Details

sample160.0ms

Algorithm

intervals

Results

17.0ms	35×	body	2560	valid
14.0ms	179×	body	80	valid
12.0ms	30×	body	1280	valid
9.0ms	76×	body	80	nan
5.0ms	8×	body	5120	valid
3.0ms	10×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
41.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
123.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
120.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.8s

Counts

112 → 112

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	164	1638
1	385	1535
2	1104	1355
3	3200	1340
done	5001	1332

prune414.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.5b	(/ (/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.9b	(/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
74×	`times-frac`
70×	`add-cube-cbrt`
60×	`prod-diff`
40×	`sqrt-prod`
28×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 214

Calls

4 calls:

55.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
128.0ms	(/ (/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
80.0ms	(/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
237.0ms	(/ (/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
250.0ms	(/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

226 → 226

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	323	7623
1	782	5803
2	2384	4779
done	5001	4692

prune612.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.3b	(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
70×	`add-cube-cbrt`
60×	`prod-diff`
44×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-r`
21×	`distribute-lft-neg-in`
17×	`add-exp-log`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube`
10×	`fma-neg`
8×	`pow1` `add-log-exp`
7×	`neg-mul-1` `associate-/r*`
4×	`expm1-log1p-u` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `diff-log` `1-exp` `cbrt-unprod` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 210

Calls

4 calls:

179.0ms	(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
53.0ms	(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
155.0ms	(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
102.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

222 → 222

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	270	6737
1	618	4822
2	1391	3992
3	4209	3430
done	5000	3427

prune589.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

localize34.0ms

Local error

Found 4 expressions with local error:

5.9b	(/ (/ (* c a) (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))) a)
10.3b	(/ (* c a) (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))))
18.7b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
90×	`add-cube-cbrt` `prod-diff`
82×	`times-frac`
74×	`log-prod` `exp-sum`
40×	`sqrt-prod`
37×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
21×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/l*`
14×	`distribute-lft-out--`
11×	`associate-/r*`
10×	`neg-mul-1` `fma-neg` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 251

Calls

4 calls:

101.0ms	(/ (/ (* c a) (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))) a)
77.0ms	(/ (* c a) (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))))
64.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (/ (* c a) (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))) a)
253.0ms	(/ (* c a) (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))))
136.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

263 → 263

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	393	11329
1	899	7086
2	2500	5689
done	5000	5560

prune894.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

regimes270.0ms

Accuracy

80.7% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 29.9b

bsearch192.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	5.713258900191085e+74
9	-7.826064039423189e-132	-1.1138670077130767e-140	-7.664666030704839e-132

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	32	38
done	32	38

end0.0ms

sample3.3s

Algorithm

intervals

Results

952.0ms	1026×	body	2560	valid
621.0ms	907×	body	1280	valid
598.0ms	5865×	body	80	valid
233.0ms	2910×	body	80	nan
163.0ms	439×	body	640	valid
85.0ms	245×	body	320	valid
58.0ms	127×	body	5120	valid
12.0ms	110×	body	160	valid