Details

sample81.0ms

Algorithm

intervals

Results

16.0ms	35×	body	2560	valid
14.0ms	179×	body	80	valid
10.0ms	30×	body	1280	valid
6.0ms	76×	body	80	nan
5.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify157.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`times-frac` `fma-neg` `associate-/l*` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 90

Calls

3 calls:

147.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series442.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
151.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

99 → 99

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	178	2210
1	453	1916
2	1321	1636
done	5000	1564

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
66×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
30×	`add-exp-log`
22×	`sqrt-prod`
18×	`prod-diff` `associate-/r*` `add-cbrt-cube`
14×	`div-exp` `difference-of-squares`
11×	`associate-/r/`
7×	`cbrt-undiv` `flip3--` `flip--` `distribute-lft-out--`
6×	`pow1` `fma-neg` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `sqrt-div` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `inv-pow`

Counts

4 → 167

Calls

4 calls:

85.0ms	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
138.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
93.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series901.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
303.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
131.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

179 → 179

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	265	4500
1	617	3949
2	1696	3478
done	5000	3333

prune556.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`add-exp-log`
21×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
12×	`add-cbrt-cube`
10×	`prod-exp`
7×	`associate-r`
6×	`pow1` `fma-neg` `associate-l`
5×	`add-log-exp`
4×	`flip3--` `div-exp` `flip--` `cbrt-unprod` `difference-of-squares`
3×	`expm1-log1p-u` `times-frac` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `rec-exp` `sqrt-div` `1-exp` `associate-*l/` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

307.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
104.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series467.0ms

Counts

3 → 9

Calls

3 calls:

212.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
147.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	204	2473
1	509	2071
2	1550	1739
done	5001	1667

prune396.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

88.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
35.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
127.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

128 → 128

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	113	2856
1	268	2310
2	718	1948
3	2711	1774
done	5001	1674

prune513.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes320.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.0b

bsearch169.0ms

Steps

Iters	Range		Point
9	2.3136842542622443e-90	1.8034474160827886e-84	3.091361180800597e-86
6	-3.779251410483496e+105	-5.080294099506613e+104	-1.361733299857302e+105

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.6s

Algorithm

intervals

Results

933.0ms	1023×	body	2560	valid
691.0ms	5866×	body	80	valid
595.0ms	442×	body	640	valid
412.0ms	906×	body	1280	valid
284.0ms	2914×	body	80	nan
69.0ms	127×	body	5120	valid
48.0ms	244×	body	320	valid
15.0ms	109×	body	160	valid