Details

sample55.0ms

Algorithm

intervals

Results

12.0ms	38×	body	2560	valid
10.0ms	178×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
63.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
115.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
68.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	195	2476
1	480	2169
2	1441	1861
done	5000	1789

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite210.0ms

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`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

99.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
71.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
107.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
52.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

164 → 164

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	261	4025
1	587	3484
2	1652	3082
done	5001	2938

prune532.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

122.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
66.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
116.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
68.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts

130 → 130

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	199	2768
1	466	2451
2	1257	2182
3	4617	2092
done	5000	2092

prune653.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 119

Calls

4 calls:

194.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
98.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
148.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

131 → 131

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	219	2739
1	519	2312
2	1478	1989
done	5001	1917

prune598.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.1b

regimes361.0ms

Accuracy

84.1% (4.6b remaining)

Error of 10.1b against oracle of 5.5b and baseline of 34.3b

bsearch175.0ms

Steps

Iters	Range		Point
8	4.924640387312937e-45	5.473977791176249e-42	5.2024432226242543e-45
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.2s

Algorithm

intervals

Results

631.0ms	5806×	body	80	valid
582.0ms	1087×	body	2560	valid
531.0ms	446×	body	640	valid
477.0ms	930×	body	1280	valid
237.0ms	2994×	body	80	nan
131.0ms	117×	body	5120	valid
46.0ms	210×	body	320	valid
15.0ms	116×	body	160	valid