Details

sample119.0ms

Algorithm

intervals

Results

27.0ms	199×	body	80	valid
25.0ms	30×	body	2560	valid
18.0ms	29×	body	1280	valid
16.0ms	90×	body	80	nan
5.0ms	11×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify145.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	170
5	170
4	156
3	124
2	79
1	52
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
0.6b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
19.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

79.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
10.0ms	(- (* b b) (* (* 4 a) c))
35.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
69.0ms	(- (* b b) (* (* 4 a) c))
104.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
120.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

88 → 88

Iterations

Iter	Nodes
3	5179
2	1628
1	669
0	153

prune955.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1/2 a))
0.6b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
19.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`insert-posit16` `difference-of-squares`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

115.0ms	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1/2 a))
15.0ms	(- (* b b) (* (* 4 a) c))
51.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1/2 a))
52.0ms	(- (* b b) (* (* 4 a) c))
104.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.0s

Counts

97 → 97

Iterations

Iter	Nodes
3	6014
2	1909
1	760
0	177

prune868.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
0.6b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
19.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`insert-posit16`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 122

Calls

4 calls:

41.0ms	(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
7.0ms	(- (* b b) (* (* 4 a) c))
35.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
68.0ms	(- (* b b) (* (* 4 a) c))
122.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
73.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify692.0ms

Counts

134 → 134

Iterations

Iter	Nodes
2	2331
1	923
0	223

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.3b

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
19.6b	(sqrt (- (* b b) (* (* 4 a) c)))
19.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite104.0ms

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×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

35.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
43.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
110.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
105.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
86.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify594.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2191
2	794
1	344
0	82

prune834.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.3b

regimes414.0ms

Accuracy

85.2% (4.1b remaining)

Error of 9.3b against oracle of 5.2b and baseline of 33.1b

bsearch203.0ms

Steps

Iters	Range		Point
9	9.392283277667625e-73	1.0297697901410487e-64	1.1310477508076152e-72
9	-2.1289244816744743e+133	-2.3153117107728934e+126	-1.1783617127509567e+133

simplify4.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.0s	1062×	body	2560	valid
932.0ms	927×	body	1280	valid
852.0ms	5798×	body	80	valid
429.0ms	2873×	body	80	nan
247.0ms	420×	body	640	valid
149.0ms	111×	body	5120	valid
86.0ms	245×	body	320	valid
23.0ms	96×	body	160	valid