Details

sample121.0ms

Algorithm

intervals

Results

31.0ms	210×	body	80	valid
22.0ms	84×	body	80	nan
19.0ms	23×	body	2560	valid
18.0ms	25×	body	1280	valid
5.0ms	8×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify475.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

59.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
7.0ms	(- (* b b) (* (* 4 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
61.0ms	(- (* b b) (* (* 4 a) c))
118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
88.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1358
1	406
0	153

prune510.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

71.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
17.0ms	(- (* b b) (* (* 4 a) c))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
53.0ms	(- (* b b) (* (* 4 a) c))
98.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
126.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1787
1	469
0	178

prune489.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt 1/2) (- (sqrt (+ (* c (* -4 a)) (* b b))) b))
0.8b	(+ (* c (* -4 a)) (* b b))
1.0b	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
20.8b	(sqrt (+ (* c (* -4 a)) (* b b)))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
4×	`insert-posit16` `difference-of-squares`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip3--` `sqrt-div` `associate-*r/` `flip-+` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

221.0ms	(* (sqrt 1/2) (- (sqrt (+ (* c (* -4 a)) (* b b))) b))
19.0ms	(+ (* c (* -4 a)) (* b b))
87.0ms	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
19.0ms	(sqrt (+ (* c (* -4 a)) (* b b)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (sqrt 1/2) (- (sqrt (+ (* c (* -4 a)) (* b b))) b))
88.0ms	(+ (* c (* -4 a)) (* b b))
110.0ms	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
99.0ms	(sqrt (+ (* c (* -4 a)) (* b b)))

simplify2.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
3	4238
2	882
1	283
0	120

prune429.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.5b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`sum-log` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
2×	`neg-sub0` `+-commutative` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `neg-log` `associate-+l-` `flip-+` `flip--`

Counts

4 → 64

Calls

4 calls:

18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
91.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
85.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2649
2	693
1	219
0	84

prune459.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.5b

regimes368.0ms

Accuracy

81% (5.2b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.1b

bsearch441.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.546013236023957e-67
7	6.366271362828677e-80	2.0474353944207673e-78	1.6168702840263923e-79
8	1.9015403840268286e-125	4.787339246176752e-121	1.3353078790738604e-121
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify14.0ms

Iterations

Iter	Nodes
done	45
3	45
2	42
1	39
0	30

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	5870×	body	80	valid
795.0ms	1084×	body	2560	valid
682.0ms	907×	body	1280	valid
431.0ms	3007×	body	80	nan
422.0ms	232×	body	320	valid
310.0ms	447×	body	640	valid
89.0ms	101×	body	5120	valid
25.0ms	109×	body	160	valid