Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	103×	body	80	nan
7.0ms	37×	body	2560	valid
5.0ms	175×	body	80	valid
5.0ms	32×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify951.0ms

Counts

183 → 183

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1414	3549
done	5001	3001

prune344.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
6.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
11.2b	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
23.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
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 → 219

Calls

4 calls:

78.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
118.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
75.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
20.0ms	(sqrt (- (pow b_2 2) (* a c)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
161.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
196.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
68.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify989.0ms

Counts

231 → 231

Iterations

Useful iterations: done (981.0ms)

Iter	Nodes	Cost
0	340	6455
1	796	5486
2	2408	5170
done	5000	5113

prune578.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

10.5b	(/ (+ 0 (* a c)) (fma (sqrt (sqrt (- (pow b_2 2) (* a c)))) (sqrt (sqrt (- (pow b_2 2) (* a c)))) (- b_2)))
14.6b	(fma (sqrt (sqrt (- (pow b_2 2) (* a c)))) (sqrt (sqrt (- (pow b_2 2) (* a c)))) (- b_2))
23.4b	(sqrt (- (pow b_2 2) (* a c)))
23.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

4 → 75

Calls

4 calls:

19.0ms	(/ (+ 0 (* a c)) (fma (sqrt (sqrt (- (pow b_2 2) (* a c)))) (sqrt (sqrt (- (pow b_2 2) (* a c)))) (- b_2)))
0.0ms	(fma (sqrt (sqrt (- (pow b_2 2) (* a c)))) (sqrt (sqrt (- (pow b_2 2) (* a c)))) (- b_2))
17.0ms	(sqrt (- (pow b_2 2) (* a c)))
20.0ms	(sqrt (- (pow b_2 2) (* a c)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

435.0ms	(/ (+ 0 (* a c)) (fma (sqrt (sqrt (- (pow b_2 2) (* a c)))) (sqrt (sqrt (- (pow b_2 2) (* a c)))) (- b_2)))
101.0ms	(fma (sqrt (sqrt (- (pow b_2 2) (* a c)))) (sqrt (sqrt (- (pow b_2 2) (* a c)))) (- b_2))
62.0ms	(sqrt (- (pow b_2 2) (* a c)))
68.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify2.1s

Counts

87 → 87

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	155	2205
1	346	1439
2	1082	1285
3	4256	1254
done	5000	1252

prune321.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

7.4b	(/ (/ (+ 0 (* a c)) (- (* (fabs (cbrt (- (pow b_2 2) (* a c)))) (sqrt (cbrt (- (pow b_2 2) (* a c))))) b_2)) a)
10.9b	(/ (+ 0 (* a c)) (- (* (fabs (cbrt (- (pow b_2 2) (* a c)))) (sqrt (cbrt (- (pow b_2 2) (* a c))))) b_2))
24.2b	(cbrt (- (pow b_2 2) (* a c)))
24.2b	(cbrt (- (pow b_2 2) (* a c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`cbrt-prod` `associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `cbrt-div` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `pow1/3` `clear-num`
1×	`flip3-+` `flip-+`

Counts

4 → 143

Calls

4 calls:

83.0ms	(/ (/ (+ 0 (* a c)) (- (* (fabs (cbrt (- (pow b_2 2) (* a c)))) (sqrt (cbrt (- (pow b_2 2) (* a c))))) b_2)) a)
50.0ms	(/ (+ 0 (* a c)) (- (* (fabs (cbrt (- (pow b_2 2) (* a c)))) (sqrt (cbrt (- (pow b_2 2) (* a c))))) b_2))
7.0ms	(cbrt (- (pow b_2 2) (* a c)))
8.0ms	(cbrt (- (pow b_2 2) (* a c)))

series904.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ (/ (+ 0 (* a c)) (- (* (fabs (cbrt (- (pow b_2 2) (* a c)))) (sqrt (cbrt (- (pow b_2 2) (* a c))))) b_2)) a)
389.0ms	(/ (+ 0 (* a c)) (- (* (fabs (cbrt (- (pow b_2 2) (* a c)))) (sqrt (cbrt (- (pow b_2 2) (* a c))))) b_2))
91.0ms	(cbrt (- (pow b_2 2) (* a c)))
88.0ms	(cbrt (- (pow b_2 2) (* a c)))

simplify1.1s

Counts

155 → 155

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	333	6544
1	850	5994
2	2785	5583
done	5000	5565

prune615.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

regimes298.0ms

Accuracy

80.3% (5.3b remaining)

Error of 10.5b against oracle of 5.3b and baseline of 32.1b

bsearch70.0ms

Steps

Iters	Range		Point
6	2.0335150395734557e+19	1.0746392320557105e+20	1.0610691325078738e+20
9	-2.2937511015552136e-106	-2.1895844909113535e-111	-1.9134719200570835e-110

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	38
1	32	36
done	32	36

end0.0ms

sample1.0s

Algorithm

intervals

Results

194.0ms	1077×	body	2560	valid
181.0ms	5759×	body	80	valid
132.0ms	915×	body	1280	valid
78.0ms	2830×	body	80	nan
52.0ms	465×	body	640	valid
23.0ms	249×	body	320	valid
23.0ms	105×	body	5120	valid
7.0ms	115×	body	160	valid