Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	34×	body	2560	valid
6.0ms	41×	body	1280	valid
5.0ms	173×	body	80	valid
3.0ms	94×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	7×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	45	13
4	47	13
done	47	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

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:

44.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify764.0ms

Counts

183 → 183

Iterations

Useful iterations: done (758.0ms)

Iter	Nodes	Cost
0	242	5993
1	548	4363
2	1447	3549
done	5001	3540

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b_2 b_2 (- (* c a)))
2.5b	(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
9.3b	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
26.1b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1` `flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef`

Counts

4 → 186

Calls

4 calls:

0.0ms	(fma b_2 b_2 (- (* c a)))
28.0ms	(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
20.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
1.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma b_2 b_2 (- (* c a)))
104.0ms	(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
137.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
67.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.1s

Counts

198 → 198

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	294	6530
1	698	5551
2	2102	4861
done	5001	4859

prune566.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b_2 b_2 (- (* c a)))
2.6b	(* (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
9.3b	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
26.1b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
52×	`times-frac`
49×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/r*` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+` `fma-udef`

Counts

4 → 140

Calls

4 calls:

0.0ms	(fma b_2 b_2 (- (* c a)))
44.0ms	(* (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
20.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
1.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma b_2 b_2 (- (* c a)))
105.0ms	(* (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
151.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
68.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.4s

Counts

152 → 152

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	241	4012
1	669	3374
2	1925	2735
done	5000	2732

prune415.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0b	(fma b_2 b_2 (- (* c a)))
12.9b	(/ (fma c a 0) a)
26.1b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

6.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
0.0ms	(fma b_2 b_2 (- (* c a)))
2.0ms	(/ (fma c a 0) a)
1.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
41.0ms	(fma b_2 b_2 (- (* c a)))
26.0ms	(/ (fma c a 0) a)
68.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.5s

Counts

107 → 107

Iterations

Useful iterations: 3 (560.0ms)

Iter	Nodes	Cost
0	155	1640
1	295	1386
2	682	1153
3	2339	1076
done	5000	1076

prune250.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

regimes196.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 28.8b

bsearch135.0ms

Steps

Iters	Range		Point
9	2.944023772201993e+37	9.447687191993962e+42	9.347996314154137e+42
9	1.8023897654493317e-219	3.228939373144292e-214	1.8748711030469548e-219
8	-6.10058349091927e+155	-9.408528429616011e+151	-1.0245899460467552e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	54
1	43	54
2	45	54
done	45	54

end0.0ms

sample994.0ms

Algorithm

intervals

Results

207.0ms	1077×	body	2560	valid
193.0ms	5775×	body	80	valid
157.0ms	972×	body	1280	valid
85.0ms	2867×	body	80	nan
55.0ms	456×	body	640	valid
25.0ms	109×	body	5120	valid
21.0ms	234×	body	320	valid
7.0ms	111×	body	160	valid