Details

sample122.0ms

Algorithm

intervals

Results

47.0ms	306×	body	80	nan
31.0ms	131×	body	320	valid
18.0ms	122×	body	160	valid
0.0ms	3×	body	80	valid

simplify13.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	314	36
4	633	36
5	1023	36
6	1325	36
7	1628	36
8	2988	36
done	5001	36

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize25.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite520.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `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:

35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
43.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
421.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

459.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
465.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
88.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	172	1528
1	402	1345
2	1358	1225
done	5001	1180

prune700.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 34.6b

localize57.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
6.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `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:

22.0ms	(- (* g g) (* h h))
68.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
22.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
530.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
77.0ms	(sqrt (- (* g g) (* h h)))
82.0ms	(sqrt (- (* g g) (* h h)))

simplify3.4s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	146	1220
1	334	1078
2	1124	960
3	4776	938
done	5000	938

prune741.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.0b

localize61.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

14.0ms	(- (* g g) (* h h))
9.0ms	(- (* g g) (* h h))
11.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
51.0ms	(- (* g g) (* h h))
71.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

82 → 82

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	62	912
1	132	824
2	347	722
3	1112	722
done	5001	712

prune621.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.0b

localize31.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

14.0ms	(- (* g g) (* h h))
14.0ms	(- (* g g) (* h h))
26.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* g g) (* h h))
52.0ms	(- (* g g) (* h h))
82.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	62	912
1	132	824
2	347	722
3	1112	722
done	5001	712

prune436.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 34.0b

regimes831.0ms

Accuracy

67.3% (1.2b remaining)

Error of 31.9b against oracle of 30.8b and baseline of 34.3b

bsearch319.0ms

Steps

Iters	Range		Point
12	-8.46579077171639e-185	-2.054593841555946e-229	-8.359356862874829e-185

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	84
1	42	84
done	42	84

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.8s	3717×	body	320	valid
1.3s	4133×	body	160	valid
1.0s	8068×	body	80	nan
15.0ms	150×	body	80	valid