Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

36.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
48.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify725.0ms

Counts

161 → 161

Iterations

Useful iterations: done (714.0ms)

Iter	Nodes	Cost
0	278	4083
1	663	3911
2	1940	3753
done	5000	3752

prune470.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) (/ 1 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-l`
16×	`add-cbrt-cube`
13×	`associate-r`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 108

Calls

4 calls:

56.0ms	(* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) (/ 1 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) (/ 1 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify860.0ms

Counts

120 → 120

Iterations

Useful iterations: done (856.0ms)

Iter	Nodes	Cost
0	220	2461
1	621	2249
2	1704	1967
done	5000	1966

prune294.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

36.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
43.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	156	1888
1	372	1774
2	1039	1658
3	3435	1650
done	5000	1648

prune240.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

26.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
48.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

174 → 174

Iterations

Useful iterations: 3 (874.0ms)

Iter	Nodes	Cost
0	260	4494
1	577	3975
2	1419	3678
3	4425	3598
done	5000	3598

prune277.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes186.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.8b

bsearch102.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	42
1	36	42
done	36	42

end0.0ms

sample1.2s

Algorithm

intervals

Results

268.0ms	1074×	body	2560	valid
248.0ms	5844×	body	80	valid
179.0ms	907×	body	1280	valid
110.0ms	2890×	body	80	nan
70.0ms	452×	body	640	valid
30.0ms	102×	body	5120	valid
27.0ms	234×	body	320	valid
9.0ms	119×	body	160	valid