Details

sample79.0ms

Algorithm

intervals

Results

21.0ms	43×	body	2560	valid
15.0ms	189×	body	80	valid
9.0ms	24×	body	1280	valid
6.0ms	85×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	5120	valid

simplify64.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

118.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

107 → 107

Iterations

Iter	Nodes
done	5005
3	3743
2	1046
1	388
0	162

prune590.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.9b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

52.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
64.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
248.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
248.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2110
1	614
0	241

prune705.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize35.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.9b	(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
11.2b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
40×	`add-sqr-sqrt`
30×	`add-cbrt-cube`
25×	`*-un-lft-identity`
23×	`times-frac`
17×	`prod-exp`
16×	`div-exp` `add-cube-cbrt`
13×	`associate-r`
12×	`associate-l`
9×	`cbrt-undiv` `cbrt-unprod`
8×	`difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`associate-/r*` `add-log-exp`
4×	`flip3--` `associate-/r/` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `div-inv` `unswap-sqr`
2×	`sqrt-div`
1×	`frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `-commutative` `associate-/l`

Counts

4 → 122

Calls

4 calls:

43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
168.0ms	(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
69.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
204.0ms	(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
283.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	2327
1	648
0	232

prune623.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 93

Calls

4 calls:

103.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
11.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
54.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1306
1	455
0	181

prune453.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 4.7b

regimes569.0ms

Accuracy

83.6% (4.7b remaining)

Error of 10.0b against oracle of 5.3b and baseline of 33.6b

bsearch238.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
8	-8.174058392489458e-91	-5.8455127160568266e-95	-6.822071483797687e-95
9	-3.834213106287376e+36	-1.7857077290843617e+30	-2.4515142736560382e+31

simplify33.0ms

Iterations

Iter	Nodes
done	40
1	40
0	34

end0.0ms

sample3.0s

Algorithm

intervals

Results

814.0ms	5819×	body	80	valid
614.0ms	2973×	body	80	nan
544.0ms	1105×	body	2560	valid
367.0ms	877×	body	1280	valid
152.0ms	439×	body	640	valid
81.0ms	252×	body	320	valid
62.0ms	125×	body	5120	valid
15.0ms	122×	body	160	valid