Details

sample136.0ms

Algorithm

intervals

Results

15.0ms	32×	body	2560	valid
14.0ms	172×	body	80	valid
14.0ms	34×	body	1280	valid
8.0ms	105×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	9×	body	160	valid
1.0ms	5×	body	320	valid

simplify63.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
2.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite293.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

156.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
83.0ms	(- (* b_2 b_2) (* a c))
166.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
147.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	1492
1	569
0	242

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b	(- (* b_2 b_2) (* a c))
2.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite357.0ms

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×	`add-exp-log` `associate-r`
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` `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×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

231.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
20.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
76.0ms	(- (* b_2 b_2) (* a c))
158.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
148.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	1666
1	633
0	261

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize60.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
11.4b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
18.3b	(- (* b_2 b_2) (* b_2 b_2))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-/r` `sqrt-prod` `flip--` `associate-/l`
2×	`sub-neg` `fma-neg` `sqrt-div` `diff-log` `prod-diff` `associate-/l/`
1×	`cbrt-undiv` `associate-+l-` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
168.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
19.0ms	(- (* b_2 b_2) (* b_2 b_2))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* b_2 b_2) (* a c))
36.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
2.0ms	(- (* b_2 b_2) (* b_2 b_2))
177.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	2469
2	831
1	337
0	147

prune944.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite194.0ms

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-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 99

Calls

4 calls:

88.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
49.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series802.0ms

Counts

4 → 12

Calls

4 calls:

444.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
142.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
84.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5004
3	3427
2	1101
1	368
0	154

prune946.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

regimes639.0ms

Accuracy

89.8% (3.2b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 37.2b

bsearch399.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	5.748502676649783e+143
10	-7.365577167502996e-116	-4.228998172927506e-127	-4.296272708131499e-127
9	-4.447404991929899e+78	-8.380652639018829e+71	-5.999462245480892e+73

simplify14.0ms

Iterations

Iter	Nodes
done	37
1	37
0	31

end0.0ms

sample4.1s

Algorithm

intervals

Results

773.0ms	1055×	body	2560	valid
723.0ms	5836×	body	80	valid
717.0ms	227×	body	320	valid
457.0ms	909×	body	1280	valid
390.0ms	2820×	body	80	nan
215.0ms	452×	body	640	valid
130.0ms	105×	body	5120	valid
112.0ms	126×	body	160	valid