Details

sample37.0ms

Algorithm

intervals

Results

11.0ms	201×	body	80	valid
4.0ms	20×	body	640	valid
3.0ms	10×	body	1280	valid
2.0ms	17×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (29.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	76	11
4	161	10
5	466	10
6	1868	10
done	5000	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
13.2b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

2 → 58

Calls

2 calls:

33.0ms	(/ (- x 1.0) (+ y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series173.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- x 1.0) (+ y 1.0))
118.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.0s

Counts

64 → 64

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	114	834
1	282	799
2	1133	747
done	5002	743

prune288.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
0.1b	(* (/ (- x 1.0) (+ y 1.0)) y)
4.2b	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-l`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `flip3--` `fma-def` `frac-2neg` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip--`

Counts

3 → 109

Calls

3 calls:

42.0ms	(/ (- x 1.0) (+ y 1.0))
90.0ms	(* (/ (- x 1.0) (+ y 1.0)) y)
39.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

series184.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (- x 1.0) (+ y 1.0))
61.0ms	(* (/ (- x 1.0) (+ y 1.0)) y)
78.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

simplify2.5s

Counts

118 → 118

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	172	1520
1	472	1433
2	2182	1346
done	5002	1338

prune350.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- y 1.0) y)
4.0b	(+ (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* (- y 1.0) y)) 1.0)
4.1b	(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
16.0b	(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* (- y 1.0) y))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
40×	`times-frac`
31×	`associate-l`
27×	`add-cube-cbrt`
21×	`difference-of-squares`
20×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`distribute-lft-out--`
7×	`associate-*l/` `prod-exp` `cbrt-unprod`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`frac-times` `associate-r/` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `clear-num` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

24.0ms	(* (- y 1.0) y)
59.0ms	(+ (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* (- y 1.0) y)) 1.0)
42.0ms	(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
116.0ms	(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* (- y 1.0) y))

series500.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- y 1.0) y)
226.0ms	(+ (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* (- y 1.0) y)) 1.0)
78.0ms	(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
137.0ms	(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* (- y 1.0) y))

simplify2.7s

Counts

150 → 150

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	234	2728
1	706	2619
2	3959	2376
done	5000	2376

prune565.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1.0 y) x)
0.0b	(- (+ (/ 1.0 y) x) (* 1.0 (/ x y)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`fma-def`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac` `add-log-exp`
4×	`fma-neg` `prod-diff`
3×	`distribute-lft-out`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `diff-log` `associate-*r/` `sum-log` `frac-sub` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `div-inv`

Counts

2 → 53

Calls

2 calls:

25.0ms	(+ (/ 1.0 y) x)
160.0ms	(- (+ (/ 1.0 y) x) (* 1.0 (/ x y)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (/ 1.0 y) x)
45.0ms	(- (+ (/ 1.0 y) x) (* 1.0 (/ x y)))

simplify938.0ms

Counts

59 → 59

Iterations

Useful iterations: done (936.0ms)

Iter	Nodes	Cost
0	75	681
1	209	651
2	1039	590
done	5000	559

prune172.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes101.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 22.8b

bsearch176.0ms

Steps

Iters	Range		Point
10	0.02325869037085268	6498875204.17883	111711424.78256571
11	-3.317152845340719e+16	-2.9526231381329305e-09	-116113257.18599546

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	49
1	31	39
done	31	39

end0.0ms

sample1.1s

Algorithm

intervals

Results

374.0ms	6121×	body	80	valid
204.0ms	714×	body	640	valid
122.0ms	373×	body	1280	valid
60.0ms	497×	body	320	valid
24.0ms	295×	body	160	valid