Details

sample286.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	195×	body	80	valid
5.0ms	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

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

36.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	164	1638
1	386	1535
2	1101	1355
3	3591	1340
done	5000	1338

prune336.0ms

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 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 196

Calls

4 calls:

27.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
35.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

208 → 208

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	299	4764
1	649	4074
2	1502	3649
3	4558	3500
done	5000	3499

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cbrt 1) (cbrt 1)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
60×	`times-frac`
53×	`*-un-lft-identity`
39×	`add-cube-cbrt`
24×	`associate-/r*`
22×	`sqrt-prod`
19×	`prod-diff`
16×	`add-exp-log`
14×	`difference-of-squares`
12×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`div-inv`
2×	`sub-neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 144

Calls

4 calls:

29.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

156 → 156

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	254	3346
1	589	2726
2	1397	2300
3	4237	2197
done	5001	2196

prune375.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`prod-diff`
51×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 158

Calls

4 calls:

60.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
39.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

170 → 170

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	239	4053
1	587	3273
2	1545	2573
3	4729	2352
done	5000	2352

prune312.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

regimes201.0ms

Accuracy

83.1% (4.9b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 34.3b

bsearch116.0ms

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	27	41
1	32	41
done	32	41

end0.0ms

sample1.3s

Algorithm

intervals

Results

281.0ms	851×	body	1280	valid
241.0ms	1099×	body	2560	valid
215.0ms	5881×	body	80	valid
103.0ms	2944×	body	80	nan
66.0ms	470×	body	640	valid
34.0ms	109×	body	5120	valid
23.0ms	219×	body	320	valid
7.0ms	98×	body	160	valid