Details

sample52.0ms

Algorithm

intervals

Results

13.0ms	43×	body	2560	valid
11.0ms	189×	body	80	valid
6.0ms	24×	body	1280	valid
4.0ms	85×	body	80	nan
2.0ms	12×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

123.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
54.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	1521
1	578
0	248

prune763.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 173

Calls

4 calls:

160.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
41.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1654
1	640
0	267

prune671.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

125.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
48.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	1521
1	578
0	248

prune719.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
10.6b	(- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))))
22.7b	(cbrt (- (* b_2 b_2) (* a c)))
22.7b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`fma-neg` `prod-diff`
10×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`neg-mul-1` `sub-neg` `pow1/3`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 86

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))))
110.0ms	(cbrt (- (* b_2 b_2) (* a c)))
103.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	4014
2	1158
1	398
0	161

prune582.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.7b

regimes679.0ms

Accuracy

82.5% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.6b

bsearch111.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
7	-2.1239343788780832e-66	-2.400891841159577e-68	-1.264659490877098e-67

simplify7.0ms

Iterations

Iter	Nodes
done	26
1	26
0	24

end0.0ms

sample2.5s

Algorithm

intervals

Results

534.0ms	439×	body	640	valid
469.0ms	1105×	body	2560	valid
431.0ms	877×	body	1280	valid
406.0ms	5819×	body	80	valid
263.0ms	2973×	body	80	nan
55.0ms	125×	body	5120	valid
49.0ms	252×	body	320	valid
14.0ms	122×	body	160	valid