Details

sample66.0ms

Algorithm

intervals

Results

19.0ms	116×	body	320	valid
14.0ms	137×	body	160	valid
13.0ms	268×	body	80	nan
0.0ms	3×	body	80	valid

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	122	36
3	298	36
4	575	36
5	888	36
6	1140	36
7	1414	36
8	2884	36
done	5000	36

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize22.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

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:

17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
21.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
327.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
46.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify803.0ms

Counts

80 → 80

Iterations

Useful iterations: done (801.0ms)

Iter	Nodes	Cost
0	183	1500
1	403	1315
2	1335	1211
done	5000	1165

prune433.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 36.0b

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

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:

3.0ms	(- (* g g) (* h h))
18.0ms	(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)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
329.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify758.0ms

Counts

81 → 81

Iterations

Useful iterations: done (756.0ms)

Iter	Nodes	Cost
0	144	1220
1	313	1079
2	1107	975
done	5000	953

prune469.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 35.4b

localize21.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* g g) (* h h))
5.4b	(- (* g g) (* h h))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(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)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
36.0ms	(- (* g g) (* h h))
46.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

82 → 82

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	62	912
1	134	824
2	426	722
3	1689	722
done	5000	720

prune489.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 35.4b

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms

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:

3.0ms	(- (* g g) (* h h))
19.0ms	(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)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
301.0ms	(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)))

simplify756.0ms

Counts

81 → 81

Iterations

Useful iterations: done (754.0ms)

Iter	Nodes	Cost
0	144	1220
1	313	1079
2	1107	975
done	5000	953

prune370.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 35.4b

regimes655.0ms

Accuracy

67% (1.2b remaining)

Error of 31.7b against oracle of 30.6b and baseline of 34.1b

bsearch154.0ms

Steps

Iters	Range		Point
8	8.449989266088164e-213	2.3113180137991623e-210	2.2872650708578154e-210

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	72
1	38	72
done	38	72

end0.0ms

sample1.9s

Algorithm

intervals

Results

614.0ms	3756×	body	320	valid
449.0ms	4102×	body	160	valid
412.0ms	8037×	body	80	nan
8.0ms	142×	body	80	valid