Details

sample157.0ms

Algorithm

intervals

Results

40.0ms	37×	body	2560	valid
33.0ms	194×	body	80	valid
24.0ms	28×	body	1280	valid
14.0ms	86×	body	80	nan
12.0ms	18×	body	640	valid
6.0ms	5×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify156.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.9b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b	(- (* b b) (* 4 (* a c)))
25.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite119.0ms

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:

55.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(- (* b b) (* 4 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
120.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
60.0ms	(- (* b b) (* 4 (* a c)))
97.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
3	2002
2	1255
1	400
0	154

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (* 2 a))
0.9b	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
1.0b	(- (* b b) (* a (* c 4)))
25.0b	(sqrt (- (* b b) (* a (* c 4))))

rewrite101.0ms

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:

56.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (* 2 a))
20.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
9.0ms	(- (* b b) (* a (* c 4)))
15.0ms	(sqrt (- (* b b) (* a (* c 4))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (* 2 a))
110.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
59.0ms	(- (* b b) (* a (* c 4)))
124.0ms	(sqrt (- (* b b) (* a (* c 4))))

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	2005
3	2005
2	1291
1	401
0	156

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (/ 1/2 a))
0.9b	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
1.0b	(- (* b b) (* a (* c 4)))
25.0b	(sqrt (- (* b b) (* a (* c 4))))

rewrite192.0ms

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:

126.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (/ 1/2 a))
33.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
17.0ms	(- (* b b) (* a (* c 4)))
15.0ms	(sqrt (- (* b b) (* a (* c 4))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (/ 1/2 a))
106.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
57.0ms	(- (* b b) (* a (* c 4)))
129.0ms	(sqrt (- (* b b) (* a (* c 4))))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	2005
3	2005
2	1611
1	454
0	179

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* a (* c 4)))))))
0.9b	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
1.0b	(- (* b b) (* a (* c 4)))
25.0b	(sqrt (- (* b b) (* a (* c 4))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

37.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* a (* c 4)))))))
35.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
9.0ms	(- (* b b) (* a (* c 4)))
8.0ms	(sqrt (- (* b b) (* a (* c 4))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* a (* c 4)))))))
108.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
54.0ms	(- (* b b) (* a (* c 4)))
109.0ms	(sqrt (- (* b b) (* a (* c 4))))

simplify1.0s

Counts

141 → 141

Iterations

Iter	Nodes
done	2000
3	2000
2	1736
1	574
0	231

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

regimes401.0ms

Accuracy

83.7% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 33.2b

bsearch217.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	2.5703497435733685e+102
10	-1.094129558870314e-56	-1.2317994276347943e-74	-1.8774910265390396e-73

simplify15.0ms

Iterations

Iter	Nodes
done	44
3	44
2	40
1	35
0	24

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1095×	body	2560	valid
826.0ms	5820×	body	80	valid
740.0ms	948×	body	1280	valid
342.0ms	2996×	body	80	nan
203.0ms	445×	body	640	valid
101.0ms	225×	body	320	valid
81.0ms	98×	body	5120	valid
25.0ms	116×	body	160	valid