Details

sample124.0ms

Algorithm

intervals

Results

40.0ms	268×	body	80	nan
31.0ms	113×	body	320	valid
22.0ms	137×	body	160	valid
1.0ms	6×	body	80	valid

simplify13.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize44.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
92.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
13.0ms	(sqrt (- (* g g) (* h h)))
28.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

406.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
472.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
63.0ms	(sqrt (- (* g g) (* h h)))
75.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

80 → 80

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	183	1500
1	403	1315
2	1363	1211
done	5000	1166

prune583.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 29.8b

localize32.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite114.0ms

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` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `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:

17.0ms	(- (* g g) (* h h))
57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
472.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
74.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune548.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.3b

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite82.0ms

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` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `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:

10.0ms	(- (* g g) (* h h))
37.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* g g) (* h h))
418.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
69.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune776.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize48.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite79.0ms

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))
15.0ms	(- (* g g) (* h h))
29.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* g g) (* h h))
40.0ms	(- (* g g) (* h h))
72.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: done (1.4s)

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

prune600.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.2b

regimes1.0s

Accuracy

74% (0.9b remaining)

Error of 31.6b against oracle of 30.6b and baseline of 34.2b

bsearch305.0ms

Steps

Iters	Range		Point
12	1.5968211558387336e-179	3.1402162042760483e-109	8.436549254635571e-159

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	94
1	43	94
done	43	94

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.8s	3770×	body	320	valid
1.3s	4087×	body	160	valid
925.0ms	7820×	body	80	nan
14.0ms	143×	body	80	valid