Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	288×	body	80	valid
4.0ms	78×	body	80	nan

simplify83.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
5	114
4	93
3	68
2	45
1	21
0	12

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
4.5b	(* (* x y) z)
8.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite88.0ms

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))
26.0ms	(* (* x y) z)
40.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms	(sqrt (- (* z z) (* t a)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
149.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
112.0ms	(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2365
1	368
0	134

prune606.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
1.5b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite109.0ms

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/` `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 → 112

Calls

4 calls:

20.0ms	(/ z (sqrt (- (* z z) (* t a))))
11.0ms	(- (* z z) (* t a))
66.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(sqrt (- (* z z) (* t a)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ z (sqrt (- (* z z) (* t a))))
46.0ms	(- (* z z) (* t a))
129.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
105.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	2925
1	474
0	167

prune790.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.5b	(* y (/ (* x z) (sqrt (- (* z z) (* t a)))))
7.4b	(/ (* x z) (sqrt (- (* z z) (* t a))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
59.0ms	(* y (/ (* x z) (sqrt (- (* z z) (* t a)))))
29.0ms	(/ (* x z) (sqrt (- (* z z) (* t a))))
15.0ms	(sqrt (- (* z z) (* t a)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* z z) (* t a))
128.0ms	(* y (/ (* x z) (sqrt (- (* z z) (* t a)))))
68.0ms	(/ (* x z) (sqrt (- (* z z) (* t a))))
76.0ms	(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1967
1	393
0	143

prune508.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.9b

localize34.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt (* (/ (* x z) (sqrt (- (* z z) (* t a)))) y))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*l/`

Counts

4 → 55

Calls

4 calls:

18.0ms	(cbrt (* (/ (* x z) (sqrt (- (* z z) (* t a)))) y))
7.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(sqrt (- (* z z) (* t a)))
8.0ms	(sqrt (- (* z z) (* t a)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(cbrt (* (/ (* x z) (sqrt (- (* z z) (* t a)))) y))
116.0ms	(sqrt (- (* z z) (* t a)))
112.0ms	(sqrt (- (* z z) (* t a)))
100.0ms	(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	4149
2	908
1	273
0	112

prune505.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.9b

regimes1.2s

Accuracy

85.1% (3.0b remaining)

Error of 6.6b against oracle of 3.6b and baseline of 23.6b

bsearch124.0ms

Steps

Iters	Range		Point
5	8.569373513008014e+85	2.184291877784616e+86	1.8361914330862212e+86
7	-6.400863180147889e+154	-3.8279133551988686e+153	-1.3365288255530586e+154

simplify8.0ms

Iterations

Iter	Nodes
done	42
3	42
2	40
1	35
0	27

end0.0ms

sample2.3s

Algorithm

intervals

Results

869.0ms	8834×	body	80	valid
197.0ms	2913×	body	80	nan