Details

sample73.0ms

Algorithm

intervals

Results

14.0ms	193×	body	80	valid
12.0ms	31×	body	2560	valid
7.0ms	97×	body	80	nan
6.0ms	18×	body	1280	valid
5.0ms	18×	body	640	valid
4.0ms	6×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify167.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	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: 31.6b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.6b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.1b	(sqrt (fma (* -4 a) c (* b b)))

rewrite92.0ms

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:

63.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
18.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
97.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
113.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.7s

Counts

165 → 165

Iterations

Iter	Nodes
done	5042
3	3375
2	1124
1	479
0	211

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (sqrt (fma -4 (* c a) (* b b))) b) (- a))
0.4b	(fma -4 (* c a) (* b b))
0.6b	(+ (sqrt (fma -4 (* c a) (* b b))) b)
23.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
40×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`distribute-lft-out`
10×	`associate-/r*`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
5×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `fma-udef` `div-inv`

Counts

4 → 119

Calls

4 calls:

39.0ms	(/ (+ (sqrt (fma -4 (* c a) (* b b))) b) (- a))
1.0ms	(fma -4 (* c a) (* b b))
19.0ms	(+ (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (sqrt (fma -4 (* c a) (* b b))) b) (- a))
57.0ms	(fma -4 (* c a) (* b b))
134.0ms	(+ (sqrt (fma -4 (* c a) (* b b))) b)
110.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	5007
3	2913
2	832
1	326
0	162

prune703.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (- a) (+ (sqrt (fma -4 (* c a) (* b b))) b)))
0.4b	(fma -4 (* c a) (* b b))
0.6b	(+ (sqrt (fma -4 (* c a) (* b b))) b)
23.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

298×	`times-frac`
228×	`*-un-lft-identity`
147×	`add-sqr-sqrt`
146×	`add-cube-cbrt`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
46×	`associate-/r*`
41×	`distribute-lft-out`
16×	`neg-mul-1`
15×	`add-exp-log`
9×	`add-cbrt-cube` `associate-/r/`
7×	`div-exp`
6×	`pow1` `fma-def` `sqrt-prod` `add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 259

Calls

4 calls:

31.0ms	(/ 1 (/ (- a) (+ (sqrt (fma -4 (* c a) (* b b))) b)))
1.0ms	(fma -4 (* c a) (* b b))
18.0ms	(+ (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ 1 (/ (- a) (+ (sqrt (fma -4 (* c a) (* b b))) b)))
99.0ms	(fma -4 (* c a) (* b b))
142.0ms	(+ (sqrt (fma -4 (* c a) (* b b))) b)
115.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.1s

Counts

271 → 271

Iterations

Iter	Nodes
done	5000
2	2202
1	898
0	351

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (sqrt (fma (* -4 c) a (* b b))) b))
1.6b	(- (sqrt (fma (* -4 c) a (* b b))) b)
14.8b	(/ (fma (* a c) -4 0) (- a))
23.1b	(sqrt (fma (* -4 c) a (* b b)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
53×	`add-cube-cbrt`
48×	`times-frac`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/r*`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`add-exp-log` `difference-of-squares`
8×	`add-cbrt-cube`
6×	`pow1` `fma-neg` `associate-/l*` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `neg-mul-1` `insert-posit16` `log1p-expm1-u`
3×	`div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `associate-/r/` `div-inv` `flip--`
1×	`rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-flip` `inv-pow`

Counts

4 → 164

Calls

4 calls:

31.0ms	(/ 1 (- (sqrt (fma (* -4 c) a (* b b))) b))
21.0ms	(- (sqrt (fma (* -4 c) a (* b b))) b)
10.0ms	(/ (fma (* a c) -4 0) (- a))
2.0ms	(sqrt (fma (* -4 c) a (* b b)))

series1.0s

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ 1 (- (sqrt (fma (* -4 c) a (* b b))) b))
119.0ms	(- (sqrt (fma (* -4 c) a (* b b))) b)
75.0ms	(/ (fma (* a c) -4 0) (- a))
547.0ms	(sqrt (fma (* -4 c) a (* b b)))

simplify2.3s

Counts

176 → 176

Iterations

Iter	Nodes
done	5007
3	3870
2	1101
1	470
0	243

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

regimes432.0ms

Accuracy

94% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 29.0b

bsearch260.0ms

Steps

Iters	Range		Point
8	2.5230591910300896e+45	6.095379443414697e+48	3.846543337744466e+48
7	1.4209077534274481e-263	1.24815836120412e-261	1.5207465453202035e-263
7	-1.7986711450963914e+79	-4.346986454969115e+77	-1.6441900461248674e+79

simplify15.0ms

Iterations

Iter	Nodes
done	49
1	49
0	40

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	5849×	body	80	valid
691.0ms	1066×	body	2560	valid
641.0ms	903×	body	1280	valid
333.0ms	3069×	body	80	nan
222.0ms	464×	body	640	valid
81.0ms	122×	body	5120	valid
58.0ms	218×	body	320	valid
20.0ms	114×	body	160	valid