Details

sample76.0ms

Algorithm

intervals

Results

20.0ms	114×	body	320	valid
19.0ms	301×	body	80	nan
17.0ms	139×	body	160	valid
0.0ms	3×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	122	36
3	301	36
4	574	36
5	885	36
6	1154	36
7	1428	36
8	2979	36
done	5000	36

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize17.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(sqrt (- (* g g) (* h h)))

rewrite44.0ms

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:

17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series700.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify461.0ms

Counts

80 → 80

Iterations

Useful iterations: done (459.0ms)

Iter	Nodes	Cost
0	172	1528
1	407	1345
2	1427	1225
done	5000	1194

prune433.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 34.3b

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(sqrt (- (* g g) (* h h)))

rewrite30.0ms

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:

3.0ms	(- (* g g) (* h h))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
308.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
47.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify472.0ms

Counts

81 → 81

Iterations

Useful iterations: done (469.0ms)

Iter	Nodes	Cost
0	146	1220
1	347	1078
2	1309	960
done	5000	954

prune456.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 33.7b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

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:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
5.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
33.0ms	(- (* g g) (* h h))
45.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify947.0ms

Counts

82 → 82

Iterations

Useful iterations: done (944.0ms)

Iter	Nodes	Cost
0	62	912
1	136	824
2	471	722
3	1868	722
done	5001	720

prune458.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 33.7b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(sqrt (- (* g g) (* h h)))

rewrite17.0ms

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:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
48.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify996.0ms

Counts

82 → 82

Iterations

Useful iterations: done (994.0ms)

Iter	Nodes	Cost
0	62	912
1	136	824
2	471	722
3	1868	722
done	5001	720

prune588.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 33.7b

regimes587.0ms

Accuracy

23.7% (1.3b remaining)

Error of 31.8b against oracle of 30.5b and baseline of 32.2b

bsearch137.0ms

Steps

Iters	Range		Point
8	-2.6274238018146333e-186	-4.889467702331972e-190	-2.5831109636145956e-186

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	67
1	40	67
done	40	67

end0.0ms

sample2.0s

Algorithm

intervals

Results

676.0ms	3771×	body	320	valid
484.0ms	4061×	body	160	valid
437.0ms	8066×	body	80	nan
10.0ms	168×	body	80	valid