Details

sample103.0ms

Algorithm

intervals

Results

64.0ms	273×	body	80	valid
13.0ms	82×	body	80	nan

simplify151.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	182
6	182
5	180
4	167
3	126
2	67
1	36
0	20

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize149.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma a (* -4 c) (* b b))) b)
1.0b	(- (- b) (sqrt (fma a (* -4 c) (* b b))))
22.2b	(sqrt (fma a (* -4 c) (* b b)))
22.2b	(sqrt (fma a (* -4 c) (* b b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

10.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
20.0ms	(- (- b) (sqrt (fma a (* -4 c) (* b b))))
2.0ms	(sqrt (fma a (* -4 c) (* b b)))
5.0ms	(sqrt (fma a (* -4 c) (* b b)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
109.0ms	(- (- b) (sqrt (fma a (* -4 c) (* b b))))
100.0ms	(sqrt (fma a (* -4 c) (* b b)))
143.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify2.8s

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
2	1842
1	434
0	195

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.2b

localize205.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma a (* -4 c) (* b b))) b)
4.4b	(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
6.0b	(/ a (/ b c))
22.2b	(sqrt (fma a (* -4 c) (* b b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
66×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff`
16×	`sqrt-prod`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*r/` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 157

Calls

4 calls:

14.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
35.0ms	(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
10.0ms	(/ a (/ b c))
2.0ms	(sqrt (fma a (* -4 c) (* b b)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
83.0ms	(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
36.0ms	(/ a (/ b c))
133.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify2.0s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	3594
1	726
0	284

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.2b

localize172.0ms

Local error

Found 4 expressions with local error:

10.0b	(- (- b) (* (sqrt (sqrt (fma a (* -4 c) (* b b)))) (sqrt (sqrt (fma a (* -4 c) (* b b))))))
22.2b	(sqrt (fma a (* -4 c) (* b b)))
22.2b	(sqrt (fma a (* -4 c) (* b b)))
22.2b	(sqrt (fma a (* -4 c) (* b b)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

12.0ms	(- (- b) (* (sqrt (sqrt (fma a (* -4 c) (* b b)))) (sqrt (sqrt (fma a (* -4 c) (* b b))))))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (* (sqrt (sqrt (fma a (* -4 c) (* b b)))) (sqrt (sqrt (fma a (* -4 c) (* b b))))))
124.0ms	(sqrt (fma a (* -4 c) (* b b)))
112.0ms	(sqrt (fma a (* -4 c) (* b b)))
110.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	3310
2	657
1	213
0	97

prune814.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.2b

localize171.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
0.9b	(- (sqrt (fma a (* -4 c) (* b b))) b)
22.2b	(sqrt (fma a (* -4 c) (* b b)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
134×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
81×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
8×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg`
5×	`div-inv` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `associate-/l/`

Counts

3 → 168

Calls

3 calls:

33.0ms	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
3.0ms	(sqrt (fma a (* -4 c) (* b b)))

series382.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
115.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
120.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify1.7s

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
2	2341
1	623
0	265

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.2b

regimes400.0ms

Accuracy

93.3% (0.5b remaining)

Error of 12.4b against oracle of 11.9b and baseline of 19.3b

bsearch168.0ms

Steps

Iters	Range		Point
10	3.302865865338161e+140	2.8302951796802603e+150	5.03307751825146e+142

simplify7.0ms

Iterations

Iter	Nodes
done	39
2	39
1	38
0	34

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.4s	8746×	body	80	valid
583.0ms	2913×	body	80	nan