Details

sample138.0ms

Algorithm

intervals

Results

47.0ms	39×	body	2560	valid
26.0ms	188×	body	80	valid
21.0ms	31×	body	1280	valid
12.0ms	87×	body	80	nan
7.0ms	13×	body	640	valid
4.0ms	3×	body	5120	valid
3.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	115
5	115
4	107
3	85
2	47
1	25
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.4b	(- (* b b) (* (* 4 a) c))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite137.0ms

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:

66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
15.0ms	(- (* b b) (* (* 4 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
26.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
63.0ms	(- (* b b) (* (* 4 a) c))
131.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
118.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1513
1	437
0	166

prune663.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* a 2) (- (sqrt (fma b b (* a (* -4 c)))) b)))
0.4b	(- (sqrt (fma b b (* a (* -4 c)))) b)
0.5b	(fma b b (* a (* -4 c)))
23.1b	(sqrt (fma b b (* a (* -4 c))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

42.0ms	(/ 1 (/ (* a 2) (- (sqrt (fma b b (* a (* -4 c)))) b)))
9.0ms	(- (sqrt (fma b b (* a (* -4 c)))) b)
0.0ms	(fma b b (* a (* -4 c)))
1.0ms	(sqrt (fma b b (* a (* -4 c))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ 1 (/ (* a 2) (- (sqrt (fma b b (* a (* -4 c)))) b)))
133.0ms	(- (sqrt (fma b b (* a (* -4 c)))) b)
78.0ms	(fma b b (* a (* -4 c)))
128.0ms	(sqrt (fma b b (* a (* -4 c))))

simplify1.6s

Counts

160 → 160

Iterations

Iter	Nodes
done	5002
2	1821
1	579
0	242

prune705.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`distribute-lft-neg-in` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `sum-log` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `neg-log` `associate-+l-` `flip-+` `flip--`

Counts

4 → 92

Calls

4 calls:

33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
130.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
125.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	3347
2	774
1	236
0	88

prune710.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

regimes388.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.6b

bsearch203.0ms

Steps

Iters	Range		Point
8	1.287554927770862e-68	8.304725640954512e-66	4.5810084990875205e-68
8	-3.370135567630554e+133	-1.481129451033522e+129	-2.1144981103869975e+131

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end1.0ms

sample5.1s

Algorithm

intervals

Results

1.6s	1064×	body	2560	valid
889.0ms	5890×	body	80	valid
843.0ms	901×	body	1280	valid
705.0ms	447×	body	640	valid
403.0ms	2854×	body	80	nan
145.0ms	95×	body	5120	valid
121.0ms	207×	body	320	valid
39.0ms	133×	body	160	valid