Details

sample334.0ms

Algorithm

intervals

Results

7.0ms	184×	body	80	valid
6.0ms	35×	body	2560	valid
5.0ms	30×	body	1280	valid
3.0ms	91×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7
done	49	7

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

73.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063
done	5002	2063

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

88.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
35.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5002	1940
done	5002	1940

prune295.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune9.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 2 (/ b_2 a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

14.0ms

(* 2 (/ b_2 a))

series19.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 2 (/ b_2 a))

simplify64.0ms

Counts

37 → 37

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	166	134
1	730	124
2	2975	124
3	5002	124
done	5002	124

prune66.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.9b

regimes174.0ms

Accuracy

84.6% (4.3b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 34.3b

bsearch92.0ms

Steps

Iters	Range		Point
8	1.2146045965263502e+46	6.67231609761305e+48	6.568668442325333e+48
11	-4.915395666956115e-72	-4.878563939054666e-98	-2.763265898390889e-72

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15
done	34	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

197.0ms	1077×	body	2560	valid
182.0ms	5840×	body	80	valid
135.0ms	902×	body	1280	valid
81.0ms	2840×	body	80	nan
53.0ms	420×	body	640	valid
23.0ms	104×	body	5120	valid
21.0ms	246×	body	320	valid
5.0ms	92×	body	160	valid