Details

sample74.0ms

Algorithm

intervals

Results

14.0ms	34×	body	2560	valid
14.0ms	196×	body	80	valid
8.0ms	20×	body	1280	valid
5.0ms	78×	body	80	nan
4.0ms	15×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify166.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	121	17
4	153	17
5	160	17
6	164	17
done	164	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

162.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
53.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(- (* b b) (* 4.0 (* a c)))
120.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
106.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

169 → 169

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	243	6690
1	616	4729
2	2482	3764
done	5002	3675

prune556.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 205

Calls

4 calls:

18.0ms	(- (* b b) (* 4.0 (* a c)))
52.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b b) (* 4.0 (* a c)))
201.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
115.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
92.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

217 → 217

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	311	8365
1	780	6147
2	3274	5140
done	5001	5052

prune597.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
0.3b	(fma b b (- (* (* a c) 4.0)))
0.3b	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
22.4b	(sqrt (fma b b (- (* (* a c) 4.0))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

180×	`prod-diff`
136×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
23×	`add-exp-log`
19×	`neg-mul-1`
13×	`add-cbrt-cube`
10×	`fma-neg` `prod-exp`
8×	`add-log-exp`
7×	`pow1` `associate-r` `associate-l`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `times-frac` `flip--`
2×	`cbrt-undiv` `frac-times` `rec-exp` `diff-log` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 280

Calls

4 calls:

108.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
1.0ms	(fma b b (- (* (* a c) 4.0)))
37.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
3.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
77.0ms	(fma b b (- (* (* a c) 4.0)))
118.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
125.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))

simplify842.0ms

Counts

292 → 292

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	342	17663
1	999	11950
done	5000	9143

prune617.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* a c) 4.0))
0.3b	(- (- b) (sqrt (- (* b b) (* (* a c) 4.0))))
22.4b	(sqrt (- (* b b) (* (* a c) 4.0)))
22.4b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

9.0ms	(- (* b b) (* (* a c) 4.0))
44.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 4.0))))
19.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))
12.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* a c) 4.0))
92.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 4.0))))
83.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))
111.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify1.5s

Counts

152 → 152

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	179	6137
1	426	4154
2	1645	3279
done	5001	2639

prune622.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

regimes257.0ms

Accuracy

86% (4.0b remaining)

Error of 9.8b against oracle of 5.8b and baseline of 34.3b

bsearch388.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	1920982614230223.5
10	-1.3330344523059006e-149	-1.6749016460307825e-159	-3.721169858947978e-153
6	-2.350179250111568e+55	-1.828939172749339e+54	-7.359940312872037e+54

simplify19.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	50	105
1	63	99
2	69	99
3	72	99
done	72	99

end0.0ms

sample3.2s

Algorithm

intervals

Results

939.0ms	5765×	body	80	valid
600.0ms	1057×	body	2560	valid
377.0ms	933×	body	1280	valid
316.0ms	2861×	body	80	nan
197.0ms	446×	body	640	valid
97.0ms	115×	body	5120	valid
79.0ms	230×	body	320	valid
15.0ms	120×	body	160	valid