Details

sample136.0ms

Algorithm

intervals

Results

51.0ms	119×	body	320	valid
26.0ms	125×	body	160	valid
25.0ms	277×	body	80	nan
1.0ms	12×	body	80	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4870
7	2196
6	1617
5	1088
4	640
3	315
2	125
1	44
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize79.0ms

Local error

Found 4 expressions with local error:

9.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.5b	(sqrt (- (* g g) (* h h)))
32.5b	(sqrt (- (* g g) (* h h)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

48.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
54.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series944.0ms

Counts

4 → 12

Calls

4 calls:

366.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
448.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
68.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1506
1	415
0	172

prune914.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 34.3b

localize107.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.5b	(sqrt (- (* g g) (* h h)))
32.5b	(sqrt (- (* g g) (* h h)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
58.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
17.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* g g) (* h h))
437.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
67.0ms	(sqrt (- (* g g) (* h h)))
87.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1610
1	336
0	144

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.1b

localize54.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.5b	(sqrt (- (* g g) (* h h)))
32.5b	(sqrt (- (* g g) (* h h)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

9.0ms	(- (* g g) (* h h))
30.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
22.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
750.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
57.0ms	(sqrt (- (* g g) (* h h)))
69.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1610
1	336
0	144

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.1b

localize151.0ms

Local error

Found 4 expressions with local error:

32.5b	(sqrt (- (* g g) (* h h)))
32.5b	(sqrt (- (* g g) (* h h)))
32.5b	(sqrt (- (* g g) (* h h)))
32.5b	(sqrt (- (* g g) (* h h)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
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` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

17.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))
87.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	1979
3	713
2	268
1	107
0	46

prune940.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.1b

regimes1.6s

Accuracy

49.5% (1.7b remaining)

Error of 32.6b against oracle of 30.9b and baseline of 34.2b

bsearch287.0ms

Steps

Iters	Range		Point
11	4.0786015123651703e-175	1.9402420999172678e-152	1.5784372908607257e-162

simplify8.0ms

Iterations

Iter	Nodes
done	45
1	45
0	36

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.9s	4096×	body	160	valid
1.6s	3746×	body	320	valid
1.0s	7955×	body	80	nan
16.0ms	158×	body	80	valid