Details

sample68.0ms

Algorithm

intervals

Results

39.0ms	284×	body	80	valid
10.0ms	87×	body	80	nan

simplify112.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize21.0ms

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)))

rewrite60.0ms

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` `insert-posit16`
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 → 80

Calls

4 calls:

9.0ms	(- (* z z) (* t a))
14.0ms	(* (* x y) z)
28.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms	(sqrt (- (* z z) (* t a)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* z z) (* t a))
28.0ms	(* (* x y) z)
116.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
77.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1429
1	362
0	138

prune615.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
3.1b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

16.0ms	(/ z (sqrt (- (* z z) (* t a))))
15.0ms	(- (* z z) (* t a))
75.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
15.0ms	(sqrt (- (* z z) (* t a)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ z (sqrt (- (* z z) (* t a))))
62.0ms	(- (* z z) (* t a))
132.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
81.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5003
2	1661
1	476
0	171

prune804.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b	(* x (/ z (sqrt (- (* z z) (* t a)))))
0.8b	(- (* z z) (* t a))
1.6b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite139.0ms

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` `insert-posit16`
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 → 96

Calls

4 calls:

60.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
15.0ms	(- (* z z) (* t a))
46.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
61.0ms	(- (* z z) (* t a))
152.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
112.0ms	(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1393
1	428
0	166

prune617.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.8b	(- (* z z) (* t a))
3.1b	(* (* y x) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
32×	`add-sqr-sqrt`
30×	`add-cbrt-cube`
27×	`prod-exp`
25×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`pow1` `add-cube-cbrt`
15×	`cbrt-unprod`
14×	`sqrt-prod`
9×	`pow-prod-down`
6×	`div-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`sqrt-div` `associate-l` `associate-*r/` `insert-posit16`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--`
2×	`associate-/r/` `un-div-inv` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 112

Calls

4 calls:

61.0ms	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
9.0ms	(- (* z z) (* t a))
47.0ms	(* (* y x) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
17.0ms	(sqrt (- (* z z) (* t a)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
44.0ms	(- (* z z) (* t a))
98.0ms	(* (* y x) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
86.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

124 → 124

Iterations

Iter	Nodes
done	5003
2	1578
1	493
0	184

prune530.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.6b

regimes703.0ms

Accuracy

86% (2.7b remaining)

Error of 6.2b against oracle of 3.6b and baseline of 22.7b

bsearch156.0ms

Steps

Iters	Range		Point
11	8.688990858178343e+139	1.8631465804193512e+160	1.0460513044759073e+153
9	-1.0384869655897532e+157	-1.2115114540629089e+151	-1.4291886083756086e+152

simplify5.0ms

Iterations

Iter	Nodes
done	30
2	30
1	27
0	21

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	8869×	body	80	valid
414.0ms	2941×	body	80	nan