Details

sample46.0ms

Algorithm

intervals

Results

16.0ms	280×	body	80	valid
5.0ms	106×	body	80	nan

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	103
6	103
5	97
4	70
3	53
2	36
1	21
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
6.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.5b	(sqrt (- (* z z) (* t a)))

rewrite110.0ms

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×	`sqrt-div`
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` `diff-log` `associate-l` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

12.0ms	(- (* z z) (* t a))
28.0ms	(* (* x y) z)
52.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms	(sqrt (- (* z z) (* t a)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* z z) (* t a))
45.0ms	(* (* x y) z)
123.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
85.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1403
1	359
0	134

prune602.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.4b	(- (* z z) (* t a))
2.8b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.5b	(sqrt (- (* z z) (* t a)))

rewrite70.0ms

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×	`sqrt-div` `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` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

22.0ms	(/ (sqrt (- (* z z) (* t a))) z)
6.0ms	(- (* z z) (* t a))
18.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
15.0ms	(sqrt (- (* z z) (* t a)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (sqrt (- (* z z) (* t a))) z)
63.0ms	(- (* z z) (* t a))
113.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
102.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1895
1	557
0	210

prune882.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.0b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.2b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.5b	(sqrt (- (* z z) (* t a)))

rewrite114.0ms

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×	`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` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 227

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
14.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
51.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.0ms	(sqrt (- (* z z) (* t a)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* z z) (* t a))
75.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
132.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify2.5s

Counts

239 → 239

Iterations

Iter	Nodes
done	5001
2	2702
1	920
0	330

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
0.9b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.2b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.5b	(sqrt (- (* z z) (* t a)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

11.0ms	(- (* z z) (* t a))
66.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
56.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
14.0ms	(sqrt (- (* z z) (* t a)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* z z) (* t a))
76.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
167.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
98.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1364
1	425
0	161

prune703.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

regimes924.0ms

Accuracy

86.8% (2.5b remaining)

Error of 5.8b against oracle of 3.2b and baseline of 22.5b

bsearch134.0ms

Steps

Iters	Range		Point
7	4.621680354172573e+105	4.8838286355542577e+107	3.280936158314262e+107
9	-1.0872942423520943e+158	-2.0715321217766484e+152	-5.979373433067622e+153

simplify10.0ms

Iterations

Iter	Nodes
done	30
2	30
1	27
0	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	8871×	body	80	valid
254.0ms	2937×	body	80	nan