Details

sample123.0ms

Algorithm

intervals

Results

41.0ms	35×	body	2560	valid
17.0ms	179×	body	80	valid
14.0ms	30×	body	1280	valid
8.0ms	76×	body	80	nan
5.0ms	8×	body	5120	valid
3.0ms	9×	body	640	valid
3.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize14.0ms

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)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt` `times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`flip3--` `flip--` `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 → 60

Calls

3 calls:

116.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
77.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
107.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts

69 → 69

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	144	1372
1	370	1279
2	1151	1147
3	4159	1139
done	5000	1139

prune319.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

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)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
30×	`add-exp-log`
28×	`add-cube-cbrt`
18×	`associate-/r*` `add-cbrt-cube`
14×	`div-exp` `difference-of-squares`
11×	`associate-/r/`
10×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `flip--` `distribute-lft-out--`
6×	`pow1` `div-inv` `add-log-exp`
4×	`prod-exp` `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 → 135

Calls

4 calls:

86.0ms	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
67.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
76.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series764.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
204.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
135.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	229	3624
1	535	3276
2	1551	2964
done	5000	2884

prune455.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
61×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
43×	`associate-l`
40×	`add-cube-cbrt`
18×	`add-exp-log`
12×	`add-cbrt-cube`
6×	`pow1` `div-exp` `associate-r`
5×	`prod-exp` `sqrt-prod` `add-log-exp`
4×	`flip3--` `flip--` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `sub-neg` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 109

Calls

3 calls:

208.0ms	(* (/ (/ 1 2.0) a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
64.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series406.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(* (/ (/ 1 2.0) a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
127.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

118 → 118

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	236	2513
1	604	2366
2	1755	2078
done	5000	2042

prune600.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize18.0ms

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)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

46.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
76.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
128.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

72 → 72

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	81	1248
1	190	1104
2	570	1036
3	1885	1028
done	5000	1016

prune328.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes308.0ms

Accuracy

83.5% (4.7b remaining)

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

bsearch192.0ms

Steps

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

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	43
1	37	43
2	39	43
done	39	43

end0.0ms

sample3.1s

Algorithm

intervals

Results

823.0ms	906×	body	1280	valid
559.0ms	5866×	body	80	valid
558.0ms	1023×	body	2560	valid
290.0ms	2914×	body	80	nan
218.0ms	442×	body	640	valid
72.0ms	127×	body	5120	valid
49.0ms	244×	body	320	valid
15.0ms	109×	body	160	valid