Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	130×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify148.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite209.0ms

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-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

21.0ms	(/ x (+ x 1.0))
50.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series318.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ x (+ x 1.0))
59.0ms	(/ (+ x 1.0) (- x 1.0))
203.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.9s

Counts: 113 → 113

prune336.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.0b	(/ x (+ x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.4b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite188.0ms

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--` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 141

Calls

4 calls:

12.0ms	(/ 1 (- x 1.0))
13.0ms	(/ x (+ x 1.0))
88.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
67.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1 (- x 1.0))
39.0ms	(/ x (+ x 1.0))
71.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
199.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify1.1s

Counts: 153 → 153

prune329.0ms

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 1.0) (/ 1 (- x 1.0))))
0.0b	(log (exp (* (+ x 1.0) (/ 1 (- x 1.0)))))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.4b	(- (/ x (+ x 1.0)) (log (exp (* (+ x 1.0) (/ 1 (- x 1.0))))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`associate-r`
18×	`times-frac`
16×	`add-cube-cbrt`
13×	`add-exp-log`
12×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`log-prod`
5×	`log-pow` `distribute-lft-out--` `difference-of-squares`
4×	`exp-to-pow` `associate-l` `prod-exp`
3×	`associate--r+` `unswap-sqr`
2×	`frac-times` `exp-prod` `flip3--` `flip3-+` `div-exp` `associate-*l/` `sum-log` `associate-/r/` `flip--` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `rem-exp-log` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

10.0ms	(exp (* (+ x 1.0) (/ 1 (- x 1.0))))
10.0ms	(log (exp (* (+ x 1.0) (/ 1 (- x 1.0)))))
54.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
77.0ms	(- (/ x (+ x 1.0)) (log (exp (* (+ x 1.0) (/ 1 (- x 1.0))))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(exp (* (+ x 1.0) (/ 1 (- x 1.0))))
50.0ms	(log (exp (* (+ x 1.0) (/ 1 (- x 1.0)))))
48.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
217.0ms	(- (/ x (+ x 1.0)) (log (exp (* (+ x 1.0) (/ 1 (- x 1.0))))))

simplify888.0ms

Counts: 106 → 106

prune282.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (/ (* (/ (+ x 1.0) (- x 1.0)) (+ x 1.0)) (- x 1.0))) (+ (* (+ x 1.0) (/ 1 (- x 1.0))) (/ x (+ x 1.0))))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
4.5b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (/ (* (/ (+ x 1.0) (- x 1.0)) (+ x 1.0)) (- x 1.0)))

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
93×	`times-frac`
89×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
39×	`associate-r`
27×	`add-exp-log`
24×	`swap-sqr`
23×	`add-cbrt-cube`
22×	`associate-l`
19×	`distribute-lft-out`
18×	`associate-/r/`
13×	`pow1`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `difference-of-squares`
7×	`frac-times` `div-exp` `associate-*l/` `unswap-sqr`
6×	`cbrt-undiv` `frac-add` `frac-sub` `cbrt-unprod` `div-inv` `add-log-exp`
5×	`associate-*r/` `associate-/l/`
4×	`associate-/l*`
3×	`flip3--` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`pow-prod-down` `un-div-inv` `*-commutative`
1×	`pow2` `sub-neg` `rec-exp` `frac-2neg` `pow-plus` `diff-log` `1-exp` `div-sub` `clear-num` `pow-sqr` `pow-prod-up`

Counts

4 → 198

Calls

4 calls:

224.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (/ (* (/ (+ x 1.0) (- x 1.0)) (+ x 1.0)) (- x 1.0))) (+ (* (+ x 1.0) (/ 1 (- x 1.0))) (/ x (+ x 1.0))))
80.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
47.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
50.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (/ (* (/ (+ x 1.0) (- x 1.0)) (+ x 1.0)) (- x 1.0)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

492.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (/ (* (/ (+ x 1.0) (- x 1.0)) (+ x 1.0)) (- x 1.0))) (+ (* (+ x 1.0) (/ 1 (- x 1.0))) (/ x (+ x 1.0))))
58.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
65.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
269.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (/ (* (/ (+ x 1.0) (- x 1.0)) (+ x 1.0)) (- x 1.0)))

simplify705.0ms

Counts: 210 → 210

prune656.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch153.0ms

Steps

Iters	Range		Point
6	9556.682540875734	100426.34546533476	11064.559685376029
10	-4418200179179808.0	-1501.2167507114543	-9509.628904788262

simplify634.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

478.0ms	1741×	body	1280	valid
459.0ms	614×	body	320	valid
235.0ms	1222×	body	640	valid
172.0ms	4107×	body	80	valid
69.0ms	316×	body	160	valid