Details

sample146.0ms

Algorithm

intervals

Results

14.0ms	36×	body	2560	valid
13.0ms	188×	body	80	valid
7.0ms	24×	body	1280	valid
6.0ms	108×	body	80	nan
4.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite135.0ms

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:

82.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify995.0ms

Counts

92 → 92

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	151	1534
1	378	1440
2	1557	1268
done	5001	1260

prune398.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.0b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
146.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
109.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
239.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
225.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

218 → 218

Iterations

Useful iterations: 2 (801.0ms)

Iter	Nodes	Cost
0	307	6418
1	777	5561
2	4237	5359
done	5000	5359

prune754.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
8.0b	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
28×	`add-exp-log`
27×	`associate-r`
26×	`times-frac`
19×	`add-cube-cbrt`
18×	`add-cbrt-cube`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`associate-/l/`
5×	`cbrt-undiv`
4×	`frac-times` `distribute-rgt-neg-in` `flip3-+` `associate-*l/` `cbrt-unprod` `flip-+`
3×	`flip3--` `associate-l` `associate-/r*` `flip--` `unswap-sqr`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `-commutative` `associate-/l`

Counts

4 → 118

Calls

4 calls:

41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms	(/ (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
163.0ms	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series638.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
220.0ms	(/ (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
235.0ms	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts

130 → 130

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	236	2749
1	652	2226
2	4443	1942
done	5001	1942

prune477.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(* (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
8.0b	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite436.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
48×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
40×	`associate-r` `prod-exp`
32×	`times-frac`
30×	`add-cbrt-cube`
24×	`add-cube-cbrt`
20×	`div-exp`
12×	`pow1` `frac-times` `associate-*l/` `cbrt-unprod`
10×	`rec-exp` `1-exp`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`sqrt-prod`
6×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`distribute-rgt-neg-in` `associate-r/` `associate-l*` `pow-prod-down` `un-div-inv`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`sqrt-div` `diff-log` `associate-/r/` `*-commutative` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 151

Calls

4 calls:

30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
187.0ms	(* (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
185.0ms	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
216.0ms	(* (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
235.0ms	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify640.0ms

Counts

163 → 163

Iterations

Useful iterations: done (625.0ms)

Iter	Nodes	Cost
0	281	3815
1	859	3007
done	5000	2556

prune597.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

regimes267.0ms

Accuracy

86.2% (3.8b remaining)

Error of 9.0b against oracle of 5.3b and baseline of 32.5b

bsearch273.0ms

Steps

Iters	Range	Point
8	2.2795539252788044e+111	1.0533334563517102e+114	2.858094688970481e+111
9	7.987875384506669e-199	1.7042216608330097e-193	5.513214641062073e-195
10	-2.8734245235493903e+48	-2.602501271628617e+37	-2.8472042802820317e+48

Iters

Range

Point

2.2795539252788044e+111

1.0533334563517102e+114

2.858094688970481e+111

7.987875384506669e-199

1.7042216608330097e-193

5.513214641062073e-195

-2.8734245235493903e+48

-2.602501271628617e+37

-2.8472042802820317e+48

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	36	63
1	43	61
2	44	61
done	44	61

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	1080×	body	2560	valid
562.0ms	5858×	body	80	valid
286.0ms	899×	body	1280	valid
183.0ms	2901×	body	80	nan
168.0ms	450×	body	640	valid
91.0ms	227×	body	320	valid
77.0ms	108×	body	160	valid
53.0ms	112×	body	5120	valid