Details

sample99.0ms

Algorithm

intervals

Results

26.0ms	37×	body	2560	valid
20.0ms	186×	body	80	valid
15.0ms	28×	body	1280	valid
10.0ms	91×	body	80	nan
7.0ms	19×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify224.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`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`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
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` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
45.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
26.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
4.0ms	(sqrt (fma (* -4 a) c (* b b)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma (* -4 a) c (* b b))
118.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
107.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
119.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts

179 → 179

Iterations

Iter	Nodes
done	2000
3	2000
2	1190
1	497
0	222

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) a)
0.6b	(+ (* (* -4 a) c) (* b b))
1.1b	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
22.9b	(sqrt (+ (* (* -4 a) c) (* b b)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `diff-log` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 173

Calls

4 calls:

107.0ms	(/ (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) a)
30.0ms	(+ (* (* -4 a) c) (* b b))
50.0ms	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
27.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) a)
80.0ms	(+ (* (* -4 a) c) (* b b))
113.0ms	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
115.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

simplify1.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	2008
3	2008
2	1565
1	578
0	239

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) (/ 1 a))
0.6b	(+ (* (* -4 a) c) (* b b))
1.1b	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
22.9b	(sqrt (+ (* (* -4 a) c) (* b b)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
60×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
10×	`fma-neg` `add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `flip3-+` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `flip-+`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `sub-neg` `fma-def` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 171

Calls

4 calls:

167.0ms	(* (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) (/ 1 a))
16.0ms	(+ (* (* -4 a) c) (* b b))
58.0ms	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
33.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) (/ 1 a))
77.0ms	(+ (* (* -4 a) c) (* b b))
122.0ms	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
111.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

simplify1.3s

Counts

183 → 183

Iterations

Iter	Nodes
done	2003
3	2003
2	1732
1	641
0	258

prune2.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b) (sqrt (fma -4 (* c a) (* b b))))))
0.6b	(fma -4 (* c a) (* b b))
1.1b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
22.9b	(sqrt (fma -4 (* c a) (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
10×	`fma-neg`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `div-exp`
6×	`pow1`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `diff-log` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 253

Calls

4 calls:

16.0ms	(/ 1 (/ a (- (- b) (sqrt (fma -4 (* c a) (* b b))))))
0.0ms	(fma -4 (* c a) (* b b))
10.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1 (/ a (- (- b) (sqrt (fma -4 (* c a) (* b b))))))
69.0ms	(fma -4 (* c a) (* b b))
95.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
126.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.4s

Counts

265 → 265

Iterations

Iter	Nodes
done	2001
3	2001
2	1787
1	761
0	331

prune3.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

regimes371.0ms

Accuracy

79.6% (5.8b remaining)

Error of 11.3b against oracle of 5.5b and baseline of 33.7b

bsearch244.0ms

Steps

Iters	Range		Point
8	6.45623811977989e+97	1.5556153764929518e+101	1.786204067849289e+100
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.2890050783826923e-183

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	32

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	1101×	body	2560	valid
1.0s	5836×	body	80	valid
808.0ms	915×	body	1280	valid
679.0ms	500×	body	640	valid
394.0ms	2978×	body	80	nan
161.0ms	106×	body	5120	valid
77.0ms	194×	body	320	valid
34.0ms	117×	body	160	valid