Details

sample117.0ms

Algorithm

intervals

Results

35.0ms	34×	body	1280	valid
18.0ms	195×	body	80	valid
10.0ms	18×	body	2560	valid
9.0ms	107×	body	80	nan
5.0ms	13×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify230.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
7	104
6	103
5	101
4	93
3	78
2	43
1	25
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize97.0ms

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)))

rewrite375.0ms

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:

183.0ms	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) (* 2.0 a))
139.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
19.0ms	(- (* b b) (* (* a 4.0) c))
26.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) (* 2.0 a))
238.0ms	(- (sqrt (- (* b b) (* (* a 4.0) c))) b)
177.0ms	(- (* b b) (* (* a 4.0) c))
193.0ms	(sqrt (- (* b b) (* (* a 4.0) c)))

simplify2.9s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
2	1590
1	519
0	195

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize52.0ms

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))))

rewrite416.0ms

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:

202.0ms	(/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* 2.0 a))
136.0ms	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
28.0ms	(- (* b b) (* c (* a 4.0)))
43.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* 2.0 a))
212.0ms	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
170.0ms	(- (* b b) (* c (* a 4.0)))
169.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

simplify3.7s

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

localize45.0ms

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))))

rewrite461.0ms

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:

264.0ms	(/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* 2.0 a))
131.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
24.0ms	(- (* b b) (* c (* 4.0 a)))
28.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* 2.0 a))
191.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
107.0ms	(- (* b b) (* c (* 4.0 a)))
178.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify2.7s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1572
1	518
0	195

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize56.0ms

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))))

rewrite373.0ms

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:

166.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
149.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
20.0ms	(- (* b b) (* c (* 4.0 a)))
24.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series873.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)))
212.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
121.0ms	(- (* b b) (* c (* 4.0 a)))
194.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify3.6s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
2	2056
1	658
0	261

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

regimes698.0ms

Accuracy

82.2% (5.2b remaining)

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

bsearch309.0ms

Steps

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

simplify16.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.1s	1080×	body	2560	valid
952.0ms	483×	body	640	valid
765.0ms	5755×	body	80	valid
597.0ms	922×	body	1280	valid
364.0ms	2818×	body	80	nan
162.0ms	97×	body	5120	valid
147.0ms	238×	body	320	valid
93.0ms	117×	body	160	valid