Details

sample114.0ms

Algorithm

intervals

Results

29.0ms	33×	body	1280	valid
23.0ms	182×	body	80	valid
20.0ms	25×	body	2560	valid
9.0ms	77×	body	80	nan
8.0ms	17×	body	640	valid
4.0ms	12×	body	320	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	160	valid

simplify168.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.6b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.6b	(sqrt (fma (* -4 a) c (* b b)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
33.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
20.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(fma (* -4 a) c (* b b))
133.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
92.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
89.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.9s

Counts

179 → 179

Iterations

Iter	Nodes
3	3048
2	1154
1	495
0	222

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c (* -4 a) (* b b))
0.1b	(/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) a)
1.6b	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
22.6b	(sqrt (fma c (* -4 a) (* b b)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
23.0ms	(/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) a)
23.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma c (* -4 a) (* b b))
148.0ms	(/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) a)
127.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
133.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.9s

Counts

179 → 179

Iterations

Iter	Nodes
3	3053
2	1153
1	497
0	223

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (- b) (sqrt (fma c (* -4 a) (* b b)))))
0.2b	(/ 1 (/ a (- (- b) (sqrt (fma c (* -4 a) (* b b))))))
1.6b	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
22.6b	(sqrt (fma c (* -4 a) (* b b)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
10×	`fma-neg`
8×	`div-exp` `add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `flip3--` `div-inv` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `diff-log` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 290

Calls

4 calls:

13.0ms	(/ a (- (- b) (sqrt (fma c (* -4 a) (* b b)))))
25.0ms	(/ 1 (/ a (- (- b) (sqrt (fma c (* -4 a) (* b b))))))
29.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ a (- (- b) (sqrt (fma c (* -4 a) (* b b)))))
153.0ms	(/ 1 (/ a (- (- b) (sqrt (fma c (* -4 a) (* b b))))))
98.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
107.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify10.1s

Counts

302 → 302

Iterations

Iter	Nodes
3	5098
2	1887
1	784
0	340

prune4.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
1.6b	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
22.6b	(sqrt (fma c (* -4 a) (* b b)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
16.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt a)
242.0ms	(cbrt a)
128.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
105.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify4.1s

Counts

147 → 147

Iterations

Iter	Nodes
4	5476
3	1827
2	735
1	355
0	170

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

regimes363.0ms

Accuracy

81.9% (5.1b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 33.9b

bsearch458.0ms

Steps

Iters	Range		Point
7	1.602087361235081e+82	9.448026055101687e+83	7.548494687587984e+83
8	-2.6682979144053964e-160	-2.716876171205868e-163	-2.1997396407715757e-160
9	-1.5961089098309294e-80	-4.1988061237604837e-88	-2.4426257271971575e-81
9	-1.0131296714337304e-54	-1.526718807569313e-59	-6.178777554815223e-59

simplify15.0ms

Iterations

Iter	Nodes
2	38
1	38
0	34

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.2s	1036×	body	2560	valid
1.2s	953×	body	1280	valid
904.0ms	5858×	body	80	valid
542.0ms	103×	body	5120	valid
417.0ms	2920×	body	80	nan
254.0ms	466×	body	640	valid
120.0ms	227×	body	320	valid
56.0ms	113×	body	160	valid