Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	181×	body	80	valid
6.0ms	27×	body	2560	valid
6.0ms	31×	body	1280	valid
3.0ms	21×	body	640	valid
3.0ms	81×	body	80	nan
2.0ms	8×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	119	17
4	141	17
5	147	17
6	150	17
done	150	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`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 → 157

Calls

4 calls:

45.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify688.0ms

Counts

169 → 169

Iterations

Useful iterations: done (682.0ms)

Iter	Nodes	Cost
0	243	6690
1	578	4705
2	1789	3760
done	5001	3759

prune383.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 205

Calls

4 calls:

28.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify997.0ms

Counts

217 → 217

Iterations

Useful iterations: done (986.0ms)

Iter	Nodes	Cost
0	311	8365
1	706	6123
2	1990	5076
done	5000	5068

prune396.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

55.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
47.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify915.0ms

Counts

177 → 177

Iterations

Useful iterations: done (909.0ms)

Iter	Nodes	Cost
0	269	6947
1	642	4848
2	1984	3851
done	5000	3850

prune357.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

15.1b	(- (- b) (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 87

Calls

4 calls:

8.0ms	(- (- b) (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

99 → 99

Iterations

Useful iterations: 3 (935.0ms)

Iter	Nodes	Cost
0	114	3377
1	286	1845
2	903	1544
3	3905	1474
done	5000	1474

prune337.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes239.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 34.4b

bsearch112.0ms

Steps

Iters	Range		Point
10	1.1889782913455773e+76	6.845935134449847e+90	1.964008874546701e+84
8	-2.5526520307548834e-35	-5.158362140144754e-39	-9.665680960493338e-39

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	35
1	30	35
done	30	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

251.0ms	1059×	body	2560	valid
231.0ms	5841×	body	80	valid
177.0ms	909×	body	1280	valid
112.0ms	2943×	body	80	nan
69.0ms	464×	body	640	valid
31.0ms	102×	body	5120	valid
26.0ms	234×	body	320	valid
10.0ms	111×	body	160	valid