Details

sample96.0ms

Algorithm

intervals

Results

20.0ms	34×	body	1280	valid
18.0ms	195×	body	80	valid
10.0ms	18×	body	2560	valid
10.0ms	107×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify186.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	103
7	103
6	102
5	100
4	92
3	77
2	43
1	25
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) (* 2.0 a))
0.8b	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
1.0b	(- (* b b) (* (* a 4.0) c))
21.8b	(sqrt (- (* b b) (* (* a 4.0) c)))

rewrite348.0ms

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:

193.0ms	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) (* 2.0 a))
106.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
18.0ms	(- (* b b) (* (* a 4.0) c))
24.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) (* 2.0 a))
146.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
75.0ms	(- (* b b) (* (* a 4.0) c))
142.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

simplify2.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
2	1590
1	519
0	195

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* 2.0 a))
0.8b	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
1.0b	(- (* b b) (* c (* a 4.0)))
21.8b	(sqrt (- (* b b) (* c (* a 4.0))))

rewrite333.0ms

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:

161.0ms	(/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* 2.0 a))
113.0ms	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
18.0ms	(- (* b b) (* c (* a 4.0)))
34.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* 2.0 a))
152.0ms	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
95.0ms	(- (* b b) (* c (* a 4.0)))
143.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

simplify2.6s

Counts

118 → 118

Iterations

Iter	Nodes
done	5002
2	1667
1	524
0	195

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* 2.0 a))
0.8b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
1.0b	(- (* b b) (* c (* 4.0 a)))
21.8b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite340.0ms

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:

175.0ms	(/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* 2.0 a))
113.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
21.0ms	(- (* b b) (* c (* 4.0 a)))
24.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* 2.0 a))
136.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
100.0ms	(- (* b b) (* c (* 4.0 a)))
126.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify2.9s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1572
1	518
0	195

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
0.8b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
1.0b	(- (* b b) (* c (* 4.0 a)))
21.8b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite323.0ms

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:

111.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
104.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
74.0ms	(- (* b b) (* c (* 4.0 a)))
23.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
169.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
96.0ms	(- (* b b) (* c (* 4.0 a)))
148.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify3.5s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
2	2056
1	658
0	261

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

regimes695.0ms

Accuracy

82.2% (5.2b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 34.7b

bsearch271.0ms

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
6	-4.525167845450207e+100	-9.36795079059543e+99	-2.7668189408748547e+100

simplify12.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample4.2s

Algorithm

intervals

Results

922.0ms	1080×	body	2560	valid
816.0ms	483×	body	640	valid
697.0ms	922×	body	1280	valid
664.0ms	5755×	body	80	valid
401.0ms	2818×	body	80	nan
68.0ms	238×	body	320	valid
67.0ms	97×	body	5120	valid
22.0ms	117×	body	160	valid