Details

sample105.0ms

Algorithm

intervals

Results

24.0ms	27×	body	1280	valid
19.0ms	195×	body	80	valid
18.0ms	35×	body	640	valid
7.0ms	101×	body	80	nan
6.0ms	17×	body	320	valid
3.0ms	12×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	27	11
3	52	11
4	110	11
5	249	11
6	590	11
7	1855	11
done	5000	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ (pow (/ y (+ z y)) y) y))
0.0b	(/ y (+ z y))
6.4b	(pow (/ y (+ z y)) y)

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
8×	`add-exp-log` `distribute-lft-out`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `pow-unpow` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`div-exp` `pow-exp` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sum-log` `sqr-pow`

Counts

3 → 87

Calls

3 calls:

102.0ms	(+ x (/ (pow (/ y (+ z y)) y) y))
22.0ms	(/ y (+ z y))
14.0ms	(pow (/ y (+ z y)) y)

series533.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(+ x (/ (pow (/ y (+ z y)) y) y))
67.0ms	(/ y (+ z y))
333.0ms	(pow (/ y (+ z y)) y)

simplify2.6s

Counts

96 → 96

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	164	1143
1	405	1072
2	1038	1017
3	3016	1012
done	5000	1011

prune277.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.8b	(pow (/ (cbrt y) (cbrt (+ z y))) y)
2.8b	(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

2.0ms	(cbrt y)
2.0ms	(cbrt y)
39.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
56.0ms	(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

series1.7s

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt y)
311.0ms	(cbrt y)
370.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
701.0ms	(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

simplify3.2s

Counts

136 → 136

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	301	2387
1	693	2217
2	1534	1994
3	4582	1975
done	5000	1973

prune684.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
1.8b	(pow (/ (cbrt y) (cbrt (+ z y))) y)
1.8b	(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)
1.8b	(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

54×	`unpow-prod-down`
49×	`*-un-lft-identity`
48×	`cbrt-prod`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log` `pow-unpow`
7×	`pow1`
6×	`distribute-lft-out`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`cbrt-div` `associate-/r/`
1×	`flip3-+` `pow1/3` `div-exp` `flip-+` `div-inv`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt y)
32.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
5.0ms	(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)
5.0ms	(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)

series797.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt y)
405.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
54.0ms	(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)
32.0ms	(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)

simplify3.1s

Counts

128 → 128

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	247	2058
1	541	1915
2	1140	1856
3	3023	1846
done	5000	1840

prune787.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
6.4b	(pow (/ y (+ z y)) y)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
9×	`cbrt-prod`
7×	`add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3` `distribute-lft-out`
2×	`pow-exp` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
33.0ms	(pow (/ y (+ z y)) y)

series1.1s

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt x)
251.0ms	(cbrt x)
304.0ms	(cbrt x)
314.0ms	(pow (/ y (+ z y)) y)

simplify2.5s

Counts

86 → 86

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	140	741
1	314	691
2	703	664
3	1897	650
done	5000	649

prune419.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

-103.4% (1.8b remaining)

Error of 2.0b against oracle of 0.2b and baseline of 1.1b

bsearch215.0ms

Steps

Iters	Range		Point
9	4.677893477719556e+118	2.9580431597534113e+125	4.7668968669307006e+118
8	4.861077116233833e+20	3.339550470087394e+24	2.7983300664584073e+24

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	108
1	35	74
done	35	74

end0.0ms

sample3.5s

Algorithm

intervals

Results

944.0ms	898×	body	640	valid
677.0ms	799×	body	1280	valid
661.0ms	6551×	body	80	valid
302.0ms	598×	body	320	valid
225.0ms	3160×	body	80	nan
59.0ms	308×	body	160	valid