Details

sample78.0ms

Algorithm

intervals

Results

20.0ms	39×	body	2560	valid
15.0ms	180×	body	80	valid
12.0ms	29×	body	1280	valid
6.0ms	21×	body	640	valid
6.0ms	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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.3b

localize50.0ms

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)))

rewrite100.0ms

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:

57.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(- (* b b) (* (* 3 a) c))
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
110.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
58.0ms	(- (* b b) (* (* 3 a) c))
124.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5003
2	1423
1	442
0	170

prune581.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize42.0ms

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)))

rewrite32.0ms

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))
16.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
10.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -3 a) c (* b b)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma (* -3 a) c (* b b))
166.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
146.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
102.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.7s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	1608
1	620
0	278

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize28.0ms

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)))

rewrite45.0ms

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))
35.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
7.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
1.0ms	(sqrt (fma (* -3 a) c (* b b)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma (* -3 a) c (* b b))
170.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
138.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
137.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify3.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	4513
2	987
1	348
0	152

prune561.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3))
0.2b	(/ 1 (/ a (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)))
1.0b	(- (sqrt (fma (* -3 a) c (* b b))) b)
19.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
563×	`add-sqr-sqrt`
464×	`*-un-lft-identity`
366×	`add-cube-cbrt`
98×	`difference-of-squares`
93×	`associate-/r*`
64×	`sqrt-prod`
49×	`distribute-lft-out--`
30×	`add-exp-log`
22×	`div-inv`
18×	`add-cbrt-cube` `div-exp` `prod-diff`
9×	`cbrt-undiv`
6×	`pow1` `fma-neg` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-flip` `flip--` `inv-pow`

Counts

4 → 482

Calls

4 calls:

11.0ms	(/ a (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3))
26.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)))
15.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -3 a) c (* b b)))

series739.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(/ a (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3))
178.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)))
122.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
111.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify3.1s

Counts

494 → 494

Iterations

Iter	Nodes
done	5000
2	4915
1	1611
0	604

prune2.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.2b

regimes414.0ms

Accuracy

84.4% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 33.3b

bsearch171.0ms

Steps

Iters	Range		Point
9	1.542649851819534e-86	4.188981380654902e-77	1.2158870426682226e-82
6	-1.2115114540629089e+151	-9.504756559616229e+149	-7.397994825724217e+150

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	5901×	body	80	valid
539.0ms	1057×	body	2560	valid
449.0ms	895×	body	1280	valid
287.0ms	456×	body	640	valid
251.0ms	2938×	body	80	nan
107.0ms	106×	body	5120	valid
45.0ms	211×	body	320	valid
13.0ms	94×	body	160	valid