Details

sample324.0ms

Algorithm

intervals

Results

18.0ms	31×	body	2560	valid
18.0ms	198×	body	80	valid
14.0ms	28×	body	1280	valid
10.0ms	87×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

504.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
52.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5005
3	3743
2	1046
1	388
0	162

prune480.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.1b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

42.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
64.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
246.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
269.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2110
1	614
0	241

prune713.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.7b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.1b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

38.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
38.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
315.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
240.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1675
1	537
0	207

prune676.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize36.0ms

Local error

Found 4 expressions with local error:

1.7b	(* a (/ c (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
4.1b	(/ (* a (/ c (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
4.1b	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
33×	`associate-r`
32×	`times-frac`
26×	`add-cube-cbrt`
25×	`log-prod` `exp-sum`
18×	`add-cbrt-cube`
16×	`add-exp-log`
8×	`pow1` `difference-of-squares`
7×	`sqrt-prod`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `exp-prod` `exp-diff` `prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `add-log-exp`
3×	`associate-/r` `flip3--` `associate-l*` `flip--` `unswap-sqr`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `log-pow` `-commutative` `associate-/l` `rem-exp-log` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

142.0ms	(* a (/ c (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
55.0ms	(/ (* a (/ c (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
25.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(* a (/ c (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
219.0ms	(/ (* a (/ c (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
113.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
done	5004
2	1969
1	639
0	254

prune624.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

regimes545.0ms

Accuracy

88.3% (3.0b remaining)

Error of 8.7b against oracle of 5.7b and baseline of 31.7b

bsearch446.0ms

Steps

Iters	Range		Point
9	6.2301214455520334e+75	1.9082112581546424e+85	4.428811787936615e+82
9	-7.352001906045209e-176	-4.997881658352918e-184	-6.721230302992335e-178
8	-1.4293623029319875e-05	-2.882721318515647e-09	-1.2640598463005194e-05
10	-3.1098446226995644e+21	-2892672522.251662	-269812493880.8871
2	-1.7519468684694774e+129	-1.481129451033522e+129	-1.5149816282130165e+129

simplify33.0ms

Iterations

Iter	Nodes
done	64
1	64
0	55

end0.0ms

sample2.9s

Algorithm

intervals

Results

664.0ms	1060×	body	2560	valid
535.0ms	5839×	body	80	valid
477.0ms	121×	body	160	valid
359.0ms	889×	body	1280	valid
262.0ms	2843×	body	80	nan
151.0ms	456×	body	640	valid
62.0ms	114×	body	5120	valid
45.0ms	228×	body	320	valid