Details

sample95.0ms

Algorithm

intervals

Results

23.0ms	173×	body	80	valid
22.0ms	39×	body	2560	valid
12.0ms	30×	body	1280	valid
8.0ms	89×	body	80	nan
6.0ms	16×	body	640	valid
4.0ms	5×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify499.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.0b

localize45.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.4b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
26.8b	(sqrt (fma (* -4 a) c (* b b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
60×	`prod-diff`
57×	`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`
7×	`neg-mul-1` `associate-/l*` `add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
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` `div-inv`

Counts

3 → 156

Calls

3 calls:

27.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
17.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
84.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
120.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts

165 → 165

Iterations

Iter	Nodes
3	2842
2	1111
1	477
0	211

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize18.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune50.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

localize43.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
1.4b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
26.8b	(sqrt (fma (* -4 a) c (* b b)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`prod-diff`
53×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
12×	`add-exp-log`
11×	`times-frac`
10×	`fma-neg`
8×	`add-cbrt-cube`
7×	`neg-mul-1` `associate-l` `add-log-exp`
6×	`pow1`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `unswap-sqr`
2×	`frac-times` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

3 → 154

Calls

3 calls:

38.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series296.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
97.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
86.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.2s

Counts

163 → 163

Iterations

Iter	Nodes
3	3112
2	1319
1	538
0	230

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.6b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) a)
1.4b	(+ (sqrt (fma c (* -4 a) (* b b))) b)
26.8b	(sqrt (fma c (* -4 a) (* b b)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
6×	`fma-def` `sqrt-prod`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `neg-mul-1`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `flip-+` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

3 → 107

Calls

3 calls:

22.0ms	(/ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) a)
6.0ms	(+ (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series367.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(/ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) a)
126.0ms	(+ (sqrt (fma c (* -4 a) (* b b))) b)
121.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify932.0ms

Counts

116 → 116

Iterations

Iter	Nodes
3	2019
2	788
1	325
0	155

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.6b

regimes389.0ms

Accuracy

86.7% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 39.3b

bsearch294.0ms

Steps

Iters	Range		Point
9	2.662790715355376e+61	3.00977400694497e+66	2.9822108876570007e+66
9	-6.352668374011919e-47	-5.750941040768736e-55	-7.406397712303184e-53

simplify13.0ms

Iterations

Iter	Nodes
3	38
2	38
1	35
0	26

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.1s	916×	body	1280	valid
1.1s	1064×	body	2560	valid
957.0ms	5799×	body	80	valid
412.0ms	2970×	body	80	nan
221.0ms	444×	body	640	valid
132.0ms	120×	body	5120	valid
99.0ms	243×	body	320	valid
62.0ms	125×	body	160	valid