Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	195×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	81×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify728.0ms

Counts

102 → 102

Iterations

Useful iterations: done (726.0ms)

Iter	Nodes	Cost
0	167	1697
1	436	1584
2	1482	1361
done	5000	1351

prune304.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

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:

26.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

164 → 164

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	261	4025
1	597	3484
2	1727	3082
done	5000	3056

prune303.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

56.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify845.0ms

Counts

112 → 112

Iterations

Useful iterations: done (840.0ms)

Iter	Nodes	Cost
0	194	2017
1	510	1794
2	1760	1516
done	5000	1515

prune305.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(/ (/ (+ (* b (- b b)) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0b	(/ (+ (* b (- b b)) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms	(/ (/ (+ (* b (- b b)) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
35.0ms	(/ (+ (* b (- b b)) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms	(/ (/ (+ (* b (- b b)) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
167.0ms	(/ (+ (* b (- b b)) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

244 → 244

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	340	10825
1	838	8207
2	2703	6699
done	5000	6697

prune557.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

regimes218.0ms

Accuracy

83.1% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch145.0ms

Steps

Iters	Range		Point
10	3.056596725548563e-78	7.076105677608322e-63	3.446447862996811e-75
10	-1.852183237050365e+100	-1.9127319211193897e+86	-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

246.0ms	1096×	body	2560	valid
232.0ms	5880×	body	80	valid
158.0ms	852×	body	1280	valid
105.0ms	2945×	body	80	nan
71.0ms	471×	body	640	valid
29.0ms	109×	body	5120	valid
22.0ms	211×	body	320	valid
8.0ms	107×	body	160	valid