Details

sample241.0ms

Algorithm

intervals

Results

85.0ms	135×	body	160	valid
76.0ms	121×	body	320	valid
50.0ms	266×	body	80	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	2529
5	1599
4	844
3	368
2	117
1	45
0	19

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.4b

localize83.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite133.0ms

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` `insert-posit16` `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 → 72

Calls

4 calls:

31.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series902.0ms

Counts

4 → 12

Calls

4 calls:

405.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
368.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
65.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify4.6s

Counts

84 → 84

Iterations

Iter	Nodes
3	4819
2	1257
1	407
0	171

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 35.3b

localize63.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
9.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite119.0ms

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` `insert-posit16` `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 → 73

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
62.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* g g) (* h h))
443.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
86.0ms	(sqrt (- (* g g) (* h h)))
82.0ms	(sqrt (- (* g g) (* h h)))

simplify3.1s

Counts

85 → 85

Iterations

Iter	Nodes
3	3949
2	1028
1	321
0	145

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 34.6b

localize57.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
9.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite90.0ms

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` `insert-posit16` `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 → 73

Calls

4 calls:

17.0ms	(- (* g g) (* h h))
46.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
415.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
56.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify3.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	3949
2	1028
1	321
0	145

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 34.6b

localize65.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite70.0ms

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` `insert-posit16` `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 → 73

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
32.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* g g) (* h h))
399.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
58.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify2.8s

Counts

85 → 85

Iterations

Iter	Nodes
3	4228
2	1081
1	341
0	146

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.5b

regimes1.4s

Accuracy

56.1% (1.7b remaining)

Error of 31.3b against oracle of 29.6b and baseline of 33.4b

bsearch381.0ms

Steps

Iters	Range		Point
10	1.5957771751230817e-159	7.866015919465401e-146	7.3048056976364e-159

simplify40.0ms

Iterations

Iter	Nodes
2	40
1	40
0	33

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.0s	3651×	body	320	valid
2.4s	4188×	body	160	valid
1.7s	8074×	body	80	nan
31.0ms	161×	body	80	valid