Details

sample75.0ms

Algorithm

intervals

Results

15.0ms	151×	body	160	valid
13.0ms	277×	body	80	nan
12.0ms	533×	pre	80	true
7.0ms	48×	body	320	valid
3.0ms	57×	body	80	valid

simplify92.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	79
2	43
1	25
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* c a))))
0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
0.2b	(- (* b b) (* 4.0 (* c a)))
37.2b	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
68.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
11.0ms	(- (* b b) (* 4.0 (* c a)))
66.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

series320.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
108.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
52.0ms	(- (* b b) (* 4.0 (* c a)))
86.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

simplify1.8s

Counts

195 → 195

Iterations

Iter	Nodes
done	5001
2	2320
1	798
0	321

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune126.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* a c) b)
0.2b	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 77

Calls

2 calls:

13.0ms	(/ (* a c) b)
29.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series69.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (* a c) b)
31.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify1.8s

Counts

83 → 83

Iterations

Iter	Nodes
done	5049
2	1836
1	456
0	171

prune729.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* a c) b)
0.2b	(/ (* a c) b)
0.2b	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
0.5b	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
48×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `add-cube-cbrt`
34×	`sqrt-prod`
30×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
12×	`swap-sqr`
11×	`cbrt-undiv` `div-exp` `div-inv`
10×	`associate-r` `associate-l`
9×	`associate-/r` `associate-/l`
8×	`sqrt-pow1` `pow1/2`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

8.0ms	(/ (* a c) b)
8.0ms	(/ (* a c) b)
82.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
57.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (* a c) b)
26.0ms	(/ (* a c) b)
72.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
79.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.6s

Counts

176 → 176

Iterations

Iter	Nodes
done	5060
2	2149
1	563
0	237

prune1.0s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 5.4b

regimes1.0s

Accuracy

11.3% (6.6b remaining)

Error of 11.7b against oracle of 5.1b and baseline of 12.6b

bsearch4.0ms

Steps

Iters	Range		Point
0	1.1367127926867939e-06	1.150970403537976e-06	1.1438415981123848e-06

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	8186×	body	80	nan
786.0ms	4769×	body	160	valid
679.0ms	16186×	pre	80	true
300.0ms	1336×	body	320	valid
189.0ms	1895×	body	80	valid