Details

sample137.0ms

Algorithm

intervals

Results

42.0ms	128×	body	320	valid
40.0ms	236×	body	80	nan
25.0ms	123×	body	160	valid
0.0ms	5×	body	80	valid

simplify5.0s

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: 33.1b

localize65.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite109.0ms

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:

27.0ms	(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))))))
17.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

418.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
380.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
64.0ms	(sqrt (- (* g g) (* h h)))
63.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1507
1	415
0	172

prune931.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.4b

localize79.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite57.0ms

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

Counts

4 → 69

Calls

4 calls:

11.0ms	(- (* g g) (* h h))
26.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* g g) (* h h))
445.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
70.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1672
1	358
0	146

prune879.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.3b

localize96.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite80.0ms

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`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
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))
31.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
16.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series669.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
477.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
65.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1672
1	358
0	146

prune1.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.3b

localize73.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite96.0ms

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:

6.0ms	(- (* g g) (* h h))
43.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
27.0ms	(sqrt (- (* g g) (* h h)))

series638.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
455.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
71.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1610
1	336
0	144

prune754.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.1b

regimes1.7s

Accuracy

51.5% (1.8b remaining)

Error of 31.6b against oracle of 29.8b and baseline of 33.5b

bsearch263.0ms

Steps

Iters	Range		Point
9	-3.2336746362726576e-157	-4.961541153282132e-164	-3.572798755567818e-163

simplify11.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.6s	3756×	body	320	valid
1.5s	8091×	body	80	nan
1.3s	4076×	body	160	valid
17.0ms	168×	body	80	valid