Details

sample93.0ms

Algorithm

intervals

Results

16.0ms	43×	body	2560	valid
11.0ms	176×	body	80	valid
10.0ms	31×	body	1280	valid
6.0ms	106×	body	80	nan
5.0ms	18×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify99.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite287.0ms

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:

154.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
93.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
94.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
133.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	193	2476
1	481	2169
2	1419	1861
done	5000	1789

prune470.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune36.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(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:

83.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
71.0ms	(- (* b b) (* 4.0 (* a c)))
125.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
110.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

164 → 164

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	259	4025
1	588	3484
2	1633	3082
done	5000	2938

prune523.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (/ c b) (/ b a))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
202×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
190×	`add-cube-cbrt`
169×	`prod-diff`
27×	`div-inv`
13×	`fma-neg`
4×	`difference-of-squares`
3×	`add-log-exp`
2×	`distribute-lft-out--`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 203

Calls

1 calls:

49.0ms

(- (/ c b) (/ b a))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(- (/ c b) (/ b a))

simplify4.2s

Counts

206 → 206

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	310	7860
1	681	6866
2	1473	4941
3	4664	3536
done	5000	3536

prune216.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.2b

regimes347.0ms

Accuracy

82.2% (6.0b remaining)

Error of 11.9b against oracle of 5.9b and baseline of 39.8b

bsearch102.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
7	-1.8340745317516165e+50	-1.0728429653156412e+49	-1.5476666036365373e+50

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.3s

Algorithm

intervals

Results

926.0ms	1074×	body	2560	valid
738.0ms	5876×	body	80	valid
379.0ms	3010×	body	80	nan
360.0ms	885×	body	1280	valid
172.0ms	492×	body	640	valid
59.0ms	107×	body	5120	valid
46.0ms	218×	body	320	valid
15.0ms	92×	body	160	valid