Details

sample88.0ms

Algorithm

intervals

Results

19.0ms	36×	body	2560	valid
18.0ms	84×	body	80	nan
18.0ms	187×	body	80	valid
11.0ms	26×	body	1280	valid
4.0ms	12×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.0b	(- (* b b) (* (* 3 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

77.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
7.0ms	(- (* b b) (* (* 3 a) c))
38.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
51.0ms	(- (* b b) (* (* 3 a) c))
92.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
88.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify683.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
2	1265
1	396
0	157

prune420.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a c) 3)
1.0b	(- (* b b) (* (* a c) 3))
1.1b	(- (sqrt (- (* b b) (* (* a c) 3))) b)
23.7b	(sqrt (- (* b b) (* (* a c) 3)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

21.0ms	(* (* a c) 3)
7.0ms	(- (* b b) (* (* a c) 3))
44.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
11.0ms	(sqrt (- (* b b) (* (* a c) 3)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* a c) 3)
69.0ms	(- (* b b) (* (* a c) 3))
128.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
109.0ms	(sqrt (- (* b b) (* (* a c) 3)))

simplify672.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2000
2	883
1	298
0	123

prune352.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.0b	(- (* b b) (* (* 3 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

13.0ms	(* (* 3 a) c)
10.0ms	(- (* b b) (* (* 3 a) c))
30.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3 a) c)
60.0ms	(- (* b b) (* (* 3 a) c))
120.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
85.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify612.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2001
2	910
1	297
0	123

prune406.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
1.0b	(- (* b b) (* (* 3 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`associate-r`
19×	`times-frac`
16×	`add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`insert-posit16` `distribute-lft-out--`
3×	`flip3--` `associate-l` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

92.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
11.0ms	(- (* b b) (* (* 3 a) c))
43.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
65.0ms	(- (* b b) (* (* 3 a) c))
93.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
99.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify707.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	2001
2	1520
1	448
0	179

prune366.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes564.0ms

Accuracy

84.4% (4.5b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 33.9b

bsearch467.0ms

Steps

Iters	Range		Point
8	2.469533614662255e-16	6.384179586440732e-13	2.518503630513393e-16
9	2.201345904528094e-30	9.673336284784144e-25	3.3885604098642834e-26
10	5.0092461758030895e-88	5.0325836698121444e-76	5.850891614847679e-83
10	-2.64779304316231e+160	-6.749854855548698e+149	-7.028459812939689e+151

simplify10.0ms

Iterations

Iter	Nodes
done	54
1	54
0	42

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.0s	2979×	body	80	nan
841.0ms	1103×	body	2560	valid
807.0ms	5759×	body	80	valid
643.0ms	957×	body	1280	valid
302.0ms	482×	body	640	valid
166.0ms	115×	body	5120	valid
73.0ms	222×	body	320	valid
53.0ms	127×	body	160	valid