Details

sample100.0ms

Algorithm

intervals

Results

19.0ms	31×	body	1280	valid
19.0ms	205×	body	80	valid
17.0ms	31×	body	2560	valid
8.0ms	89×	body	80	nan
5.0ms	12×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify154.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

22.0ms	(* 4.0 (* a c))
94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
42.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* a c))
120.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
119.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
104.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

173 → 173

Iterations

Iter	Nodes
done	5002
2	2609
1	639
0	253

prune916.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

97.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms	(* (* 4.0 a) c)
36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms	(* (* 4.0 a) c)
99.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

173 → 173

Iterations

Iter	Nodes
done	5002
2	3168
1	658
0	256

prune808.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ (/ 1 a) 2.0))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
83×	`add-cube-cbrt`
71×	`times-frac`
60×	`prod-diff`
46×	`associate-r`
35×	`sqrt-prod`
24×	`add-exp-log`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube`
12×	`pow1`
10×	`fma-neg`
8×	`associate-l` `prod-exp` `add-log-exp`
7×	`neg-mul-1`
6×	`div-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3--` `pow-prod-down` `log1p-expm1-u` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv`
2×	`frac-times` `sqrt-div` `diff-log` `associate-l/` `-commutative`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `associate-*r/`

Counts

4 → 205

Calls

4 calls:

150.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ (/ 1 a) 2.0))
17.0ms	(* (* 4.0 a) c)
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ (/ 1 a) 2.0))
37.0ms	(* (* 4.0 a) c)
125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify529.0ms

Counts

217 → 217

Iterations

Iter	Nodes
done	5001
1	993
0	367

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b) (sqrt (fma b b (* c (- (* 4.0 a)))))) (sqrt 2.0))
0.4b	(/ (/ (cbrt 1) a) (sqrt 2.0))
0.7b	(- (- b) (sqrt (fma b b (* c (- (* 4.0 a))))))
19.5b	(sqrt (fma b b (* c (- (* 4.0 a)))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
239×	`add-sqr-sqrt`
238×	`*-un-lft-identity`
206×	`add-cube-cbrt`
134×	`sqrt-prod`
63×	`cbrt-prod`
60×	`prod-diff`
29×	`distribute-rgt-neg-in` `associate-/l*`
21×	`distribute-lft-neg-in`
16×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
11×	`add-exp-log`
10×	`add-cbrt-cube` `fma-neg`
9×	`div-inv`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `diff-log` `flip--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log`

Counts

4 → 354

Calls

4 calls:

77.0ms	(/ (- (- b) (sqrt (fma b b (* c (- (* 4.0 a)))))) (sqrt 2.0))
28.0ms	(/ (/ (cbrt 1) a) (sqrt 2.0))
23.0ms	(- (- b) (sqrt (fma b b (* c (- (* 4.0 a))))))
1.0ms	(sqrt (fma b b (* c (- (* 4.0 a)))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (- (- b) (sqrt (fma b b (* c (- (* 4.0 a)))))) (sqrt 2.0))
71.0ms	(/ (/ (cbrt 1) a) (sqrt 2.0))
128.0ms	(- (- b) (sqrt (fma b b (* c (- (* 4.0 a))))))
103.0ms	(sqrt (fma b b (* c (- (* 4.0 a)))))

simplify1.7s

Counts

366 → 366

Iterations

Iter	Nodes
done	5002
2	3918
1	1119
0	477

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

regimes459.0ms

Accuracy

85.7% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 34.2b

bsearch156.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	3.087668654677018e+130
8	-8.904680992578465e-52	-2.849527055171251e-56	-4.356959927988237e-56

simplify4.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1025×	body	2560	valid
528.0ms	5841×	body	80	valid
438.0ms	921×	body	1280	valid
305.0ms	2877×	body	80	nan
175.0ms	457×	body	640	valid
128.0ms	245×	body	320	valid
69.0ms	122×	body	5120	valid
16.0ms	116×	body	160	valid