Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	183×	body	80	valid
6.0ms	28×	body	640	valid
3.0ms	11×	body	1280	valid
3.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.4b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite17.0ms

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:

14.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series161.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ y (+ y 1.0))
102.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify684.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
2	898
1	213
0	94

prune380.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.4b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ 1.0 y))
0.1b	(* y (/ 1 (+ 1.0 y)))
6.5b	(fma (* y (/ 1 (+ 1.0 y))) (- x 1.0) 1.0)

rewrite74.0ms

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:

22.0ms	(/ 1 (+ 1.0 y))
48.0ms	(* y (/ 1 (+ 1.0 y)))
1.0ms	(fma (* y (/ 1 (+ 1.0 y))) (- x 1.0) 1.0)

series186.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ 1 (+ 1.0 y))
70.0ms	(* y (/ 1 (+ 1.0 y)))
71.0ms	(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

prune643.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.4b

localize76.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
5.8b	(fma (* (* (/ (cbrt y) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt y)) (/ (cbrt y) (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt y)
305.0ms	(cbrt y)
322.0ms	(cbrt y)
133.0ms	(fma (* (* (/ (cbrt y) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt y)) (/ (cbrt y) (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

simplify1.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	2113
2	391
1	119
0	59

prune518.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.4b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
0.3b	(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
12.6b	(fma (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ y (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

7.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
37.0ms	(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
0.0ms	(fma (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ y (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

series520.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (+ 1.0 y))
138.0ms	(cbrt (+ 1.0 y))
168.0ms	(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
79.0ms	(fma (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ y (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

simplify1.1s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1478
1	403
0	170

prune688.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.4b

regimes267.0ms

Accuracy

96.5% (0.3b remaining)

Error of 7.9b against oracle of 7.6b and baseline of 14.8b

bsearch142.0ms

Steps

Iters	Range		Point
7	8.20310876383851e+25	1.8354952509793101e+27	1.3148568876595996e+26
9	-3.8056990057746655e+20	-83422883652835.42	-3610893527941651.5

simplify4.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

741.0ms	6080×	body	80	valid
174.0ms	752×	body	640	valid
78.0ms	364×	body	1280	valid
69.0ms	306×	body	160	valid
65.0ms	498×	body	320	valid