Details

sample218.0ms

Algorithm

intervals

Results

19.0ms	190×	body	80	valid
18.0ms	36×	body	2560	valid
11.0ms	28×	body	1280	valid
8.0ms	92×	body	80	nan
5.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

119.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

92 → 92

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	151	1534
1	355	1440
2	1001	1266
3	2792	1252
done	5000	1249

prune240.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.4b	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.2b	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `sqrt-prod` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
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` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 136

Calls

4 calls:

47.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
76.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
260.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
224.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

148 → 148

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	240	3445
1	596	3204
2	2002	2940
done	5001	2870

prune478.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite131.0ms

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

Counts

4 → 90

Calls

4 calls:

49.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
52.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
45.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

102 → 102

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	151	1775
1	325	1672
2	869	1558
3	2254	1540
done	5001	1534

prune306.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
27×	`associate-r`
23×	`times-frac`
17×	`add-cube-cbrt`
13×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`flip3--` `distribute-rgt-neg-in` `prod-exp` `flip--`
3×	`diff-log` `associate-l` `unswap-sqr`
2×	`sub-neg` `sqrt-div` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

108.0ms	(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
64.0ms	(- (* b_2 b_2) (* a c))
125.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

107 → 107

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	173	1703
1	411	1478
2	1002	1318
3	2492	1302
done	5000	1296

prune321.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.5b

regimes209.0ms

Accuracy

86.8% (3.3b remaining)

Error of 8.5b against oracle of 5.2b and baseline of 30.2b

bsearch231.0ms

Steps

Iters	Range	Point
9	1.3206820209921783e+153	1.5782810135998455e+159	6.190496209585126e+153
6	-9.655534078733555e-134	-6.854174842211803e-135	-3.438769587726376e-134
10	-7.296408209838224e+27	-1014094955833491.1	-1.2846701741855862e+20

Iters

Range

Point

1.3206820209921783e+153

1.5782810135998455e+159

6.190496209585126e+153

-9.655534078733555e-134

-6.854174842211803e-135

-3.438769587726376e-134

-7.296408209838224e+27

-1014094955833491.1

-1.2846701741855862e+20

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	37	67
1	44	61
done	44	61

end0.0ms

sample2.8s

Algorithm

intervals

Results

660.0ms	850×	body	1280	valid
619.0ms	5880×	body	80	valid
413.0ms	1077×	body	2560	valid
200.0ms	2914×	body	80	nan
139.0ms	466×	body	640	valid
121.0ms	107×	body	5120	valid
35.0ms	212×	body	320	valid
18.0ms	123×	body	160	valid