Details

sample130.0ms

Algorithm

intervals

Results

34.0ms	88×	body	80	nan
24.0ms	186×	body	80	valid
23.0ms	29×	body	2560	valid
17.0ms	24×	body	1280	valid
8.0ms	17×	body	640	valid
3.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	95
7	95
6	94
5	92
4	84
3	67
2	43
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.6b	(- (* b b) (* (* 4 a) c))
24.4b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

85.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
66.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
16.0ms	(- (* b b) (* (* 4 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
97.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
76.0ms	(- (* b b) (* (* 4 a) c))
98.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
3	3742
2	1119
1	395
0	161

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.6b	(- (* b b) (* (* 4 a) c))
24.4b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 166

Calls

4 calls:

82.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
41.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
14.0ms	(- (* b b) (* (* 4 a) c))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
89.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
53.0ms	(- (* b b) (* (* 4 a) c))
96.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.0s

Counts

178 → 178

Iterations

Iter	Nodes
3	6101
2	1836
1	643
0	265

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (+ (* (* -4 a) c) (* b b))) b))
1.0b	(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
1.6b	(+ (* (* -4 a) c) (* b b))
24.4b	(sqrt (+ (* (* -4 a) c) (* b b)))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

223.0ms	(* (/ 1 a) (- (sqrt (+ (* (* -4 a) c) (* b b))) b))
114.0ms	(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
18.0ms	(+ (* (* -4 a) c) (* b b))
33.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (/ 1 a) (- (sqrt (+ (* (* -4 a) c) (* b b))) b))
89.0ms	(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
63.0ms	(+ (* (* -4 a) c) (* b b))
85.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

simplify1.5s

Counts

103 → 103

Iterations

Iter	Nodes
3	4108
2	1183
1	414
0	157

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (+ (* b b) (* (* c a) -4))) b) a)
1.0b	(- (sqrt (+ (* b b) (* (* c a) -4))) b)
1.6b	(+ (* b b) (* (* c a) -4))
24.4b	(sqrt (+ (* b b) (* (* c a) -4)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

59.0ms	(/ (- (sqrt (+ (* b b) (* (* c a) -4))) b) a)
48.0ms	(- (sqrt (+ (* b b) (* (* c a) -4))) b)
18.0ms	(+ (* b b) (* (* c a) -4))
6.0ms	(sqrt (+ (* b b) (* (* c a) -4)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (sqrt (+ (* b b) (* (* c a) -4))) b) a)
106.0ms	(- (sqrt (+ (* b b) (* (* c a) -4))) b)
48.0ms	(+ (* b b) (* (* c a) -4))
93.0ms	(sqrt (+ (* b b) (* (* c a) -4)))

simplify1.6s

Counts

99 → 99

Iterations

Iter	Nodes
3	4209
2	1190
1	410
0	161

prune896.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

regimes329.0ms

Accuracy

84.3% (4.4b remaining)

Error of 10.3b against oracle of 5.9b and baseline of 34.0b

bsearch198.0ms

Steps

Iters	Range		Point
9	2.5177836961106285e-119	1.1213560046341023e-113	7.296044290893796e-114
7	-4.611849920572465e+95	-3.3021145473587595e+93	-3.7622181721724994e+94

simplify12.0ms

Iterations

Iter	Nodes
2	35
1	35
0	29

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.4s	1091×	body	2560	valid
1.1s	5839×	body	80	valid
727.0ms	912×	body	1280	valid
662.0ms	461×	body	640	valid
442.0ms	2909×	body	80	nan
130.0ms	126×	body	5120	valid
92.0ms	226×	body	320	valid
25.0ms	98×	body	160	valid