Details

sample116.0ms

Algorithm

intervals

Results

29.0ms	256×	pre	80	true
19.0ms	196×	body	80	valid
14.0ms	23×	body	2560	valid
6.0ms	12×	body	1280	valid
6.0ms	18×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify147.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	48
4	48
3	46
2	40
1	28
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize97.0ms

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))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`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×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `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 → 96

Calls

4 calls:

123.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
72.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
116.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

409.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
106.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
86.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify4.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	2804
2	898
1	316
0	149

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize159.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.9b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite641.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 140

Calls

4 calls:

337.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
186.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
50.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
141.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
93.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify4.2s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
3	2557
2	854
1	332
0	150

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.2b

localize183.0ms

Local error

Found 4 expressions with local error:

15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
77.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
82.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
74.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify6.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
5	4365
4	1823
3	781
2	307
1	109
0	45

prune950.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.2b

localize213.0ms

Local error

Found 4 expressions with local error:

15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
72.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
72.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
72.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify6.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
5	4365
4	1823
3	781
2	307
1	109
0	45

prune853.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.2b

regimes664.0ms

Accuracy

79.3% (0.4b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 14.9b

bsearch109.0ms

Steps

Iters	Range		Point
9	-1.364866253197098e+16	-766263838.6542622	-6278403065.98233

simplify17.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample2.1s

Algorithm

intervals

Results

736.0ms	6029×	body	80	valid
444.0ms	745×	body	2560	valid
250.0ms	620×	body	1280	valid
209.0ms	8000×	pre	80	true
140.0ms	325×	body	640	valid
57.0ms	59×	body	5120	valid
31.0ms	157×	body	320	valid
9.0ms	65×	body	160	valid