Details

sample130.0ms

Algorithm

intervals

Results

30.0ms	90×	body	80	nan
19.0ms	184×	body	80	valid
18.0ms	31×	body	2560	valid
16.0ms	33×	body	1280	valid
5.0ms	12×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify166.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite225.0ms

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:

128.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms	(- (* b b) (* (* 4.0 a) c))
52.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
90.0ms	(- (* b b) (* (* 4.0 a) c))
142.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

102 → 102

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	167	1697
1	451	1588
2	2113	1361
done	5000	1352

prune874.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize50.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.5b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite403.0ms

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:

61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
170.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
126.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series886.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
268.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
342.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.0s

Counts

244 → 244

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	335	10067
1	848	7629
2	4744	6524
done	5000	6524

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.3b	(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

18.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
117.0ms	(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
35.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* b b) (* (* 4.0 a) c))
145.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
293.0ms	(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.5s

Counts

164 → 164

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	262	6878
1	691	4800
2	4730	3785
done	5000	3785

prune989.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite305.0ms

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:

206.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
17.0ms	(- (* b b) (* (* 4.0 a) c))
53.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
83.0ms	(- (* b b) (* (* 4.0 a) c))
144.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

112 → 112

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	194	2017
1	539	1844
2	2969	1522
done	5001	1513

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes553.0ms

Accuracy

83.2% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 32.7b

bsearch752.0ms

Steps

Iters	Range		Point
9	9.08791783933159e+82	1.9831525192132364e+90	1.155213356860159e+83
8	7.120367950694928e-51	1.9906506898914158e-47	1.1310446734884525e-47
6	4.02886392125618e-70	3.9850540170413814e-69	4.40565710546396e-70
8	7.520261887413394e-140	8.544177483477188e-136	2.4581158795060287e-136
10	-6.623625638726693e+82	-6.4709084601913214e+72	-1.6581383089037873e+81

simplify17.0ms

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	46	108
1	55	108
2	57	104
done	57	104

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	908×	body	1280	valid
828.0ms	1065×	body	2560	valid
808.0ms	5800×	body	80	valid
378.0ms	2982×	body	80	nan
224.0ms	452×	body	640	valid
85.0ms	122×	body	5120	valid
64.0ms	231×	body	320	valid
24.0ms	133×	body	160	valid