Details

sample198.0ms

Algorithm

intervals

Results

16.0ms	184×	body	80	valid
14.0ms	31×	body	2560	valid
12.0ms	33×	body	1280	valid
7.0ms	90×	body	80	nan
3.0ms	12×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

134.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
49.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
75.0ms	(- (* b_2 b_2) (* a c))
127.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
135.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	164	1638
1	405	1539
2	1668	1355
done	5000	1344

prune883.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize44.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.4b	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
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 → 284

Calls

4 calls:

63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
162.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
117.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
33.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
338.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
325.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify889.0ms

Counts

296 → 296

Iterations

Useful iterations: done (867.0ms)

Iter	Nodes	Cost
0	390	10604
1	974	8179
done	5000	7437

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.3b	(/ (* c a) (* a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 148

Calls

4 calls:

19.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms	(/ (* c a) (* a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
293.0ms	(/ (* c a) (* a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

160 → 160

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	237	5592
1	611	3932
2	3399	3010
done	5001	2972

prune923.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ c 1) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-sqr-sqrt`
176×	`*-un-lft-identity`
163×	`times-frac`
116×	`add-cube-cbrt`
61×	`prod-diff`
48×	`sqrt-prod`
36×	`distribute-rgt-neg-in`
30×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
13×	`associate-/l*`
11×	`add-exp-log` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `div-inv`
7×	`neg-mul-1` `associate-/r*`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 254

Calls

4 calls:

84.0ms	(/ (/ c 1) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (/ c 1) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

266 → 266

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	350	8678
1	911	6359
2	4125	5547
done	5001	5546

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

regimes405.0ms

Accuracy

95% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.5b

bsearch373.0ms

Steps

Iters	Range	Point
8	4.049254448328916e+76	2.3057443967677173e+80	1.2718773002973155e+78
9	-3.913094050847411e-200	-3.3037963711260906e-206	-3.3528823044057167e-206
10	-6.623625638726693e+82	-6.4709084601913214e+72	-1.6581383089037873e+81

Iters

Range

Point

4.049254448328916e+76

2.3057443967677173e+80

1.2718773002973155e+78

-3.913094050847411e-200

-3.3037963711260906e-206

-3.3528823044057167e-206

-6.623625638726693e+82

-6.4709084601913214e+72

-1.6581383089037873e+81

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	33	58
1	39	54
2	41	54
done	41	54

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	5796×	body	80	valid
832.0ms	1066×	body	2560	valid
478.0ms	907×	body	1280	valid
292.0ms	2977×	body	80	nan
183.0ms	451×	body	640	valid
137.0ms	124×	body	5120	valid
52.0ms	231×	body	320	valid
20.0ms	135×	body	160	valid