Details

sample66.0ms

Algorithm

intervals

Results

21.0ms	206×	body	80	valid
7.0ms	17×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	9×	body	2560	valid
3.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	40
4	40
3	38
2	34
1	27
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `pow-prod-down` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

52.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
42.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
43.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

435.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
79.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
110.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	2553
2	838
1	295
0	137

prune615.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `prod-exp` `flip-+`
3×	`sqrt-pow1` `associate-l` `associate-*r/`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `1-exp` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

5.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
70.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
37.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

472.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
108.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
123.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
84.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
3	4031
2	1181
1	410
0	161

prune509.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
6.6b	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log`
3×	`sqrt-prod`
2×	`flip3-+` `pow1/3` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x))))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(cbrt x)
260.0ms	(cbrt x)
112.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x))))))
71.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	2439
2	673
1	219
0	89

prune329.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.7b

localize59.0ms

Local error

Found 4 expressions with local error:

3.2b	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

5.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
18.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
20.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
65.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
65.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts

68 → 68

Iterations

Iter	Nodes
done	5003
3	2784
2	634
1	187
0	71

prune400.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

regimes209.0ms

Accuracy

0% (0.7b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 13.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

554.0ms	764×	body	2560	valid
420.0ms	6035×	body	80	valid
183.0ms	596×	body	1280	valid
126.0ms	8000×	pre	80	true
121.0ms	310×	body	640	valid
39.0ms	81×	body	160	valid
24.0ms	63×	body	5120	valid
23.0ms	151×	body	320	valid