Details

sample181.0ms

Algorithm

intervals

Results

18.0ms	39×	body	2560	valid
14.0ms	188×	body	80	valid
11.0ms	31×	body	1280	valid
8.0ms	87×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

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

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite171.0ms

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--` `insert-posit16` `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 → 122

Calls

4 calls:

80.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
113.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	1393
1	494
0	199

prune541.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
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` `insert-posit16` `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` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 123

Calls

4 calls:

146.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
44.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1630
1	559
0	219

prune621.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
22.8b	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 64

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
0.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b_2 b_2) (* a c))
159.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	1742
2	517
1	191
0	87

prune555.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* c a))
0.4b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
3.3b	(exp (log (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
23.1b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
8×	`add-log-exp`
7×	`fma-neg`
6×	`pow1` `log-prod` `exp-sum`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`log-div` `sub-neg` `exp-diff` `sqrt-div` `diff-log` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `log-pow` `rem-exp-log`

Counts

4 → 100

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* c a))
75.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
52.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
19.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b_2 b_2) (* c a))
92.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
85.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
78.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify3.2s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	2707
2	899
1	365
0	166

prune490.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.4b

regimes400.0ms

Accuracy

87.6% (3.3b remaining)

Error of 9.0b against oracle of 5.7b and baseline of 32.3b

bsearch228.0ms

Steps

Iters	Range		Point
9	57.56933376468871	32423374.974334765	13471615.147294592
9	2.5650146037935753e-122	1.1452426470781684e-116	3.318234109021414e-122
10	-4.186518194588193e+147	-3.370135567630554e+133	-5.300564053552496e+135

simplify6.0ms

Iterations

Iter	Nodes
done	42
1	42
0	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

798.0ms	902×	body	1280	valid
683.0ms	5888×	body	80	valid
606.0ms	1065×	body	2560	valid
233.0ms	2851×	body	80	nan
124.0ms	450×	body	640	valid
66.0ms	201×	body	320	valid
58.0ms	95×	body	5120	valid
19.0ms	137×	body	160	valid