Details

sample333.0ms

Algorithm

intervals

Results

143.0ms	9×	body	320	valid
32.0ms	9×	body	640	valid
25.0ms	182×	body	80	valid
23.0ms	30×	body	2560	valid
20.0ms	32×	body	1280	valid
12.0ms	86×	body	80	nan
4.0ms	5×	body	5120	valid
2.0ms	7×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	34
5	34
4	32
3	30
2	23
1	15
0	10

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite261.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

132.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
99.0ms	(- (* b_2 b_2) (* a c))
159.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
193.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
3	3508
2	1174
1	464
0	199

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite163.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

88.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
11.0ms	(- (* b_2 b_2) (* a c))
46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
62.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
3	3508
2	1174
1	464
0	199

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `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 → 123

Calls

4 calls:

174.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
10.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
47.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

135 → 135

Iterations

Iter	Nodes
3	4132
2	1381
1	528
0	219

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

10.0ms

(* -1/2 (/ c b_2))

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(* -1/2 (/ c b_2))

simplify1.8s

Counts

38 → 38

Iterations

Iter	Nodes
4	3227
3	1059
2	435
1	168
0	71

prune298.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.9b

regimes433.0ms

Accuracy

82.6% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 33.1b

bsearch189.0ms

Steps

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

simplify8.0ms

Iterations

Iter	Nodes
2	26
1	26
0	23

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	5849×	body	80	valid
950.0ms	1109×	body	2560	valid
550.0ms	886×	body	1280	valid
365.0ms	2875×	body	80	nan
249.0ms	420×	body	640	valid
95.0ms	114×	body	5120	valid
75.0ms	228×	body	320	valid
29.0ms	128×	body	160	valid