Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	192×	body	80	valid
8.0ms	27×	body	2560	valid
6.0ms	16×	body	320	valid
6.0ms	23×	body	1280	valid
6.0ms	105×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid

simplify166.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	114	17
4	141	17
5	151	17
6	155	17
done	155	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

89.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
29.0ms	(- (* b b) (* 4.0 (* a c)))
39.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
69.0ms	(- (* b b) (* 4.0 (* a c)))
104.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify982.0ms

Counts

89 → 89

Iterations

Useful iterations: done (978.0ms)

Iter	Nodes	Cost
0	157	1750
1	418	1650
2	1644	1474
done	5000	1466

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.6b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

65.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
174.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
80.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
244.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
280.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

153 → 153

Iterations

Useful iterations: 2 (692.0ms)

Iter	Nodes	Cost
0	250	4579
1	649	4063
2	3620	3761
done	5001	3761

prune951.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize53.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.3b	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
9.6b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
40×	`add-sqr-sqrt`
30×	`add-cbrt-cube`
25×	`*-un-lft-identity`
24×	`associate-r`
21×	`times-frac`
17×	`prod-exp`
16×	`add-cube-cbrt` `div-exp`
9×	`cbrt-undiv` `cbrt-unprod`
8×	`difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`associate-/l/` `add-log-exp`
4×	`frac-times` `flip3-+` `associate-*l/` `flip-+` `distribute-lft-out--`
3×	`rec-exp` `flip3--` `1-exp` `associate-l` `flip--` `unswap-sqr`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

65.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
67.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
221.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series800.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
268.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
307.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
126.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify525.0ms

Counts

128 → 128

Iterations

Useful iterations: done (520.0ms)

Iter	Nodes	Cost
0	243	3392
1	727	2796
done	5000	2378

prune787.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

94.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
45.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
69.0ms	(- (* b b) (* 4.0 (* a c)))
103.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

137 → 137

Iterations

Useful iterations: 2 (472.0ms)

Iter	Nodes	Cost
0	226	3421
1	588	3066
2	2593	2852
done	5001	2852

prune429.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.1b

regimes421.0ms

Accuracy

85.4% (3.9b remaining)

Error of 9.1b against oracle of 5.2b and baseline of 31.9b

bsearch196.0ms

Steps

Iters	Range	Point
9	9.357224410271438e+98	8.450543925883448e+104	5.991199458469861e+103
7	-4.3103989639009063e-82	-2.5085206973204917e-83	-2.534983011264385e-83
3	-1.713609749393423e-29	-1.2239049760790121e-29	-1.6806111715441095e-29

Iters

Range

Point

9.357224410271438e+98

8.450543925883448e+104

5.991199458469861e+103

-4.3103989639009063e-82

-2.5085206973204917e-83

-2.534983011264385e-83

-1.713609749393423e-29

-1.2239049760790121e-29

-1.6806111715441095e-29

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	37	69
1	44	67
2	45	67
done	45	67

end0.0ms

sample3.5s

Algorithm

intervals

Results

958.0ms	1054×	body	2560	valid
937.0ms	5897×	body	80	valid
364.0ms	855×	body	1280	valid
219.0ms	477×	body	640	valid
207.0ms	2885×	body	80	nan
144.0ms	112×	body	5120	valid
68.0ms	219×	body	320	valid
21.0ms	115×	body	160	valid