Details

sample75.0ms

Algorithm

intervals

Results

24.0ms	32×	body	2560	valid
12.0ms	184×	body	80	valid
10.0ms	31×	body	1280	valid
5.0ms	84×	body	80	nan
4.0ms	17×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify484.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	96
7	96
6	95
5	93
4	85
3	70
2	42
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
0.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.4b	(- (* b b) (* (* 4.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite178.0ms

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--` `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 → 84

Calls

4 calls:

94.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
65.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
108.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
60.0ms	(- (* b b) (* (* 4.0 a) c))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1136
1	388
0	158

prune621.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize71.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* b b) (* (* 4.0 a) c))
58.0ms	(- (* b b) (* (* 4.0 a) c))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
3	2175
2	510
1	157
0	62

prune491.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize61.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

69 → 69

Iterations

Iter	Nodes
done	5002
3	2175
2	510
1	157
0	62

prune567.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

localize61.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

94.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
161.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
156.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
3	2012
2	720
1	352
0	189

prune620.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.8b

regimes377.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.6b against oracle of 6.2b and baseline of 34.5b

bsearch161.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	2.8983489306952693e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify11.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	1040×	body	2560	valid
559.0ms	5835×	body	80	valid
457.0ms	906×	body	1280	valid
254.0ms	2881×	body	80	nan
174.0ms	456×	body	640	valid
57.0ms	102×	body	5120	valid
56.0ms	116×	body	160	valid
50.0ms	232×	body	320	valid