Details

sample86.0ms

Algorithm

intervals

Results

32.0ms	103×	body	80	nan
13.0ms	37×	body	2560	valid
11.0ms	191×	body	80	valid
9.0ms	30×	body	1280	valid
4.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify113.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.5b	(fma b b (* (* a -4) c))
1.6b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.3b	(sqrt (fma b b (* (* a -4) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

53.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms	(fma b b (* (* a -4) c))
17.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
80.0ms	(fma b b (* (* a -4) c))
133.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
124.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.5s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	3845
2	1007
1	423
0	180

prune571.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
0.5b	(fma b b (* (* a -4) c))
1.6b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.3b	(sqrt (fma b b (* (* a -4) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

45.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
1.0ms	(fma b b (* (* a -4) c))
22.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
63.0ms	(fma b b (* (* a -4) c))
100.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
111.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.6s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
2	1819
1	661
0	284

prune687.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (sqrt (fma (* c -4) a (* b b))) b) a)
1.6b	(- (sqrt (fma (* c -4) a (* b b))) b)
21.3b	(sqrt (fma (* c -4) a (* b b)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
29×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`fma-neg` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 103

Calls

3 calls:

28.0ms	(/ (- (sqrt (fma (* c -4) a (* b b))) b) a)
12.0ms	(- (sqrt (fma (* c -4) a (* b b))) b)
2.0ms	(sqrt (fma (* c -4) a (* b b)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- (sqrt (fma (* c -4) a (* b b))) b) a)
88.0ms	(- (sqrt (fma (* c -4) a (* b b))) b)
88.0ms	(sqrt (fma (* c -4) a (* b b)))

simplify1.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5004
3	2232
2	704
1	310
0	144

prune376.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (sqrt (fma (* c -4) a (* b b))) b)
4.1b	(/ (/ (* a (* c -4)) (+ (sqrt (fma (* c -4) a (* b b))) b)) a)
10.4b	(/ (* a (* c -4)) (+ (sqrt (fma (* c -4) a (* b b))) b))
21.3b	(sqrt (fma (* c -4) a (* b b)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
42×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `associate-/r/`
7×	`associate-/r*` `distribute-lft-out`
6×	`fma-def` `flip3-+` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

10.0ms	(+ (sqrt (fma (* c -4) a (* b b))) b)
39.0ms	(/ (/ (* a (* c -4)) (+ (sqrt (fma (* c -4) a (* b b))) b)) a)
39.0ms	(/ (* a (* c -4)) (+ (sqrt (fma (* c -4) a (* b b))) b))
2.0ms	(sqrt (fma (* c -4) a (* b b)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (sqrt (fma (* c -4) a (* b b))) b)
176.0ms	(/ (/ (* a (* c -4)) (+ (sqrt (fma (* c -4) a (* b b))) b)) a)
200.0ms	(/ (* a (* c -4)) (+ (sqrt (fma (* c -4) a (* b b))) b))
90.0ms	(sqrt (fma (* c -4) a (* b b)))

simplify1.4s

Counts

144 → 144

Iterations

Iter	Nodes
done	5002
2	2276
1	584
0	220

prune641.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

regimes236.0ms

Accuracy

87.9% (3.1b remaining)

Error of 8.7b against oracle of 5.6b and baseline of 31.1b

bsearch267.0ms

Steps

Iters	Range		Point
11	2.0729826645785407e+19	5.016256902410509e+38	6.555431533807236e+28
8	-6.368534611080111e-150	-1.347793028802048e-153	-1.3761661522305357e-153
6	-1.816545290760657e+37	-4.00557630224217e+36	-1.6519381339788066e+37

simplify9.0ms

Iterations

Iter	Nodes
done	48
1	48
0	39

end0.0ms

sample2.5s

Algorithm

intervals

Results

715.0ms	834×	body	1280	valid
514.0ms	5918×	body	80	valid
472.0ms	1071×	body	2560	valid
208.0ms	3077×	body	80	nan
149.0ms	463×	body	640	valid
75.0ms	123×	body	5120	valid
46.0ms	122×	body	160	valid
40.0ms	241×	body	320	valid