Details

sample127.0ms

Algorithm

intervals

Results

47.0ms	42×	body	2560	valid
20.0ms	176×	body	80	valid
15.0ms	23×	body	1280	valid
11.0ms	23×	body	640	valid
10.0ms	98×	body	80	nan
3.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify146.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.6b	(- (* b b) (* 4 (* a c)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

74.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
13.0ms	(- (* b b) (* 4 (* a c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
64.0ms	(- (* b b) (* 4 (* a c)))
104.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
92.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.1s

Counts

173 → 173

Iterations

Iter	Nodes
done	2005
3	2005
2	1867
1	599
0	239

prune966.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a)
0.7b	(- (- b) (sqrt (fma b b (* -4 (* a c)))))
0.8b	(fma b b (* -4 (* a c)))
21.9b	(sqrt (fma b b (* -4 (* a c))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
37×	`sqrt-prod`
27×	`associate-l`
25×	`distribute-rgt-neg-in`
22×	`times-frac`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r`
2×	`flip3--` `diff-log` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

40.0ms	(* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a)
20.0ms	(- (- b) (sqrt (fma b b (* -4 (* a c)))))
0.0ms	(fma b b (* -4 (* a c)))
2.0ms	(sqrt (fma b b (* -4 (* a c))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a)
111.0ms	(- (- b) (sqrt (fma b b (* -4 (* a c)))))
63.0ms	(fma b b (* -4 (* a c)))
93.0ms	(sqrt (fma b b (* -4 (* a c))))

simplify1.2s

Counts

179 → 179

Iterations

Iter	Nodes
done	2001
3	2001
2	1458
1	550
0	242

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.3b	(fma (* -4 a) c (* b b))
0.7b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
21.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite57.0ms

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:

40.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.0ms	(fma (* -4 a) c (* b b))
10.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
89.0ms	(fma (* -4 a) c (* b b))
113.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
94.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.4s

Counts

179 → 179

Iterations

Iter	Nodes
done	2005
3	2005
2	1187
1	497
0	222

prune907.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma -4 (* c a) (* b b)))) a)
0.6b	(fma -4 (* c a) (* b b))
0.7b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
21.9b	(sqrt (fma -4 (* c a) (* b b)))

rewrite62.0ms

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:

35.0ms	(/ (- (- b) (sqrt (fma -4 (* c a) (* b b)))) a)
0.0ms	(fma -4 (* c a) (* b b))
21.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (- b) (sqrt (fma -4 (* c a) (* b b)))) a)
88.0ms	(fma -4 (* c a) (* b b))
112.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
107.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.2s

Counts

179 → 179

Iterations

Iter	Nodes
done	2001
3	2001
2	1191
1	497
0	223

prune935.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.1b

regimes561.0ms

Accuracy

82.9% (4.7b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 33.3b

bsearch257.0ms

Steps

Iters	Range		Point
7	6.52945691119865e+99	1.3360629297740576e+102	6.384705165981893e+101
9	-3.929467862544791e-84	-4.77908653107304e-89	-5.961198324014865e-88

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.4s	5862×	body	80	valid
1.2s	903×	body	1280	valid
1.2s	1077×	body	2560	valid
436.0ms	2940×	body	80	nan
299.0ms	471×	body	640	valid
176.0ms	109×	body	5120	valid
93.0ms	219×	body	320	valid
32.0ms	117×	body	160	valid