Details

sample238.0ms

Algorithm

intervals

Results

23.0ms	195×	body	80	valid
20.0ms	34×	body	1280	valid
9.0ms	18×	body	2560	valid
9.0ms	107×	body	80	nan
9.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify169.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
0.9b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite422.0ms

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-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

234.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
106.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
21.0ms	(- (* b_2 b_2) (* c a))
51.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
129.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
57.0ms	(- (* b_2 b_2) (* c a))
145.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.9s

Counts

130 → 130

Iterations

Iter	Nodes
done	5003
2	1510
1	489
0	194

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* c a))) b_2) (/ 1 a))
0.9b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 119

Calls

4 calls:

302.0ms	(* (- (sqrt (- (* b_2 b_2) (* c a))) b_2) (/ 1 a))
123.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
20.0ms	(- (* b_2 b_2) (* c a))
36.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (- (sqrt (- (* b_2 b_2) (* c a))) b_2) (/ 1 a))
131.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
75.0ms	(- (* b_2 b_2) (* c a))
113.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1592
1	555
0	215

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize64.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* c a))
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

20.0ms	(- (* b_2 b_2) (* c a))
20.0ms	(- (* b_2 b_2) (* c a))
28.0ms	(sqrt (- (* b_2 b_2) (* c a)))
25.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b_2 b_2) (* c a))
74.0ms	(- (* b_2 b_2) (* c a))
118.0ms	(sqrt (- (* b_2 b_2) (* c a)))
122.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify3.4s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	1480
2	461
1	161
0	67

prune810.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

32.0ms

(* -1/2 (/ c b_2))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(* -1/2 (/ c b_2))

simplify2.8s

Counts

37 → 37

Iterations

Iter	Nodes
done	5001
3	1739
2	519
1	172
0	70

prune242.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 5.9b

regimes790.0ms

Accuracy

82.3% (5.1b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 34.6b

bsearch173.0ms

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
6	-4.525167845450207e+100	-9.36795079059543e+99	-2.7668189408748547e+100

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	5756×	body	80	valid
804.0ms	924×	body	1280	valid
666.0ms	1086×	body	2560	valid
344.0ms	2815×	body	80	nan
155.0ms	476×	body	640	valid
82.0ms	97×	body	5120	valid
52.0ms	239×	body	320	valid
32.0ms	116×	body	160	valid