Details

sample111.0ms

Algorithm

intervals

Results

37.0ms	43×	body	2560	valid
16.0ms	190×	body	80	valid
10.0ms	24×	body	1280	valid
7.0ms	85×	body	80	nan
3.0ms	12×	body	640	valid
3.0ms	12×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify433.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	132
4	127
3	106
2	61
1	28
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize76.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

131.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms	(- (* b b) (* 4.0 (* a c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series694.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
112.0ms	(- (* b b) (* 4.0 (* a c)))
177.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
170.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify7.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5029
3	4634
2	1246
1	406
0	159

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

196.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms	(- (* b b) (* 4.0 (* a c)))
41.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series632.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
110.0ms	(- (* b b) (* 4.0 (* a c)))
158.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
175.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	1653
1	476
0	185

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) (/ 1 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt` `times-frac`
50×	`*-un-lft-identity`
40×	`associate-l`
34×	`add-cube-cbrt`
26×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`associate-r`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`div-exp` `prod-exp` `add-log-exp`
7×	`pow1` `distribute-lft-out`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `insert-posit16`
3×	`neg-mul-1` `sqrt-prod`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `div-inv` `flip--`
1×	`distribute-lft-neg-out` `frac-times` `+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `distribute-frac-neg` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

260.0ms	(* (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) (/ 1 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) (/ 1 a))
108.0ms	(- (* b b) (* 4.0 (* a c)))
143.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
121.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	2207
1	710
0	245

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 c) a))
0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
22.0b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

113.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
11.0ms	(- (* b b) (* (* 4.0 c) a))
47.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
95.0ms	(- (* b b) (* (* 4.0 c) a))
159.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
132.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify7.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	4847
2	1296
1	411
0	161

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes1.1s

Accuracy

82.4% (5.1b remaining)

Error of 10.5b against oracle of 5.4b and baseline of 34.3b

bsearch195.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
7	-2.1239343788780832e-66	-2.400891841159577e-68	-1.264659490877098e-67

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.0s	5823×	body	80	valid
651.0ms	2975×	body	80	nan
587.0ms	1103×	body	2560	valid
511.0ms	877×	body	1280	valid
124.0ms	440×	body	640	valid
69.0ms	125×	body	5120	valid
53.0ms	249×	body	320	valid
18.0ms	121×	body	160	valid