Details

sample138.0ms

Algorithm

intervals

Results

12.0ms	184×	body	80	valid
11.0ms	32×	body	2560	valid
9.0ms	32×	body	1280	valid
4.0ms	84×	body	80	nan
3.0ms	16×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify342.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 118

Calls

4 calls:

83.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
93.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
99.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
50.0ms	(- (* b_2 b_2) (* a c))
113.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1377
1	490
0	195

prune732.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize58.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	1495
2	455
1	161
0	67

prune654.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize55.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
21.8b	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 60

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
0.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b_2 b_2) (* a c))
158.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	1738
2	513
1	187
0	84

prune584.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)) a)
0.2b	(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

109.0ms	(/ (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)) a)
49.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
7.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)) a)
96.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
62.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4661
2	1173
1	402
0	164

prune603.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.7b

regimes328.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 34.4b

bsearch121.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	3.1423118580081215e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample2.9s

Algorithm

intervals

Results

919.0ms	1043×	body	2560	valid
457.0ms	5833×	body	80	valid
428.0ms	911×	body	1280	valid
375.0ms	2878×	body	80	nan
116.0ms	449×	body	640	valid
108.0ms	232×	body	320	valid
53.0ms	102×	body	5120	valid
15.0ms	119×	body	160	valid