Details

sample138.0ms

Algorithm

intervals

Results

35.0ms	82×	body	80	nan
29.0ms	198×	body	80	valid
20.0ms	29×	body	1280	valid
13.0ms	17×	body	2560	valid
8.0ms	13×	body	640	valid
7.0ms	10×	body	320	valid
4.0ms	4×	body	5120	valid
3.0ms	10×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.2b	(- (* b b) (* (* c a) 4))
2.7b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
22.2b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite217.0ms

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)
16.0ms	(- (* b b) (* (* c a) 4))
66.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
49.0ms	(- (* b b) (* (* c a) 4))
118.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
118.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
3	3521
2	1091
1	400
0	161

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
1.2b	(- (* b b) (* (* c a) 4))
2.7b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
22.2b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 166

Calls

4 calls:

43.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
7.0ms	(- (* b b) (* (* c a) 4))
36.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
76.0ms	(- (* b b) (* (* c a) 4))
117.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
75.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.5s

Counts

178 → 178

Iterations

Iter	Nodes
3	6102
2	1878
1	647
0	265

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
1.2b	(- (* b b) (* (* c a) 4))
2.7b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
22.2b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

133.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
13.0ms	(- (* b b) (* (* c a) 4))
60.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
79.0ms	(- (* b b) (* (* c a) 4))
93.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
101.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.1s

Counts

104 → 104

Iterations

Iter	Nodes
3	4499
2	1452
1	444
0	169

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b b) (* (* c a) 4))) b)))
1.2b	(- (* b b) (* (* c a) 4))
2.7b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
22.2b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
4×	`insert-posit16`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 427

Calls

4 calls:

50.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b b) (* (* c a) 4))) b)))
7.0ms	(- (* b b) (* (* c a) 4))
65.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b b) (* (* c a) 4))) b)))
70.0ms	(- (* b b) (* (* c a) 4))
121.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
109.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.7s

Counts

439 → 439

Iterations

Iter	Nodes
2	3605
1	1752
0	594

prune5.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

regimes371.0ms

Accuracy

78.1% (6.1b remaining)

Error of 11.9b against oracle of 5.8b and baseline of 33.5b

bsearch331.0ms

Steps

Iters	Range		Point
3	1.897422751335727e-16	2.3824489835354504e-16	1.922674299151799e-16
7	4.1266326978064226e-111	9.799836324706106e-110	4.664677641347216e-111
8	9.808312070140145e-191	3.260010576758525e-187	3.207624111695675e-187
10	-4.8388360275630777e+135	-9.113678877832951e+119	-1.3725796156555912e+127

simplify14.0ms

Iterations

Iter	Nodes
2	52
1	52
0	41

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.3s	5930×	body	80	valid
989.0ms	1043×	body	2560	valid
552.0ms	886×	body	1280	valid
530.0ms	121×	body	5120	valid
365.0ms	2880×	body	80	nan
258.0ms	495×	body	640	valid
101.0ms	202×	body	320	valid
54.0ms	116×	body	160	valid