Details

sample93.0ms

Algorithm

intervals

Results

28.0ms	186×	body	80	valid
21.0ms	39×	body	2560	valid
12.0ms	29×	body	1280	valid
8.0ms	90×	body	80	nan
3.0ms	10×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify113.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.0b	(- (* b b) (* (* 3 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

28.0ms	(* (* 3 a) c)
15.0ms	(- (* b b) (* (* 3 a) c))
70.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 3 a) c)
59.0ms	(- (* b b) (* (* 3 a) c))
99.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
98.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.7s

Counts

76 → 76

Iterations

Iter	Nodes
3	3323
2	951
1	295
0	123

prune843.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a c) 3)
1.0b	(- (* b b) (* (* a c) 3))
1.3b	(- (sqrt (- (* b b) (* (* a c) 3))) b)
21.7b	(sqrt (- (* b b) (* (* a c) 3)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

15.0ms	(* (* a c) 3)
9.0ms	(- (* b b) (* (* a c) 3))
39.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
8.0ms	(sqrt (- (* b b) (* (* a c) 3)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* a c) 3)
59.0ms	(- (* b b) (* (* a c) 3))
102.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
99.0ms	(sqrt (- (* b b) (* (* a c) 3)))

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
3	3341
2	922
1	296
0	123

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* a c) (sqrt 3)) (sqrt 3))
1.0b	(- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3)))
1.3b	(- (sqrt (- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3)))) b)
21.7b	(sqrt (- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt` `sqrt-prod`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 70

Calls

4 calls:

62.0ms	(* (* (* a c) (sqrt 3)) (sqrt 3))
8.0ms	(- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3)))
39.0ms	(- (sqrt (- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3)))) b)
8.0ms	(sqrt (- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3))))

series827.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (* (* a c) (sqrt 3)) (sqrt 3))
174.0ms	(- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3)))
274.0ms	(- (sqrt (- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3)))) b)
272.0ms	(sqrt (- (* b b) (* (* (* a c) (sqrt 3)) (sqrt 3))))

simplify4.4s

Counts

82 → 82

Iterations

Iter	Nodes
3	5358
2	1240
1	346
0	140

prune951.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.9b

localize54.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

37.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
35.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
117.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
88.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
103.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify879.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2023
2	606
1	189
0	82

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.8b

regimes646.0ms

Accuracy

84.1% (3.6b remaining)

Error of 14.7b against oracle of 11.1b and baseline of 33.7b

bsearch174.0ms

Steps

Iters	Range		Point
5	1.4610887943711312e+25	4.899560055505696e+25	1.487621333916267e+25
10	-1.0499721897563905e+163	-8.354690034354516e+151	-4.898678560179045e+152

simplify12.0ms

Iterations

Iter	Nodes
2	38
1	38
0	31

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	1107×	body	2560	valid
1.0s	5846×	body	80	valid
644.0ms	933×	body	1280	valid
380.0ms	2917×	body	80	nan
279.0ms	455×	body	640	valid
136.0ms	211×	body	320	valid
95.0ms	111×	body	5120	valid
26.0ms	111×	body	160	valid