Details

sample105.0ms

Algorithm

intervals

Results

28.0ms	210×	body	80	valid
19.0ms	23×	body	2560	valid
15.0ms	25×	body	1280	valid
15.0ms	84×	body	80	nan
3.0ms	8×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.0b	(fma b b (* (* a -4) c))
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
20.8b	(sqrt (fma b b (* (* a -4) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

32.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms	(fma b b (* (* a -4) c))
11.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
90.0ms	(fma b b (* (* a -4) c))
133.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
103.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	3845
2	1007
1	423
0	180

prune627.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (fma b b (* (* a -4) c))) b))
1.0b	(fma b b (* (* a -4) c))
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
20.8b	(sqrt (fma b b (* (* a -4) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

15.0ms	(/ a (- (sqrt (fma b b (* (* a -4) c))) b))
0.0ms	(fma b b (* (* a -4) c))
15.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(/ a (- (sqrt (fma b b (* (* a -4) c))) b))
61.0ms	(fma b b (* (* a -4) c))
137.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
88.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5003
3	3114
2	942
1	371
0	175

prune658.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
1.0b	(fma b b (* (* a -4) c))
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
20.8b	(sqrt (fma b b (* (* a -4) c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`add-cube-cbrt`
18×	`frac-times` `prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `flip3--` `flip--`
10×	`associate-/l*`
9×	`associate-/r` `add-cbrt-cube` `associate-r/`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `clear-num` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`frac-2neg` `un-div-inv` `unswap-sqr`
2×	`div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 141

Calls

4 calls:

69.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
0.0ms	(fma b b (* (* a -4) c))
12.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
68.0ms	(fma b b (* (* a -4) c))
132.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
114.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.7s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
2	1582
1	581
0	232

prune775.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (sqrt (fma b b (* (* a -4) c))) b))
1.0b	(fma b b (* (* a -4) c))
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
20.8b	(sqrt (fma b b (* (* a -4) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

17.0ms	(/ 1 (- (sqrt (fma b b (* (* a -4) c))) b))
1.0ms	(fma b b (* (* a -4) c))
29.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
4.0ms	(sqrt (fma b b (* (* a -4) c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ 1 (- (sqrt (fma b b (* (* a -4) c))) b))
65.0ms	(fma b b (* (* a -4) c))
129.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
138.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.4s

Counts

129 → 129

Iterations

Iter	Nodes
done	5013
3	3172
2	979
1	384
0	177

prune498.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.5b

regimes486.0ms

Accuracy

80.9% (5.2b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.1b

bsearch482.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.546013236023957e-67
7	6.366271362828677e-80	2.0474353944207673e-78	1.6168702840263923e-79
8	1.9015403840268286e-125	4.787339246176752e-121	1.3353078790738604e-121
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify18.0ms

Iterations

Iter	Nodes
done	47
1	47
0	37

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.3s	5870×	body	80	valid
1.1s	1084×	body	2560	valid
941.0ms	3007×	body	80	nan
707.0ms	907×	body	1280	valid
256.0ms	447×	body	640	valid
114.0ms	101×	body	5120	valid
88.0ms	232×	body	320	valid
53.0ms	109×	body	160	valid