Details

sample65.0ms

Algorithm

intervals

Results

12.0ms	196×	body	80	valid
12.0ms	34×	body	2560	valid
6.0ms	20×	body	1280	valid
4.0ms	78×	body	80	nan
3.0ms	15×	body	640	valid
3.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify176.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	121	17
4	153	17
5	160	17
6	164	17
done	164	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

97.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(- (* b b) (* 4.0 (* a c)))
59.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
71.0ms	(- (* b b) (* 4.0 (* a c)))
152.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
114.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

169 → 169

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	243	6690
1	616	4729
2	2482	3764
done	5002	3675

prune610.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 205

Calls

4 calls:

12.0ms	(- (* b b) (* 4.0 (* a c)))
91.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
40.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
32.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b b) (* 4.0 (* a c)))
177.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
110.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

217 → 217

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	311	8365
1	780	6147
2	3274	5140
done	5001	5052

prune547.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
119.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* 4.0 (* a c)))
146.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
101.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
104.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

177 → 177

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	269	6947
1	689	4918
2	3067	3859
done	5001	3766

prune488.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) 2.0) a)
0.3b	(fma b b (- (* (* a c) 4.0)))
0.3b	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
22.4b	(sqrt (fma b b (- (* (* a c) 4.0))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-/r*`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `flip--` `fma-udef` `associate-/l/`

Counts

4 → 236

Calls

4 calls:

51.0ms	(/ (/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) 2.0) a)
0.0ms	(fma b b (- (* (* a c) 4.0)))
43.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
2.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) 2.0) a)
99.0ms	(fma b b (- (* (* a c) 4.0)))
135.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
119.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))

simplify1.9s

Counts

248 → 248

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	348	9371
1	832	7347
2	3519	6408
done	5001	6319

prune776.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

regimes236.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 34.3b

bsearch164.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	2000198799923726.5
9	-1.946844531042053e-60	-2.7723426366012918e-67	-1.0759531795364344e-63

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	30	43
1	40	39
2	48	39
done	48	39

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	1057×	body	2560	valid
819.0ms	933×	body	1280	valid
708.0ms	5765×	body	80	valid
212.0ms	2861×	body	80	nan
140.0ms	446×	body	640	valid
89.0ms	115×	body	5120	valid
49.0ms	230×	body	320	valid
18.0ms	120×	body	160	valid