Details

sample93.0ms

Algorithm

intervals

Results

22.0ms	31×	body	2560	valid
20.0ms	190×	body	80	valid
16.0ms	31×	body	1280	valid
8.0ms	84×	body	80	nan
5.0ms	13×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify170.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.0b	(- (* b b) (* 4 (* a c)))
1.7b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite76.0ms

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:

41.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
8.0ms	(- (* b b) (* 4 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
60.0ms	(- (* b b) (* 4 (* a c)))
115.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
126.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify769.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2000
2	1254
1	400
0	154

prune454.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
1.0b	(- (* b b) (* 4 (* a c)))
1.7b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite106.0ms

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:

64.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
13.0ms	(- (* b b) (* 4 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
56.0ms	(- (* b b) (* 4 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
102.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify820.0ms

Counts

141 → 141

Iterations

Iter	Nodes
done	2002
2	1799
1	571
0	229

prune582.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) a)
1.0b	(+ (* b b) (* (* -4 a) c))
1.7b	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
23.4b	(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite137.0ms

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

Counts

4 → 94

Calls

4 calls:

77.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) a)
15.0ms	(+ (* b b) (* (* -4 a) c))
36.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
6.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 a) c)))) a)
50.0ms	(+ (* b b) (* (* -4 a) c))
95.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
88.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify680.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	2000
2	1247
1	411
0	163

prune545.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

localize69.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
23.4b	(sqrt (+ (* b b) (* (* -4 a) c)))
23.4b	(sqrt (+ (* b b) (* (* -4 a) c)))
23.4b	(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `flip3--` `neg-log` `flip--`

Counts

4 → 67

Calls

4 calls:

24.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
10.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
10.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
10.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
74.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
102.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))
107.0ms	(sqrt (+ (* b b) (* (* -4 a) c)))

simplify386.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2002
2	648
1	211
0	88

prune413.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.0b

regimes411.0ms

Accuracy

84% (4.5b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 33.3b

bsearch197.0ms

Steps

Iters	Range		Point
7	1.9723660647371773e+81	3.4101289177416236e+83	1.7665622931893247e+83
7	-8.865960730997555e-39	-3.628908962658003e-41	-5.7874989996849275e-40

simplify9.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.5s	5928×	body	80	valid
1.5s	1051×	body	2560	valid
708.0ms	917×	body	1280	valid
484.0ms	2986×	body	80	nan
259.0ms	423×	body	640	valid
141.0ms	116×	body	5120	valid
93.0ms	224×	body	320	valid
34.0ms	122×	body	160	valid