Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
7.0ms	36×	body	1280	valid
6.0ms	165×	body	80	valid
3.0ms	87×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

34.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify733.0ms

Counts

161 → 161

Iterations

Useful iterations: done (728.0ms)

Iter	Nodes	Cost
0	278	4083
1	663	3911
2	2141	3753
done	5001	3752

prune437.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-r`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-l`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 117

Calls

4 calls:

70.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify837.0ms

Counts

129 → 129

Iterations

Useful iterations: done (833.0ms)

Iter	Nodes	Cost
0	263	2757
1	698	2456
2	2326	2210
done	5000	2201

prune336.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify930.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (245.0ms)

Iter	Nodes	Cost
0	80	1248
1	189	1104
2	600	1036
3	2066	1028
done	5000	1028

prune259.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

9.7b	(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.3b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.3b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 53

Calls

4 calls:

8.0ms	(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
94.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
97.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

65 → 65

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	139	1448
1	333	1373
2	975	1165
3	3342	1149
done	5001	1148

prune321.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes178.0ms

Accuracy

81.7% (5.1b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 33.8b

bsearch109.0ms

Steps

Iters	Range		Point
9	2.365685850767504e-168	1.2053288471691685e-161	1.1860189201379418e-161
8	-1.4395777107888637e+138	-2.299948591329529e+133	-1.9827654008890006e+134

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

243.0ms	1025×	body	2560	valid
234.0ms	5914×	body	80	valid
165.0ms	891×	body	1280	valid
110.0ms	2997×	body	80	nan
66.0ms	450×	body	640	valid
31.0ms	107×	body	5120	valid
23.0ms	209×	body	320	valid
8.0ms	104×	body	160	valid