Details

sample209.0ms

Algorithm

intervals

Results

15.0ms	29×	body	2560	valid
15.0ms	187×	body	80	valid
10.0ms	103×	body	80	nan
10.0ms	25×	body	1280	valid
5.0ms	16×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize30.0ms

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))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite130.0ms

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:

67.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
65.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

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

prune611.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize48.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.7b	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite318.0ms

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:

62.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
126.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
90.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
265.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
209.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify593.0ms

Counts

296 → 296

Iterations

Useful iterations: done (572.0ms)

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

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ a (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.7b	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
74×	`times-frac`
70×	`add-cube-cbrt`
60×	`prod-diff`
40×	`sqrt-prod`
28×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`fma-neg`
8×	`add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
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`

Counts

4 → 214

Calls

4 calls:

50.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
99.0ms	(/ a (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
67.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(/ a (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
251.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

226 → 226

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	316	7605
1	818	5821
2	4226	4878
done	5000	4876

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (/ 1 (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite530.0ms

Algorithm

rewrite-expression-head

Rules

3917×	`times-frac`
2018×	`add-sqr-sqrt`
2017×	`*-un-lft-identity`
1509×	`add-cube-cbrt`
254×	`distribute-lft-out--` `difference-of-squares`
160×	`sqrt-prod`
148×	`distribute-rgt-neg-in`
144×	`div-inv`
130×	`add-exp-log`
126×	`div-exp`
99×	`associate-/r/`
86×	`associate-/r*`
61×	`prod-diff`
49×	`1-exp`
45×	`flip3--` `flip--`
28×	`rec-exp`
25×	`add-cbrt-cube`
21×	`distribute-lft-neg-in`
15×	`cbrt-undiv`
13×	`associate-/l*`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 1409

Calls

4 calls:

152.0ms	(/ (/ 1 1) (/ 1 (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
12.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (/ 1 1) (/ 1 (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
56.0ms	(- (* b_2 b_2) (* a c))
123.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

1421 → 1421

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	1698	59902
done	5001	50314

prune5.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

regimes382.0ms

Accuracy

81.3% (4.5b remaining)

Error of 9.7b against oracle of 5.2b and baseline of 29.1b

bsearch124.0ms

Steps

Iters	Range		Point
9	9.357224410271438e+98	8.450543925883448e+104	8.592947913777282e+101
7	-4.3103989639009063e-82	-2.5085206973204917e-83	-1.7158765789797625e-82

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	36
1	27	36
done	27	36

end0.0ms

sample3.0s

Algorithm

intervals

Results

710.0ms	2888×	body	80	nan
559.0ms	1074×	body	2560	valid
505.0ms	5853×	body	80	valid
347.0ms	919×	body	1280	valid
150.0ms	458×	body	640	valid
79.0ms	209×	body	320	valid
53.0ms	112×	body	5120	valid
13.0ms	107×	body	160	valid