Details

sample177.0ms

Algorithm

intervals

Results

16.0ms	32×	body	2560	valid
14.0ms	184×	body	80	valid
12.0ms	32×	body	1280	valid
5.0ms	84×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify189.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 118

Calls

4 calls:

74.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
56.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1980
1	492
0	195

prune866.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize48.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	3185
2	595
1	169
0	67

prune592.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize102.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	3185
2	595
1	169
0	67

prune598.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.8b

localize84.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
25.5b	(cbrt (- (* b_2 b_2) (* a c)))
25.5b	(cbrt (- (* b_2 b_2) (* a c)))
25.5b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

108.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))
9.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
108.0ms	(cbrt (- (* b_2 b_2) (* a c)))
129.0ms	(cbrt (- (* b_2 b_2) (* a c)))
137.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

109 → 109

Iterations

Iter	Nodes
done	5002
3	3206
2	863
1	369
0	186

prune912.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.8b

regimes540.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.6b against oracle of 6.1b and baseline of 34.7b

bsearch140.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	3.1423118580081215e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	26

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	1043×	body	2560	valid
515.0ms	5833×	body	80	valid
359.0ms	911×	body	1280	valid
218.0ms	2878×	body	80	nan
106.0ms	449×	body	640	valid
45.0ms	102×	body	5120	valid
43.0ms	232×	body	320	valid
14.0ms	119×	body	160	valid