Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	275×	body	80	valid
5.0ms	95×	body	80	nan

simplify302.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	106
6	106
5	97
4	77
3	58
2	37
1	22
0	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.7b	(* (* x y) z)
8.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.8b	(sqrt (- (* z z) (* t a)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

22.0ms	(- (* z z) (* t a))
44.0ms	(* (* x y) z)
49.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.0ms	(sqrt (- (* z z) (* t a)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* z z) (* t a))
52.0ms	(* (* x y) z)
247.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
150.0ms	(sqrt (- (* z z) (* t a)))

simplify3.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
2	1504
1	384
0	150

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.4b	(- (* z z) (* t a))
3.9b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.8b	(sqrt (- (* z z) (* t a)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 146

Calls

4 calls:

23.0ms	(/ (sqrt (- (* z z) (* t a))) z)
11.0ms	(- (* z z) (* t a))
27.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
32.0ms	(sqrt (- (* z z) (* t a)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (sqrt (- (* z z) (* t a))) z)
62.0ms	(- (* z z) (* t a))
254.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
125.0ms	(sqrt (- (* z z) (* t a)))

simplify3.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5002
2	2008
1	588
0	226

prune2.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.7b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.4b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.8b	(sqrt (- (* z z) (* t a)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`*-un-lft-identity` `add-cube-cbrt`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 241

Calls

4 calls:

11.0ms	(- (* z z) (* t a))
37.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
105.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
35.0ms	(sqrt (- (* z z) (* t a)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* z z) (* t a))
172.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
212.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
119.0ms	(sqrt (- (* z z) (* t a)))

simplify4.8s

Counts

253 → 253

Iterations

Iter	Nodes
done	5001
2	2763
1	955
0	346

prune3.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.8b

localize85.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.7b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
2.4b	(* x (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)))
22.8b	(sqrt (- (* z z) (* t a)))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
371×	`add-sqr-sqrt`
342×	`*-un-lft-identity`
338×	`add-cube-cbrt`
215×	`associate-r`
122×	`sqrt-prod`
41×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`associate-/l*`
18×	`div-exp` `div-inv`
10×	`prod-exp`
9×	`cbrt-undiv` `unswap-sqr`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `associate-/r` `1-exp` `associate-l*`
2×	`flip3--` `sqrt-div` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `associate-/r/` `un-div-inv` `-commutative` `associate-/l/`

Counts

4 → 399

Calls

4 calls:

22.0ms	(- (* z z) (* t a))
33.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
232.0ms	(* x (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)))
14.0ms	(sqrt (- (* z z) (* t a)))

series862.0ms

Counts

4 → 12

Calls

4 calls:

380.0ms	(- (* z z) (* t a))
152.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
221.0ms	(* x (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)))
109.0ms	(sqrt (- (* z z) (* t a)))

simplify6.8s

Counts

411 → 411

Iterations

Iter	Nodes
done	5010
2	4315
1	2098
0	692

prune5.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.8b

regimes3.1s

Accuracy

76.8% (4.6b remaining)

Error of 8.1b against oracle of 3.5b and baseline of 23.2b

bsearch180.0ms

Steps

Iters	Range		Point
8	2.4182442546267315e+58	2.530003709242839e+61	7.016332579849617e+58
9	-1.4797030189529656e+112	-1.6711358187060892e+105	-1.6969835156997758e+105

simplify40.0ms

Iterations

Iter	Nodes
done	40
2	40
1	37
0	29

end0.0ms

sample1.8s

Algorithm

intervals

Results

668.0ms	8817×	body	80	valid
204.0ms	2853×	body	80	nan