Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
6.0ms	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

simplify45.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize10.0ms

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)))

rewrite68.0ms

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:

38.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 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)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ (- (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)
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify749.0ms

Counts

161 → 161

Iterations

Useful iterations: done (743.0ms)

Iter	Nodes	Cost
0	280	4083
1	665	3911
2	2175	3753
done	5001	3752

prune446.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

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)))

rewrite101.0ms

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:

72.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
46.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify839.0ms

Counts

129 → 129

Iterations

Useful iterations: done (835.0ms)

Iter	Nodes	Cost
0	265	2757
1	700	2456
2	2361	2210
done	5000	2201

prune349.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

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)))

rewrite46.0ms

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)
20.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify988.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (235.0ms)

Iter	Nodes	Cost
0	81	1248
1	190	1104
2	600	1036
3	2063	1028
done	5000	1028

prune240.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize21.0ms

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)))

rewrite20.0ms

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)
4.0ms	(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)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

65 → 65

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	141	1448
1	336	1373
2	1000	1165
3	3459	1149
done	5000	1148

prune312.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes182.0ms

Accuracy

81.7% (5.1b remaining)

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

bsearch112.0ms

Steps

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

simplify2.0ms

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

226.0ms	5914×	body	80	valid
221.0ms	1025×	body	2560	valid
162.0ms	891×	body	1280	valid
113.0ms	2997×	body	80	nan
63.0ms	450×	body	640	valid
29.0ms	107×	body	5120	valid
24.0ms	209×	body	320	valid
7.0ms	104×	body	160	valid