Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	199×	body	80	valid
2.0ms	26×	body	640	valid
1.0ms	18×	body	320	valid
1.0ms	10×	body	1280	valid
0.0ms	3×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 4 (18.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	72	11
4	141	10
5	283	10
6	401	10
7	514	10
8	616	10
9	865	10
10	1205	10
11	1704	10
done	5000	10

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite14.0ms

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:

12.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series96.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (- x 1.0) (+ y 1.0))
66.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.7s

Counts

64 → 64

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	114	834
1	277	799
2	801	745
3	3560	739
done	5000	738

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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)

series412.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
64.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
66.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
62.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify722.0ms

Counts

55 → 55

Iterations

Useful iterations: done (720.0ms)

Iter	Nodes	Cost
0	76	843
1	182	832
2	484	731
3	1809	692
done	5001	690

prune174.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0))
4.0b	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`cbrt-div` `flip3-+` `flip-+` `fma-udef`
1×	`+-commutative` `fma-def` `pow1/3` `sum-log`

Counts

4 → 49

Calls

4 calls:

8.0ms	(cbrt (+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0))
10.0ms	(+ (* (/ (- 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)

series423.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0))
72.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)
65.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
63.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	104	1049
1	264	998
2	752	897
3	2903	842
done	5000	840

prune208.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
1.4b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 102

Calls

3 calls:

10.0ms	(* (- 1.0 x) y)
13.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series152.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- 1.0 x) y)
72.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
49.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify910.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (173.0ms)

Iter	Nodes	Cost
0	202	2757
1	546	2323
2	2238	1851
done	5001	1851

prune178.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes120.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch75.0ms

Steps

Iters	Range		Point
8	28638621.607503247	50024088429.266525	212488777.89840698
10	-7.884632933156152e+16	-925426.909356872	-198843285.26894423

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	19	39
1	26	30
done	26	30

end0.0ms

sample436.0ms

Algorithm

intervals

Results

156.0ms	6133×	body	80	valid
62.0ms	719×	body	640	valid
41.0ms	347×	body	1280	valid
34.0ms	515×	body	320	valid
13.0ms	286×	body	160	valid