Details

sample105.0ms

Algorithm

intervals

Results

23.0ms	196×	body	80	valid
20.0ms	26×	body	2560	valid
15.0ms	26×	body	1280	valid
11.0ms	96×	body	80	nan
8.0ms	16×	body	640	valid
5.0ms	6×	body	5120	valid
2.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	44
4	44
3	41
2	32
1	18
0	10

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

79.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
61.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	2655
2	1010
1	381
0	158

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
83.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* a c))
176.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
217.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify904.0ms

Counts

196 → 196

Iterations

Iter	Nodes
2	2197
1	729
0	302

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.4b	(/ (/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))) a)
9.6b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

303×	`times-frac`
168×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
111×	`add-cube-cbrt`
41×	`add-exp-log` `associate-/l*`
28×	`difference-of-squares`
24×	`div-exp`
23×	`add-cbrt-cube`
18×	`div-inv`
17×	`sqrt-prod`
14×	`distribute-lft-out--`
11×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`associate-/r*` `prod-exp` `associate-/r/`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 225

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(/ (/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))) a)
60.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(/ (/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))) a)
149.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

237 → 237

Iterations

Iter	Nodes
2	2760
1	1085
0	428

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* 1 c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`associate-l`
23×	`*-un-lft-identity`
20×	`prod-exp`
18×	`times-frac`
16×	`add-cbrt-cube`
15×	`add-cube-cbrt`
10×	`pow1`
8×	`add-log-exp` `difference-of-squares`
7×	`1-exp` `sqrt-prod`
6×	`div-exp` `cbrt-unprod`
4×	`flip3--` `flip--` `distribute-lft-out--`
3×	`rec-exp` `pow-prod-down`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `associate-l/` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

106.0ms	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* 1 c))
32.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* 1 c))
91.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

106 → 106

Iterations

Iter	Nodes
3	2804
2	1031
1	443
0	180

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

regimes283.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 29.4b

bsearch317.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	3.613539017061943e+138
9	1.468078879799126e-291	1.4554634128686194e-286	4.615068992038193e-289
8	-6.440043566032316e+77	-5.00182377876139e+74	-6.447353158240281e+75

simplify5.0ms

Iterations

Iter	Nodes
2	37
1	37
0	31

end0.0ms

sample3.5s

Algorithm

intervals

Results

770.0ms	1057×	body	2560	valid
696.0ms	2883×	body	80	nan
656.0ms	5844×	body	80	valid
560.0ms	957×	body	1280	valid
316.0ms	462×	body	640	valid
97.0ms	109×	body	5120	valid
57.0ms	198×	body	320	valid
20.0ms	110×	body	160	valid