Details

sample201.0ms

Algorithm

intervals

Results

72.0ms	140×	body	160	valid
62.0ms	111×	body	320	valid
44.0ms	257×	body	80	nan
1.0ms	5×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.4b

localize49.0ms

Local error

Found 4 expressions with local error:

7.3b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.7b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.6b	(sqrt (- (* g g) (* h h)))
30.6b	(sqrt (- (* g g) (* h h)))

rewrite128.0ms

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:

59.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
480.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
55.0ms	(sqrt (- (* g g) (* h h)))
73.0ms	(sqrt (- (* g g) (* h h)))

simplify4.5s

Counts

84 → 84

Iterations

Iter	Nodes
3	4638
2	1243
1	407
0	171

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.3b

localize90.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.6b	(sqrt (- (* g g) (* h h)))
30.6b	(sqrt (- (* g g) (* h h)))

rewrite104.0ms

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:

8.0ms	(- (* g g) (* h h))
49.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series971.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
409.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
58.0ms	(sqrt (- (* g g) (* h h)))
466.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

85 → 85

Iterations

Iter	Nodes
3	4228
2	1081
1	341
0	146

prune1.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 29.6b

localize62.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.6b	(sqrt (- (* g g) (* h h)))
30.6b	(sqrt (- (* g g) (* h h)))

rewrite111.0ms

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:

16.0ms	(- (* g g) (* h h))
55.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
446.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

85 → 85

Iterations

Iter	Nodes
3	4228
2	1081
1	341
0	146

prune1.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 29.6b

localize55.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.3b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.6b	(sqrt (- (* g g) (* h h)))
30.6b	(sqrt (- (* g g) (* h h)))

rewrite87.0ms

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:

8.0ms	(- (* g g) (* h h))
40.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
393.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
80.0ms	(sqrt (- (* g g) (* h h)))
75.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

85 → 85

Iterations

Iter	Nodes
3	3949
2	1028
1	321
0	145

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 29.6b

regimes1.6s

Accuracy

55% (1.6b remaining)

Error of 31.1b against oracle of 29.4b and baseline of 33.1b

bsearch356.0ms

Steps

Iters	Range		Point
10	-3.4322081486421384e-167	-6.3154320628549744e-177	-3.385095528440214e-167

simplify14.0ms

Iterations

Iter	Nodes
2	39
1	39
0	31

end0.0ms

sample7.7s

Algorithm

intervals

Results

2.6s	3722×	body	320	valid
2.6s	8027×	body	80	nan
2.0s	4141×	body	160	valid
25.0ms	137×	body	80	valid