Details

sample74.0ms

Algorithm

intervals

Results

14.0ms	36×	body	2560	valid
13.0ms	187×	body	80	valid
10.0ms	30×	body	1280	valid
5.0ms	79×	body	80	nan
2.0ms	10×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- a) c (* b_2 b_2))
0.1b	(/ (- (- b_2) (sqrt (fma (- a) c (* b_2 b_2)))) a)
0.9b	(- (- b_2) (sqrt (fma (- a) c (* b_2 b_2))))
22.6b	(sqrt (fma (- a) c (* b_2 b_2)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

1.0ms	(fma (- a) c (* b_2 b_2))
69.0ms	(/ (- (- b_2) (sqrt (fma (- a) c (* b_2 b_2)))) a)
15.0ms	(- (- b_2) (sqrt (fma (- a) c (* b_2 b_2))))
1.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (- a) c (* b_2 b_2))
123.0ms	(/ (- (- b_2) (sqrt (fma (- a) c (* b_2 b_2)))) a)
103.0ms	(- (- b_2) (sqrt (fma (- a) c (* b_2 b_2))))
119.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

simplify1.3s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	1719
1	488
0	217

prune779.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))))
0.2b	(/ 1 (/ a (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2)))))))
0.9b	(+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))
22.6b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
228×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
54×	`associate-/r*`
33×	`distribute-lft-out`
17×	`add-exp-log`
16×	`neg-mul-1`
11×	`add-cbrt-cube` `associate-/r/`
10×	`distribute-neg-frac`
8×	`div-exp`
6×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 293

Calls

4 calls:

24.0ms	(/ a (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))))
32.0ms	(/ 1 (/ a (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2)))))))
11.0ms	(+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))
2.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ a (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))))
164.0ms	(/ 1 (/ a (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2)))))))
108.0ms	(+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))
113.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify597.0ms

Counts

305 → 305

Iterations

Iter	Nodes
done	5000
1	953
0	371

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- c) a (* b_2 b_2))
0.2b	(* (/ 1 a) (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))))
0.9b	(+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))
22.6b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`associate-l` `add-exp-log`
12×	`associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `prod-exp` `log1p-expm1-u` `distribute-neg-frac`
3×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out` `unswap-sqr`
2×	`frac-times` `distribute-neg-in` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `neg-mul-1` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `distribute-rgt-neg-out` `fma-udef` `div-inv`

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma (- c) a (* b_2 b_2))
64.0ms	(* (/ 1 a) (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))))
11.0ms	(+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))
3.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (- c) a (* b_2 b_2))
136.0ms	(* (/ 1 a) (- (+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))))
124.0ms	(+ b_2 (sqrt (fma (- c) a (* b_2 b_2))))
126.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify1.8s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	2810
1	467
0	167

prune657.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* a (/ 1 (- (- b_2) (sqrt (fma (- c) a (* b_2 b_2)))))))
0.2b	(* a (/ 1 (- (- b_2) (sqrt (fma (- c) a (* b_2 b_2))))))
0.9b	(- (- b_2) (sqrt (fma (- c) a (* b_2 b_2))))
22.6b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
60×	`prod-diff` `add-cube-cbrt`
48×	`add-exp-log`
37×	`sqrt-prod`
27×	`associate-r`
26×	`times-frac`
25×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
10×	`pow1` `fma-neg`
9×	`rec-exp` `1-exp`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`flip3--` `diff-log` `pow-prod-down` `associate-*r/` `un-div-inv` `div-inv` `pow-flip` `flip--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `-commutative` `inv-pow`

Counts

4 → 199

Calls

4 calls:

39.0ms	(/ 1 (* a (/ 1 (- (- b_2) (sqrt (fma (- c) a (* b_2 b_2)))))))
95.0ms	(* a (/ 1 (- (- b_2) (sqrt (fma (- c) a (* b_2 b_2))))))
32.0ms	(- (- b_2) (sqrt (fma (- c) a (* b_2 b_2))))
3.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1 (* a (/ 1 (- (- b_2) (sqrt (fma (- c) a (* b_2 b_2)))))))
309.0ms	(* a (/ 1 (- (- b_2) (sqrt (fma (- c) a (* b_2 b_2))))))
118.0ms	(- (- b_2) (sqrt (fma (- c) a (* b_2 b_2))))
90.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify1.3s

Counts

211 → 211

Iterations

Iter	Nodes
done	5000
2	2750
1	681
0	272

prune815.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

regimes464.0ms

Accuracy

81.3% (5.3b remaining)

Error of 11.2b against oracle of 5.9b and baseline of 34.2b

bsearch119.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	1.082532154480776e+78
6	-6.6625002027150184e-136	-1.2670716760605177e-136	-6.596302400897662e-136

simplify4.0ms

Iterations

Iter	Nodes
done	33
2	33
1	32
0	24

end0.0ms

sample3.0s

Algorithm

intervals

Results

556.0ms	1048×	body	2560	valid
553.0ms	5896×	body	80	valid
484.0ms	229×	body	320	valid
316.0ms	877×	body	1280	valid
238.0ms	2811×	body	80	nan
141.0ms	446×	body	640	valid
110.0ms	121×	body	5120	valid
14.0ms	105×	body	160	valid