Details

sample98.0ms

Algorithm

intervals

Results

10.0ms	188×	body	80	valid
10.0ms	36×	body	2560	valid
5.0ms	24×	body	1280	valid
4.0ms	108×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

110.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
11.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
56.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

130 → 130

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	195	2408
1	493	2127
2	2124	1877
done	5000	1818

prune498.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 196

Calls

4 calls:

87.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
73.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

208 → 208

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	299	4764
1	748	4088
2	3809	3797
done	5000	3791

prune519.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`prod-diff`
51×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `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 → 158

Calls

4 calls:

190.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
43.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

170 → 170

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	239	4053
1	675	3367
2	3661	2580
done	5000	2576

prune491.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

131.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
60.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

130 → 130

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	195	2408
1	493	2127
2	2124	1877
done	5000	1818

prune521.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.1b

regimes299.0ms

Accuracy

85.1% (4.2b remaining)

Error of 9.5b against oracle of 5.3b and baseline of 33.7b

bsearch176.0ms

Steps

Iters	Range		Point
9	4.939518845348872e-48	4.7173742985844417e-39	1.8571687910231489e-47
9	-9.502057580036763e+144	-6.537164733756459e+138	-4.7395197774900957e+139

simplify12.0ms

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	28	43
1	34	37
2	36	35
done	36	35

end0.0ms

sample3.2s

Algorithm

intervals

Results

948.0ms	899×	body	1280	valid
528.0ms	1080×	body	2560	valid
500.0ms	5858×	body	80	valid
242.0ms	2901×	body	80	nan
207.0ms	450×	body	640	valid
67.0ms	108×	body	160	valid
57.0ms	112×	body	5120	valid
44.0ms	227×	body	320	valid