Details

sample71.0ms

Algorithm

intervals

Results

40.0ms	284×	body	80	valid
10.0ms	87×	body	80	nan

simplify99.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
10.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite64.0ms

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:

8.0ms	(- (* z z) (* t a))
16.0ms	(* (* x y) z)
29.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms	(sqrt (- (* z z) (* t a)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* z z) (* t a))
39.0ms	(* (* x y) z)
129.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1508
1	385
0	150

prune563.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
5.6b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
42×	`add-sqr-sqrt`
39×	`times-frac`
33×	`associate-r`
29×	`*-un-lft-identity` `add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
15×	`associate-l`
12×	`sqrt-div`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 132

Calls

4 calls:

16.0ms	(- (* z z) (* t a))
122.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
14.0ms	(sqrt (- (* z z) (* t a)))
10.0ms	(sqrt (- (* z z) (* t a)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* z z) (* t a))
121.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
91.0ms	(sqrt (- (* z z) (* t a)))
81.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
2	2371
1	627
0	218

prune853.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.6b

localize49.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (/ y (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

129×	`sqrt-prod`
125×	`add-sqr-sqrt`
94×	`times-frac`
51×	`*-un-lft-identity` `add-cube-cbrt`
42×	`associate-l`
33×	`associate-r`
20×	`unswap-sqr`
16×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
9×	`pow1`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 172

Calls

4 calls:

109.0ms	(* (/ y (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
19.0ms	(sqrt (- (* z z) (* t a)))
19.0ms	(sqrt (- (* z z) (* t a)))
20.0ms	(sqrt (- (* z z) (* t a)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (/ y (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
102.0ms	(sqrt (- (* z z) (* t a)))
83.0ms	(sqrt (- (* z z) (* t a)))
92.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

184 → 184

Iterations

Iter	Nodes
done	5001
2	2415
1	655
0	229

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

localize115.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

19.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))
10.0ms	(sqrt (- (* z z) (* t a)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (- (* z z) (* t a)))
111.0ms	(sqrt (- (* z z) (* t a)))
103.0ms	(sqrt (- (* z z) (* t a)))
92.0ms	(sqrt (- (* z z) (* t a)))

simplify2.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	4036
3	1240
2	398
1	133
0	53

prune723.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.6b

regimes684.0ms

Accuracy

82.2% (3.6b remaining)

Error of 7.2b against oracle of 3.6b and baseline of 23.9b

bsearch107.0ms

Steps

Iters	Range		Point
4	2.9396144040603214e+110	5.858149525987066e+110	4.645470841311438e+110
8	-1.8080852560427047e+77	-2.4062107221909806e+73	-1.3605793930191254e+75

simplify7.0ms

Iterations

Iter	Nodes
done	34
2	34
1	31
0	25

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s	8869×	body	80	valid
357.0ms	2941×	body	80	nan