Details

sample111.0ms

Algorithm

intervals

Results

38.0ms	205×	body	80	valid
16.0ms	31×	body	2560	valid
13.0ms	31×	body	1280	valid
7.0ms	89×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify182.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	365
1	29	365
2	64	365
3	121	365
4	153	365
5	160	365
6	164	365
done	164	365

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

12.0ms	(* 4.0 (* a c))
65.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 4.0 (* a c))
100.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
86.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

173 → 173

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	253	91658
1	639	82177
2	2609	73903
done	5002	72918

prune553.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(* (* 4.0 a) c)
28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(* (* 4.0 a) c)
117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

173 → 173

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	256	91698
1	658	82176
2	3168	73902
done	5002	72917

prune753.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

23.0ms	(* 4.0 (* a c))
117.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 4.0 (* a c))
128.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
132.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
96.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.6s

Counts

181 → 181

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	279	97378
1	714	85701
2	3198	76356
done	5000	75201

prune712.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize79.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (* (* 4.0 a) c))
12.2b	(cbrt (* (* 4.0 a) c))
12.2b	(cbrt (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 50

Calls

4 calls:

24.0ms	(cbrt (* (* 4.0 a) c))
10.0ms	(cbrt (* (* 4.0 a) c))
10.0ms	(cbrt (* (* 4.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series688.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (* (* 4.0 a) c))
167.0ms	(cbrt (* (* 4.0 a) c))
172.0ms	(cbrt (* (* 4.0 a) c))
203.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify2.8s

Counts

62 → 62

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	92	20221
1	225	19495
2	672	15990
3	3559	15870
done	5000	15845

prune537.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

regimes408.0ms

Accuracy

85.9% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 34.2b

bsearch196.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	3.087668654677018e+130
8	-8.904680992578465e-52	-2.849527055171251e-56	-4.356959927988237e-56

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	870
1	37	870
done	37	870

end0.0ms

sample3.8s

Algorithm

intervals

Results

975.0ms	921×	body	1280	valid
734.0ms	1025×	body	2560	valid
652.0ms	5841×	body	80	valid
462.0ms	245×	body	320	valid
253.0ms	2877×	body	80	nan
149.0ms	457×	body	640	valid
86.0ms	122×	body	5120	valid
18.0ms	116×	body	160	valid