Details

sample282.0ms

Algorithm

intervals

Results

53.0ms	97×	body	80	nan
32.0ms	185×	body	80	valid
31.0ms	33×	body	2560	valid
24.0ms	32×	body	1280	valid
7.0ms	12×	body	640	valid
6.0ms	5×	body	5120	valid
4.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

105.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
55.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
45.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
126.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	2003
3	2003
2	1029
1	378
0	158

prune497.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 166

Calls

4 calls:

54.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
48.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

178 → 178

Iterations

Iter	Nodes
done	2002
3	2002
2	1691
1	626
0	262

prune723.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
3×	`cbrt-prod` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt a)
9.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt a)
43.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify850.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2000
3	2000
2	678
1	250
0	113

prune398.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.6b	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `log-prod` `exp-sum`
5×	`sqrt-prod`
4×	`exp-prod` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`log-div` `sub-neg` `exp-diff` `sqrt-div` `diff-log` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `log-pow` `rem-exp-log`

Counts

4 → 66

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
110.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify989.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2000
3	2000
2	660
1	255
0	125

prune430.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

regimes346.0ms

Accuracy

83.4% (4.5b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 33.0b

bsearch124.0ms

Steps

Iters	Range		Point
9	2.0671083276743448e-101	1.4914771383599542e-96	3.5014024016497154e-97
5	-1.4698287087051062e+86	-6.898352246976959e+85	-9.711132829713123e+85

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1105×	body	2560	valid
859.0ms	5934×	body	80	valid
632.0ms	845×	body	1280	valid
426.0ms	2937×	body	80	nan
226.0ms	435×	body	640	valid
203.0ms	120×	body	5120	valid
75.0ms	211×	body	320	valid
28.0ms	113×	body	160	valid