Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	189×	body	80	valid
4.0ms	26×	body	640	valid
3.0ms	25×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
13	4169
12	3568
11	3113
10	2621
9	2078
8	1683
7	1107
6	562
5	259
4	129
3	73
2	33
1	16
0	8

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ 1.0 y))
16.0b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

rewrite28.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `flip-+` `fma-udef` `div-inv` `flip--`

Counts

2 → 58

Calls

2 calls:

26.0ms	(/ (- x 1.0) (+ 1.0 y))
1.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

series143.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- x 1.0) (+ 1.0 y))
98.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

simplify3.0s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	3520
2	878
1	282
0	114

prune334.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.7b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `prod-diff`
24×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/`
5×	`pow1` `associate-l` `distribute-lft-out` `add-log-exp`
4×	`associate-/r` `flip3-+` `associate-l/` `flip-+` `div-inv`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `-commutative` `associate-/l` `unswap-sqr`

Counts

3 → 102

Calls

3 calls:

17.0ms	(* (- 1.0 x) y)
34.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series254.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (- 1.0 x) y)
113.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
74.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5004
2	1813
1	551
0	202

prune598.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (* y y) (* 1.0 (* 1.0 1.0)))
2.0b	(/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0))))
15.8b	(fma (* (/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y)))) y 1.0)
17.5b	(* (/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
31×	`times-frac`
24×	`add-cube-cbrt`
19×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r*`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `unswap-sqr` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 106

Calls

4 calls:

1.0ms	(fma y (* y y) (* 1.0 (* 1.0 1.0)))
27.0ms	(/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0))))
1.0ms	(fma (* (/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y)))) y 1.0)
98.0ms	(* (/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(fma y (* y y) (* 1.0 (* 1.0 1.0)))
103.0ms	(/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0))))
219.0ms	(fma (* (/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y)))) y 1.0)
155.0ms	(* (/ (- x 1.0) (fma y (* y y) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y))))

simplify2.5s

Counts

118 → 118

Iterations

Iter	Nodes
done	5004
2	2148
1	590
0	182

prune809.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (/ 1 y) (/ x y))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

257×	`times-frac`
209×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
192×	`add-cube-cbrt`
169×	`prod-diff`
32×	`div-inv`
13×	`fma-neg`
6×	`difference-of-squares`
5×	`distribute-lft-out--`
3×	`distribute-rgt-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `frac-sub` `log1p-expm1-u` `flip--` `sub-div`

Counts

1 → 212

Calls

1 calls:

54.0ms

(- (/ 1 y) (/ x y))

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(- (/ 1 y) (/ x y))

simplify2.8s

Counts

215 → 215

Iterations

Iter	Nodes
done	5001
3	3888
2	1465
1	680
0	299

prune351.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.1b

regimes354.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.5b

bsearch139.0ms

Steps

Iters	Range		Point
9	12146952.384825662	1779227265816.5227	74766025.9185153
9	-62218760779908.9	-733100.9210806559	-140476787.34337726

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample960.0ms

Algorithm

intervals

Results

439.0ms	6080×	body	80	valid
120.0ms	730×	body	640	valid
119.0ms	370×	body	1280	valid
62.0ms	535×	body	320	valid
24.0ms	285×	body	160	valid