Details

sample69.0ms

Algorithm

intervals

Results

18.0ms	210×	body	80	valid
12.0ms	23×	body	2560	valid
11.0ms	25×	body	1280	valid
7.0ms	84×	body	80	nan
3.0ms	8×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

200×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
72×	`times-frac`
58×	`difference-of-squares`
43×	`unswap-sqr`
39×	`associate-l` `add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-lft-out--`
21×	`associate-r`
13×	`*-commutative`
12×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`swap-sqr` `associate-/l*`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 195

Calls

4 calls:

1.3s	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
98.0ms	(- (* b b) (* (* 3 a) c))
749.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
142.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
80.0ms	(- (* b b) (* (* 3 a) c))
122.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
115.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.4s

Counts

207 → 207

Iterations

Iter	Nodes
done	5005
2	2387
1	792
0	291

prune891.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (+ (* -3 (* a c)) (* b b))) b) (* 3 a))
0.8b	(+ (* -3 (* a c)) (* b b))
1.0b	(- (sqrt (+ (* -3 (* a c)) (* b b))) b)
20.8b	(sqrt (+ (* -3 (* a c)) (* b b)))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
72×	`times-frac`
39×	`add-cube-cbrt`
29×	`associate-l`
28×	`difference-of-squares`
21×	`associate-r` `sqrt-prod`
14×	`distribute-lft-out--`
12×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-out` `add-log-exp`
7×	`*-commutative` `unswap-sqr`
6×	`associate-/l*`
5×	`pow1`
4×	`insert-posit16`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 160

Calls

4 calls:

1.7s	(/ (- (sqrt (+ (* -3 (* a c)) (* b b))) b) (* 3 a))
97.0ms	(+ (* -3 (* a c)) (* b b))
876.0ms	(- (sqrt (+ (* -3 (* a c)) (* b b))) b)
186.0ms	(sqrt (+ (* -3 (* a c)) (* b b)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (- (sqrt (+ (* -3 (* a c)) (* b b))) b) (* 3 a))
99.0ms	(+ (* -3 (* a c)) (* b b))
135.0ms	(- (sqrt (+ (* -3 (* a c)) (* b b))) b)
130.0ms	(sqrt (+ (* -3 (* a c)) (* b b)))

simplify1.7s

Counts

172 → 172

Iterations

Iter	Nodes
done	5001
2	1910
1	641
0	224

prune923.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* 3 a) (- (sqrt (+ (* -3 (* a c)) (* b b))) b))
0.8b	(+ (* -3 (* a c)) (* b b))
1.0b	(- (sqrt (+ (* -3 (* a c)) (* b b))) b)
20.8b	(sqrt (+ (* -3 (* a c)) (* b b)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
72×	`times-frac`
39×	`add-cube-cbrt`
29×	`associate-l`
28×	`difference-of-squares`
21×	`associate-r` `sqrt-prod`
14×	`distribute-lft-out--`
12×	`associate-/l*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-out` `add-log-exp`
7×	`*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`pow1`
4×	`insert-posit16`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `flip--`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 159

Calls

4 calls:

799.0ms	(/ (* 3 a) (- (sqrt (+ (* -3 (* a c)) (* b b))) b))
177.0ms	(+ (* -3 (* a c)) (* b b))
902.0ms	(- (sqrt (+ (* -3 (* a c)) (* b b))) b)
176.0ms	(sqrt (+ (* -3 (* a c)) (* b b)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (* 3 a) (- (sqrt (+ (* -3 (* a c)) (* b b))) b))
88.0ms	(+ (* -3 (* a c)) (* b b))
100.0ms	(- (sqrt (+ (* -3 (* a c)) (* b b))) b)
110.0ms	(sqrt (+ (* -3 (* a c)) (* b b)))

simplify1.8s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
2	2001
1	597
0	232

prune751.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a)
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
40×	`difference-of-squares`
36×	`unswap-sqr`
29×	`sqrt-prod`
18×	`times-frac` `associate-l`
17×	`distribute-lft-out--`
16×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`add-cbrt-cube` `swap-sqr` `add-exp-log` `-commutative` `associate-/l`
5×	`pow1`
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 → 130

Calls

4 calls:

1.4s	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a)
93.0ms	(- (* b b) (* (* 3 a) c))
740.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
158.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a)
58.0ms	(- (* b b) (* (* 3 a) c))
128.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.3s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	1426
1	484
0	206

prune584.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.5b

regimes529.0ms

Accuracy

82.5% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 33.1b

bsearch372.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.7543503512431287e-69
7	6.366271362828677e-80	2.0474353944207673e-78	1.0342433475418466e-79
8	1.9015403840268286e-125	4.787339246176752e-121	2.5044838769273558e-121
5	-2.006932639140506e+153	-7.01626841651273e+152	-1.3030622379606599e+153

simplify15.0ms

Iterations

Iter	Nodes
done	64
1	64
0	48

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.0s	908×	body	1280	valid
1.0s	1084×	body	2560	valid
840.0ms	5867×	body	80	valid
552.0ms	3007×	body	80	nan
289.0ms	446×	body	640	valid
89.0ms	101×	body	5120	valid
85.0ms	236×	body	320	valid
26.0ms	108×	body	160	valid