	body	80	valid
219.0ms	1320×	body	640	valid
76.0ms	587×	body	320	valid
34.0ms	330×	body	160	valid