Details

sample229.0ms

Algorithm

intervals

Results

62.0ms	25×	body	1280	valid
26.0ms	43×	body	2560	valid
22.0ms	190×	body	80	valid
8.0ms	85×	body	80	nan
6.0ms	14×	body	640	valid
3.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite185.0ms

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:

78.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	2000
3	2000
2	1291
1	494
0	199

prune456.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite269.0ms

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:

157.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
47.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

135 → 135

Iterations

Iter	Nodes
done	2002
3	2002
2	1510
1	560
0	219

prune546.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 71

Calls

4 calls:

19.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

83 → 83

Iterations

Iter	Nodes
done	2004
4	2004
3	1558
2	467
1	166
0	69

prune591.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
23.7b	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

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:

17.0ms	(- (* 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))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	2050
4	2050
3	1742
2	517
1	191
0	87

prune472.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.5b

regimes385.0ms

Accuracy

81.9% (5.0b remaining)

Error of 10.4b against oracle of 5.4b and baseline of 33.0b

bsearch224.0ms

Steps

Iters	Range		Point
10	1.3859530517218358e-142	9.527435083115218e-125	9.080243787284695e-125
10	-2.135870217411626e+145	-4.758281296322139e+130	-1.9358476230749954e+137

simplify4.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample3.8s

Algorithm

intervals

Results

853.0ms	5928×	body	80	valid
801.0ms	1071×	body	2560	valid
770.0ms	3004×	body	80	nan
554.0ms	872×	body	1280	valid
234.0ms	471×	body	640	valid
209.0ms	109×	body	5120	valid
70.0ms	216×	body	320	valid
24.0ms	111×	body	160	valid