Details

sample116.0ms

Algorithm

intervals

Results

24.0ms	43×	body	2560	valid
17.0ms	175×	body	80	valid
16.0ms	106×	body	80	nan
13.0ms	31×	body	1280	valid
6.0ms	18×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify175.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

27.0ms	(* (* 3.0 a) c)
9.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
27.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 3.0 a) c)
67.0ms	(- (* b b) (* (* 3.0 a) c))
130.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.4s

Counts

92 → 92

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	135	1109
1	332	1006
2	1196	900
3	4683	889
done	5000	889

prune382.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize34.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.2b	(/ (/ (+ (* c (* 3.0 a)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b	(/ (+ (* c (* 3.0 a)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
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` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

41.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
135.0ms	(/ (/ (+ (* c (* 3.0 a)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
123.0ms	(/ (+ (* c (* 3.0 a)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
248.0ms	(/ (/ (+ (* c (* 3.0 a)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
291.0ms	(/ (+ (* c (* 3.0 a)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
133.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts

244 → 244

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	336	10067
1	810	7603
2	3002	6507
done	5001	6421

prune727.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.1b

localize39.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (* 3.0 a) (/ (* c (* 3.0 a)) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

95.0ms	(/ (* 3.0 a) (/ (* c (* 3.0 a)) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
19.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
28.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (* 3.0 a) (/ (* c (* 3.0 a)) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
110.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
89.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts

125 → 125

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	241	3025
1	611	2777
2	2420	2518
done	5000	2513

prune765.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.7b

localize100.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

22.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
21.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
126.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
100.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
112.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.1s

Counts

80 → 80

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	54	1228
1	139	1080
2	447	1004
3	1710	1004
done	5001	1000

prune637.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.7b

regimes937.0ms

Accuracy

92.1% (1.6b remaining)

Error of 11.0b against oracle of 9.4b and baseline of 29.7b

bsearch284.0ms

Steps

Iters	Range	Point
3	5.973091654032696e+157	8.116126331786576e+157	6.107031321392313e+157
9	6.972002709789466e-247	2.3285930425888842e-240	3.612467054529498e-241
7	-1.8340745317516165e+50	-1.0728429653156412e+49	-1.7888522273123936e+50

Iters

Range

Point

5.973091654032696e+157

8.116126331786576e+157

6.107031321392313e+157

6.972002709789466e-247

2.3285930425888842e-240

3.612467054529498e-241

-1.8340745317516165e+50

-1.0728429653156412e+49

-1.7888522273123936e+50

simplify15.0ms

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	59	174
1	71	172
done	71	172

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	5872×	body	80	valid
435.0ms	1076×	body	2560	valid
417.0ms	885×	body	1280	valid
264.0ms	3010×	body	80	nan
171.0ms	491×	body	640	valid
54.0ms	105×	body	5120	valid
42.0ms	218×	body	320	valid
13.0ms	95×	body	160	valid