Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	192×	body	80	valid
5.0ms	23×	body	640	valid
3.0ms	12×	body	1280	valid
3.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1852
5	465
4	160
3	76
2	35
1	16
0	8

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize24.0ms

Local error

Found 1 expressions with local error:

2.8b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

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

series87.0ms

Counts

1 → 3

Calls

1 calls:

87.0ms

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

simplify2.2s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
4	3391
3	674
2	180
1	61
0	29

prune77.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (- x 1.0) (/ y (+ 1.0 y)) 1.0))
2.8b	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
2.8b	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
2.8b	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

rewrite2.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

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

series674.0ms

Counts

4 → 12

Calls

4 calls:

363.0ms	(cbrt (fma (- x 1.0) (/ y (+ 1.0 y)) 1.0))
112.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
104.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
94.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

simplify3.3s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
3	2474
2	565
1	177
0	76

prune430.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.8b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.1b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite105.0ms

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:

23.0ms	(* (- 1.0 x) y)
42.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
36.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series203.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- 1.0 x) y)
106.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
51.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3181
1	552
0	202

prune573.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- 1.0 x)) (/ (+ 1.0 y) (/ y (- y 1.0))))
0.1b	(/ (- 1.0 x) (/ (* (- y 1.0) (+ 1.0 y)) y))
11.9b	(/ (* (- y 1.0) (+ 1.0 y)) y)
15.0b	(fma (/ (- (- 1.0 x)) (/ (+ 1.0 y) (/ y (- y 1.0)))) (- y 1.0) 1.0)

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

3462×	`times-frac`
2532×	`*-un-lft-identity`
1902×	`add-sqr-sqrt`
1166×	`add-cube-cbrt`
450×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
368×	`distribute-lft-out--` `difference-of-squares`
315×	`distribute-lft-out`
137×	`associate-/r/`
99×	`associate-/r*`
90×	`neg-mul-1`
84×	`div-inv`
65×	`flip3--` `flip--`
27×	`add-cbrt-cube` `add-exp-log`
20×	`associate-/l*`
13×	`cbrt-undiv` `div-exp`
12×	`associate-/l/`
4×	`expm1-log1p-u` `frac-times` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
2×	`div-sub` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `distribute-neg-frac`
1×	`neg-sub0` `distribute-frac-neg` `fma-udef`

Counts

4 → 1482

Calls

4 calls:

76.0ms	(/ (- (- 1.0 x)) (/ (+ 1.0 y) (/ y (- y 1.0))))
46.0ms	(/ (- 1.0 x) (/ (* (- y 1.0) (+ 1.0 y)) y))
32.0ms	(/ (* (- y 1.0) (+ 1.0 y)) y)
1.0ms	(fma (/ (- (- 1.0 x)) (/ (+ 1.0 y) (/ y (- y 1.0)))) (- y 1.0) 1.0)

series770.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (- (- 1.0 x)) (/ (+ 1.0 y) (/ y (- y 1.0))))
223.0ms	(/ (- 1.0 x) (/ (* (- y 1.0) (+ 1.0 y)) y))
184.0ms	(/ (* (- y 1.0) (+ 1.0 y)) y)
167.0ms	(fma (/ (- (- 1.0 x)) (/ (+ 1.0 y) (/ y (- y 1.0)))) (- y 1.0) 1.0)

simplify1.0s

Counts

1494 → 1494

Iterations

Iter	Nodes
done	5000
0	1648

prune7.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes239.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.3b

bsearch130.0ms

Steps

Iters	Range		Point
9	6968.3439428623215	12923530959.442633	105820959.87149598
6	-531429590.62988466	-72632609.50044116	-184222856.9532372

simplify4.0ms

Iterations

Iter	Nodes
done	41
1	41
0	29

end0.0ms

sample1.0s

Algorithm

intervals

Results

322.0ms	6117×	body	80	valid
158.0ms	709×	body	640	valid
125.0ms	375×	body	1280	valid
86.0ms	295×	body	160	valid
59.0ms	504×	body	320	valid