Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	197×	body	80	valid
7.0ms	27×	body	640	valid
3.0ms	11×	body	1280	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.9s

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ 1.0 y))
14.4b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

rewrite29.0ms

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/` `insert-posit16` `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 → 60

Calls

2 calls:

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

series184.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- x 1.0) (+ 1.0 y))
128.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

simplify2.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3563
2	882
1	284
0	116

prune312.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (/ (- x 1.0) (+ 1.0 y)) y 1.0))
14.4b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
14.4b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
14.4b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (fma (/ (- x 1.0) (+ 1.0 y)) y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
0.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
1.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

series656.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(cbrt (fma (/ (- x 1.0) (+ 1.0 y)) y 1.0))
110.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
108.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
94.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

simplify2.3s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
3	1681
2	514
1	182
0	78

prune458.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.5b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.2b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite84.0ms

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` `insert-posit16` `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 → 105

Calls

3 calls:

21.0ms	(* (- 1.0 x) y)
32.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
28.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series278.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (- 1.0 x) y)
138.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
81.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5003
2	1821
1	554
0	205

prune569.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize74.0ms

Local error

Found 4 expressions with local error:

6.7b	(fma 1 1.0 (- (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))))
8.3b	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
8.3b	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
31.0b	(fma (- (/ 1 (+ y 1.0))) (* (- 1.0 x) y) (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
36×	`associate-l`
32×	`*-un-lft-identity`
28×	`add-cbrt-cube`
24×	`times-frac` `prod-exp`
20×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`pow1`
12×	`cbrt-unprod`
10×	`associate-*l/`
8×	`div-exp`
6×	`pow-prod-down` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-*r/` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`flip3-+` `associate-r` `*-commutative` `flip-+` `fma-udef` `div-inv`

Counts

4 → 120

Calls

4 calls:

1.0ms	(fma 1 1.0 (- (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))))
99.0ms	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
97.0ms	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
1.0ms	(fma (- (/ 1 (+ y 1.0))) (* (- 1.0 x) y) (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(fma 1 1.0 (- (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))))
58.0ms	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
49.0ms	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
165.0ms	(fma (- (/ 1 (+ y 1.0))) (* (- 1.0 x) y) (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y)))

simplify2.2s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	1367
1	434
0	151

prune612.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

regimes266.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 22.6b

bsearch141.0ms

Steps

Iters	Range		Point
9	94859.26993337883	238702944844.10663	149371639.02682295
8	-871508905171.6743	-26711381.42537418	-160840129.45081177

simplify20.0ms

Iterations

Iter	Nodes
done	62
3	62
2	57
1	49
0	32

end0.0ms

sample1.4s

Algorithm

intervals

Results

536.0ms	362×	body	1280	valid
346.0ms	6052×	body	80	valid
230.0ms	762×	body	640	valid
80.0ms	296×	body	160	valid
70.0ms	528×	body	320	valid