Details

sample141.0ms

Algorithm

intervals

Results

33.0ms	196×	body	80	valid
26.0ms	26×	body	2560	valid
22.0ms	26×	body	1280	valid
14.0ms	96×	body	80	nan
11.0ms	16×	body	640	valid
7.0ms	6×	body	5120	valid
3.0ms	5×	body	320	valid
2.0ms	4×	body	160	valid

simplify142.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.2b	(- (* b b) (* 4 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.8b	(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×	`flip3--` `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 → 77

Calls

4 calls:

66.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
7.0ms	(- (* b b) (* 4 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
48.0ms	(- (* b b) (* 4 (* a c)))
84.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
86.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.1s

Counts

89 → 89

Iterations

Iter	Nodes
3	4251
2	1178
1	393
0	150

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (* 2 a))
1.2b	(+ (* b b) (* (* -4 c) a))
1.4b	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
19.8b	(sqrt (+ (* b b) (* (* -4 c) a)))

rewrite97.0ms

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`
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 → 76

Calls

4 calls:

63.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (* 2 a))
7.0ms	(+ (* b b) (* (* -4 c) a))
14.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
10.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (* 2 a))
60.0ms	(+ (* b b) (* (* -4 c) a))
137.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
98.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

simplify2.1s

Counts

88 → 88

Iterations

Iter	Nodes
3	4876
2	1317
1	407
0	152

prune982.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (/ 1/2 a))
1.2b	(+ (* b b) (* (* -4 c) a))
1.4b	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
19.8b	(sqrt (+ (* b b) (* (* -4 c) a)))

rewrite123.0ms

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×	`sqrt-prod`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `distribute-rgt-neg-in` `flip3-+` `sqrt-div` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

70.0ms	(* (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (/ 1/2 a))
14.0ms	(+ (* b b) (* (* -4 c) a))
26.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
11.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (/ 1/2 a))
55.0ms	(+ (* b b) (* (* -4 c) a))
103.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
108.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

simplify3.2s

Counts

96 → 96

Iterations

Iter	Nodes
3	6713
2	1570
1	457
0	175

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize50.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
19.8b	(sqrt (+ (* b b) (* (* -4 c) a)))
19.8b	(sqrt (+ (* b b) (* (* -4 c) a)))
19.8b	(sqrt (+ (* b b) (* (* -4 c) a)))

rewrite68.0ms

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`
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 → 63

Calls

4 calls:

27.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
11.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))
17.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))
11.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
105.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))
75.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))
100.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

simplify3.0s

Counts

75 → 75

Iterations

Iter	Nodes
4	5458
3	1872
2	618
1	207
0	86

prune958.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

regimes346.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 33.5b

bsearch186.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	6.359263193477048e+137
7	-3.433369562555282e-53	-1.9970851824949347e-54	-2.852138444177435e-54

simplify9.0ms

Iterations

Iter	Nodes
2	30
1	30
0	24

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1055×	body	2560	valid
964.0ms	5848×	body	80	valid
831.0ms	2886×	body	80	nan
705.0ms	960×	body	1280	valid
263.0ms	461×	body	640	valid
129.0ms	107×	body	5120	valid
76.0ms	197×	body	320	valid
30.0ms	110×	body	160	valid