Details

sample94.0ms

Algorithm

intervals

Results

24.0ms	39×	body	2560	valid
20.0ms	180×	body	80	valid
15.0ms	29×	body	1280	valid
9.0ms	21×	body	640	valid
7.0ms	70×	body	80	nan
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.0b	(- (* b b) (* (* 3 a) c))
19.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

52.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
12.0ms	(- (* b b) (* (* 3 a) c))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
113.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
64.0ms	(- (* b b) (* (* 3 a) c))
79.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5003
2	1423
1	442
0	170

prune608.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* -3 a) c (* b b))
0.2b	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
1.0b	(- (sqrt (fma (* -3 a) c (* b b))) b)
19.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

0.0ms	(fma (* -3 a) c (* b b))
33.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
23.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
3.0ms	(sqrt (fma (* -3 a) c (* b b)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma (* -3 a) c (* b b))
212.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
102.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
117.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.6s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	1608
1	620
0	278

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* -3 a) c (* b b))
0.2b	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* a 3))
1.0b	(- (sqrt (fma (* -3 a) c (* b b))) b)
19.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (* -3 a) c (* b b))
26.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* a 3))
8.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
1.0ms	(sqrt (fma (* -3 a) c (* b b)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (* -3 a) c (* b b))
163.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* a 3))
133.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
136.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify3.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	4581
2	984
1	348
0	152

prune590.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (sqrt (fma (* -3 a) c (* b b))) b)
5.6b	(/ (/ (fma (* -3 a) c 0) (+ (sqrt (fma (* -3 a) c (* b b))) b)) (* a 3))
8.6b	(/ (fma (* -3 a) c 0) (+ (sqrt (fma (* -3 a) c (* b b))) b))
19.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

11.0ms	(+ (sqrt (fma (* -3 a) c (* b b))) b)
37.0ms	(/ (/ (fma (* -3 a) c 0) (+ (sqrt (fma (* -3 a) c (* b b))) b)) (* a 3))
10.0ms	(/ (fma (* -3 a) c 0) (+ (sqrt (fma (* -3 a) c (* b b))) b))
1.0ms	(sqrt (fma (* -3 a) c (* b b)))

series829.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (sqrt (fma (* -3 a) c (* b b))) b)
279.0ms	(/ (/ (fma (* -3 a) c 0) (+ (sqrt (fma (* -3 a) c (* b b))) b)) (* a 3))
298.0ms	(/ (fma (* -3 a) c 0) (+ (sqrt (fma (* -3 a) c (* b b))) b))
123.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.8s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1427
1	480
0	202

prune801.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

regimes433.0ms

Accuracy

87.7% (3.4b remaining)

Error of 9.0b against oracle of 5.6b and baseline of 32.8b

bsearch199.0ms

Steps

Iters	Range		Point
6	1.738775184262485e-37	7.890820011983143e-37	3.633198732680569e-37
6	3.741113117015344e-128	4.125244515964402e-127	3.80416111172822e-128
6	-1.2115114540629089e+151	-9.504756559616229e+149	-7.397994825724217e+150

simplify8.0ms

Iterations

Iter	Nodes
done	45
1	45
0	40

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	1057×	body	2560	valid
904.0ms	5901×	body	80	valid
841.0ms	895×	body	1280	valid
575.0ms	106×	body	5120	valid
438.0ms	2938×	body	80	nan
245.0ms	456×	body	640	valid
88.0ms	211×	body	320	valid
24.0ms	94×	body	160	valid