Details

sample128.0ms

Algorithm

intervals

Results

28.0ms	176×	body	80	valid
27.0ms	31×	body	2560	valid
19.0ms	30×	body	1280	valid
12.0ms	85×	body	80	nan
9.0ms	16×	body	640	valid
5.0ms	6×	body	5120	valid
4.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify214.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.8b	(- (* b b) (* 4 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite123.0ms

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:

75.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
21.0ms	(- (* b b) (* 4 (* a c)))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series746.0ms

Counts

4 → 12

Calls

4 calls:

465.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
71.0ms	(- (* b b) (* 4 (* a c)))
111.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
98.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	2006
3	2006
2	1254
1	400
0	154

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
0.8b	(+ (* b b) (* (* -4 a) c))
1.2b	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
22.9b	(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite102.0ms

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×	`insert-posit16`
3×	`distribute-rgt-neg-in`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `diff-log` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

58.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
16.0ms	(+ (* b b) (* (* -4 a) c))
20.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
6.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) (* 2 a))
61.0ms	(+ (* b b) (* (* -4 a) c))
100.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
93.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2000
3	2000
2	1344
1	412
0	156

prune884.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.8b	(- (* b b) (* 4 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

61.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
8.0ms	(- (* b b) (* 4 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
57.0ms	(- (* b b) (* 4 (* a c)))
99.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	2015
3	2015
2	1553
1	452
0	177

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize52.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (* (* (cbrt (- (* b b) (* 4 (* a c)))) (cbrt (- (* b b) (* 4 (* a c))))) (cbrt (- (* b b) (* 4 (* a c))))))
23.8b	(cbrt (- (* b b) (* 4 (* a c))))
23.8b	(cbrt (- (* b b) (* 4 (* a c))))
23.8b	(cbrt (- (* b b) (* 4 (* a c))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

101.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4 (* a c)))) (cbrt (- (* b b) (* 4 (* a c))))) (cbrt (- (* b b) (* 4 (* a c))))))
9.0ms	(cbrt (- (* b b) (* 4 (* a c))))
7.0ms	(cbrt (- (* b b) (* 4 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4 (* a c))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4 (* a c)))) (cbrt (- (* b b) (* 4 (* a c))))) (cbrt (- (* b b) (* 4 (* a c))))))
143.0ms	(cbrt (- (* b b) (* 4 (* a c))))
128.0ms	(cbrt (- (* b b) (* 4 (* a c))))
148.0ms	(cbrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	2005
4	2005
3	1921
2	703
1	351
0	187

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

regimes437.0ms

Accuracy

81.7% (5.0b remaining)

Error of 10.7b against oracle of 5.7b and baseline of 33.2b

bsearch214.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
9	-2.273288360947074e-131	-1.9680749876012584e-137	-2.2415082771065304e-131

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.9s	1048×	body	2560	valid
868.0ms	5790×	body	80	valid
815.0ms	956×	body	1280	valid
430.0ms	2938×	body	80	nan
332.0ms	454×	body	640	valid
125.0ms	98×	body	5120	valid
125.0ms	220×	body	320	valid
28.0ms	105×	body	160	valid