Details

sample68.0ms

Algorithm

intervals

Results

11.0ms	185×	body	80	valid
10.0ms	32×	body	2560	valid
10.0ms	31×	body	1280	valid
6.0ms	108×	body	80	nan
5.0ms	6×	body	160	valid
3.0ms	6×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid

simplify171.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	121	17
4	153	17
5	160	17
6	164	17
done	164	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite213.0ms

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:

111.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
59.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms	(- (* b b) (* 4.0 (* a c)))
115.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
132.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

169 → 169

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	243	6690
1	616	4729
2	2482	3764
done	5002	3675

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (- 4.0) a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b)))) (* 2.0 a))
1.2b	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
23.3b	(sqrt (fma (* (- 4.0) a) c (* b b)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

0.0ms	(fma (* (- 4.0) a) c (* b b))
70.0ms	(/ (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b)))) (* 2.0 a))
26.0ms	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
3.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma (* (- 4.0) a) c (* b b))
127.0ms	(/ (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b)))) (* 2.0 a))
97.0ms	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
111.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))

simplify1.4s

Counts

161 → 161

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	218	6479
1	517	4536
2	1960	3599
done	5000	2957

prune456.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 a) (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b)))))
0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))))
1.2b	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
23.3b	(sqrt (fma (* (- 4.0) a) c (* b b)))

rewrite146.0ms

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`
30×	`add-exp-log`
28×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`add-cbrt-cube`
14×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`fma-neg`
8×	`add-log-exp`
7×	`cbrt-undiv` `neg-mul-1`
6×	`pow1` `flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `diff-log` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `inv-pow`

Counts

4 → 220

Calls

4 calls:

55.0ms	(/ (* 2.0 a) (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b)))))
47.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))))
25.0ms	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
2.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))

series686.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (* 2.0 a) (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b)))))
195.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))))
109.0ms	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
135.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))

simplify2.4s

Counts

232 → 232

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	296	8804
1	727	6575
2	3949	5984
done	5001	5983

prune705.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
23.3b	(sqrt (fma (* (- 4.0) a) c (* b b)))
23.3b	(sqrt (fma (* (- 4.0) a) c (* b b)))
23.3b	(sqrt (fma (* (- 4.0) a) c (* b b)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--`

Counts

4 → 135

Calls

4 calls:

36.0ms	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
2.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))
2.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))
2.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (- b) (sqrt (fma (* (- 4.0) a) c (* b b))))
105.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))
108.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))
133.0ms	(sqrt (fma (* (- 4.0) a) c (* b b)))

simplify905.0ms

Counts

147 → 147

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	146	5884
1	317	3894
2	1039	3078
done	5000	2441

prune637.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.9b

regimes252.0ms

Accuracy

84.1% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 34.1b

bsearch186.0ms

Steps

Iters	Range		Point
6	1.9101351599902807e+102	2.525038855038462e+103	2.3695074697097983e+103
8	-4.026984795199496e-50	-6.333853666809325e-53	-4.395648124178114e-52

simplify14.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	35
1	31	35
2	35	35
3	36	35
done	36	35

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.1s	1050×	body	2560	valid
648.0ms	5808×	body	80	valid
593.0ms	465×	body	640	valid
549.0ms	936×	body	1280	valid
376.0ms	2896×	body	80	nan
67.0ms	111×	body	5120	valid
56.0ms	234×	body	320	valid
18.0ms	105×	body	160	valid