Details

sample92.0ms

Algorithm

intervals

Results

19.0ms	182×	body	80	valid
19.0ms	32×	body	1280	valid
18.0ms	30×	body	2560	valid
9.0ms	86×	body	80	nan
4.0ms	5×	body	5120	valid
4.0ms	9×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	7×	body	160	valid

simplify122.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `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 → 88

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
9.0ms	(- (* b b) (* (* c a) 4))
43.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
60.0ms	(- (* b b) (* (* c a) 4))
127.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
96.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.3s

Counts

100 → 100

Iterations

Iter	Nodes
3	3521
2	1091
1	400
0	161

prune990.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

131.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
10.0ms	(- (* b b) (* (* c a) 4))
33.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
60.0ms	(- (* b b) (* (* c a) 4))
120.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
101.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
3	4877
2	1495
1	462
0	181

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `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 → 88

Calls

4 calls:

70.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
7.0ms	(- (* b b) (* (* c a) 4))
47.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
53.0ms	(- (* b b) (* (* c a) 4))
96.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
85.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
3	3521
2	1091
1	400
0	161

prune969.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

122.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
8.0ms	(- (* b b) (* (* c a) 4))
47.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
12.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
54.0ms	(- (* b b) (* (* c a) 4))
89.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
81.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.5s

Counts

101 → 101

Iterations

Iter	Nodes
3	4877
2	1495
1	462
0	181

prune995.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.0b

regimes230.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.1b

bsearch151.0ms

Steps

Iters	Range		Point
7	6.1141969789339016e-111	5.505912162480727e-109	9.831724396970673e-110
8	-1.7996802595953755e+64	-1.2634430355867738e+61	-1.7729369216517423e+64

simplify5.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample4.0s

Algorithm

intervals

Results

966.0ms	1109×	body	2560	valid
863.0ms	5850×	body	80	valid
806.0ms	2882×	body	80	nan
504.0ms	885×	body	1280	valid
306.0ms	419×	body	640	valid
106.0ms	229×	body	320	valid
95.0ms	114×	body	5120	valid
83.0ms	127×	body	160	valid