Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
5.0ms	38×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	9×	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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.1b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `distribute-lft-out`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

9.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series152.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ y (+ y 1.0))
90.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify632.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
2	898
1	213
0	94

prune386.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ 1.0 y))
0.1b	(* y (/ 1 (+ 1.0 y)))
5.1b	(fma (* y (/ 1 (+ 1.0 y))) (- x 1.0) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
26×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out`
6×	`pow1`
4×	`associate-/r*` `div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 92

Calls

3 calls:

18.0ms	(/ 1 (+ 1.0 y))
25.0ms	(* y (/ 1 (+ 1.0 y)))
0.0ms	(fma (* y (/ 1 (+ 1.0 y))) (- x 1.0) 1.0)

series204.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 1 (+ 1.0 y))
63.0ms	(* y (/ 1 (+ 1.0 y)))
93.0ms	(fma (* y (/ 1 (+ 1.0 y))) (- x 1.0) 1.0)

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1742
1	347
0	137

prune546.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ 1 (+ y 1.0)))
0.4b	(cbrt (/ 1 (+ y 1.0)))
0.4b	(cbrt (/ 1 (+ y 1.0)))
12.1b	(fma (* y (* (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0)))) (cbrt (/ 1 (+ y 1.0))))) (- x 1.0) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
46×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`distribute-lft-out`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`fma-udef`

Counts

4 → 97

Calls

4 calls:

5.0ms	(cbrt (/ 1 (+ y 1.0)))
6.0ms	(cbrt (/ 1 (+ y 1.0)))
10.0ms	(cbrt (/ 1 (+ y 1.0)))
1.0ms	(fma (* y (* (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0)))) (cbrt (/ 1 (+ y 1.0))))) (- x 1.0) 1.0)

series633.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (/ 1 (+ y 1.0)))
207.0ms	(cbrt (/ 1 (+ y 1.0)))
162.0ms	(cbrt (/ 1 (+ y 1.0)))
94.0ms	(fma (* y (* (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0)))) (cbrt (/ 1 (+ y 1.0))))) (- x 1.0) 1.0)

simplify1.9s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
3	3702
2	877
1	296
0	143

prune745.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
13.1b	(fma (/ (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

7.0ms	(cbrt (+ y 1.0))
7.0ms	(cbrt (+ 1.0 y))
4.0ms	(cbrt (+ 1.0 y))
0.0ms	(fma (/ (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series525.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (+ y 1.0))
135.0ms	(cbrt (+ 1.0 y))
144.0ms	(cbrt (+ 1.0 y))
104.0ms	(fma (/ (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify1.8s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	3235
2	813
1	274
0	127

prune576.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.0b

regimes264.0ms

Accuracy

95.9% (0.3b remaining)

Error of 7.3b against oracle of 7.0b and baseline of 14.5b

bsearch119.0ms

Steps

Iters	Range		Point
8	1.7518748313142936e+19	7.786916274339931e+22	9.186983134595318e+19
6	-2.0076717784505904e+49	-1.683563946501919e+48	-1.7242712175062475e+48

simplify3.0ms

Iterations

Iter	Nodes
done	30
1	30
0	22

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	6148×	body	80	valid
125.0ms	683×	body	640	valid
93.0ms	381×	body	1280	valid
71.0ms	501×	body	320	valid
26.0ms	287×	body	160	valid