Details

sample125.0ms

Algorithm

intervals

Results

43.0ms	187×	body	80	valid
26.0ms	36×	body	2560	valid
16.0ms	26×	body	1280	valid
10.0ms	84×	body	80	nan
5.0ms	12×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.3b	(fma b b (* (* a -4) c))
23.7b	(sqrt (fma b b (* (* a -4) c)))

rewrite58.0ms

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:

41.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
14.0ms	(- (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)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
96.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
77.0ms	(fma b b (* (* a -4) c))
115.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify822.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2005
2	1002
1	424
0	180

prune693.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.3b	(fma b b (* (* a -4) c))
23.7b	(sqrt (fma b b (* (* a -4) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

23.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
18.0ms	(- (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)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
108.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
58.0ms	(fma b b (* (* a -4) c))
102.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.0s

Counts

204 → 204

Iterations

Iter	Nodes
done	2000
2	1831
1	661
0	284

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (sqrt (fma c (* -4 a) (* b b))) b))
0.2b	(/ 1 (/ a (- (sqrt (fma c (* -4 a) (* b b))) b)))
1.0b	(- (sqrt (fma c (* -4 a) (* b b))) b)
23.7b	(sqrt (fma c (* -4 a) (* b b)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
30×	`associate-/r*`
18×	`prod-diff`
17×	`add-exp-log` `distribute-lft-out--`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp`
6×	`pow1` `flip3--` `fma-neg` `div-inv` `flip--` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 225

Calls

4 calls:

15.0ms	(/ a (- (sqrt (fma c (* -4 a) (* b b))) b))
24.0ms	(/ 1 (/ a (- (sqrt (fma c (* -4 a) (* b b))) b)))
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series644.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ a (- (sqrt (fma c (* -4 a) (* b b))) b))
143.0ms	(/ 1 (/ a (- (sqrt (fma c (* -4 a) (* b b))) b)))
111.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
91.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.0s

Counts

237 → 237

Iterations

Iter	Nodes
done	2001
2	1607
1	676
0	284

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* a (/ 1 (- (sqrt (fma c (* -4 a) (* b b))) b))))
0.2b	(* a (/ 1 (- (sqrt (fma c (* -4 a) (* b b))) b)))
1.0b	(- (sqrt (fma c (* -4 a) (* b b))) b)
23.7b	(sqrt (fma c (* -4 a) (* b b)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
48×	`add-exp-log`
41×	`*-un-lft-identity`
32×	`add-cube-cbrt`
24×	`associate-r`
23×	`times-frac`
19×	`sqrt-prod`
18×	`add-cbrt-cube` `div-exp` `prod-diff`
16×	`prod-exp`
10×	`pow1`
9×	`rec-exp` `1-exp`
8×	`difference-of-squares`
6×	`fma-neg` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`flip3--` `pow-prod-down` `associate-*r/` `un-div-inv` `div-inv` `pow-flip` `flip--`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `-commutative` `inv-pow`

Counts

4 → 151

Calls

4 calls:

29.0ms	(/ 1 (* a (/ 1 (- (sqrt (fma c (* -4 a) (* b b))) b))))
30.0ms	(* a (/ 1 (- (sqrt (fma c (* -4 a) (* b b))) b)))
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series645.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1 (* a (/ 1 (- (sqrt (fma c (* -4 a) (* b b))) b))))
295.0ms	(* a (/ 1 (- (sqrt (fma c (* -4 a) (* b b))) b)))
110.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
107.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify726.0ms

Counts

163 → 163

Iterations

Iter	Nodes
done	2018
2	1238
1	527
0	219

prune618.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

regimes407.0ms

Accuracy

84.8% (4.4b remaining)

Error of 9.6b against oracle of 5.2b and baseline of 33.9b

bsearch530.0ms

Steps

Iters	Range		Point
8	2.469533614662255e-16	6.384179586440732e-13	5.297236684235463e-16
9	2.201345904528094e-30	9.673336284784144e-25	1.8656332031849816e-25
10	5.0092461758030895e-88	5.0325836698121444e-76	1.739098950628615e-79
9	-7.806260788625035e+148	-1.2289413495061505e+143	-1.6844644503075447e+144

simplify91.0ms

Iterations

Iter	Nodes
done	45
3	45
2	42
1	39
0	32

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	5761×	body	80	valid
1.1s	1103×	body	2560	valid
871.0ms	957×	body	1280	valid
438.0ms	2981×	body	80	nan
300.0ms	480×	body	640	valid
143.0ms	115×	body	5120	valid
139.0ms	223×	body	320	valid
33.0ms	128×	body	160	valid