Details

sample268.0ms

Algorithm

intervals

Results

20.0ms	204×	body	80	valid
20.0ms	37×	body	1280	valid
13.0ms	25×	body	2560	valid
8.0ms	104×	body	80	nan
4.0ms	14×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite238.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

126.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
65.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
109.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(- (* b_2 b_2) (* a c))
134.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

103 → 103

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	156	1821
1	388	1727
2	1501	1611
done	5000	1603

prune369.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite258.0ms

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-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
89.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series711.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
259.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
325.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

196 → 196

Iterations

Useful iterations: 2 (880.0ms)

Iter	Nodes	Cost
0	302	5540
1	770	4801
2	4236	4619
done	5001	4619

prune807.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.5b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
11.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
52×	`times-frac`
49×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 138

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
211.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
68.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series660.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* a c))
233.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
282.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.7s

Counts

150 → 150

Iterations

Useful iterations: 2 (876.0ms)

Iter	Nodes	Cost
0	248	3414
1	736	2909
2	4721	2603
done	5000	2603

prune578.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
16.5b	(/ (* a c) a)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(/ (* a c) a)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
47.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (* a c) a)
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

75 → 75

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	125	880
1	313	806
2	1711	726
done	5001	698

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

regimes273.0ms

Accuracy

96% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 30.1b

bsearch536.0ms

Steps

Iters	Range	Point
8	1.051086597250448e+104	1.8086281629461872e+108	4.340805540534955e+107
10	-8.138706044250008e-279	-2.4810350231976038e-293	-2.5157876682752365e-293
8	-8.097032161796104e+150	-7.567364227263737e+146	-1.8427455378627112e+150

Iters

Range

Point

1.051086597250448e+104

1.8086281629461872e+108

4.340805540534955e+107

-8.138706044250008e-279

-2.4810350231976038e-293

-2.5157876682752365e-293

-8.097032161796104e+150

-7.567364227263737e+146

-1.8427455378627112e+150

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	55
1	38	55
done	38	55

end0.0ms

sample3.1s

Algorithm

intervals

Results

647.0ms	2947×	body	80	nan
589.0ms	5893×	body	80	valid
507.0ms	1042×	body	2560	valid
403.0ms	929×	body	1280	valid
185.0ms	476×	body	640	valid
83.0ms	88×	body	5120	valid
42.0ms	231×	body	320	valid
14.0ms	108×	body	160	valid