Details

sample174.0ms

Algorithm

intervals

Results

58.0ms	127×	body	160	valid
55.0ms	126×	body	320	valid
37.0ms	257×	body	80	nan
1.0ms	3×	body	80	valid

simplify911.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	1243
3	370
2	119
1	47
0	19

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.3b

localize67.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
10.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite137.0ms

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:

42.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
23.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

420.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
374.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
61.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify901.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	2002
2	1274
1	408
0	171

prune734.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.8b

localize62.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
10.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite65.0ms

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:

11.0ms	(- (* g g) (* h h))
33.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* g g) (* h h))
367.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
73.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify742.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2002
2	1042
1	322
0	145

prune787.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.3b

localize91.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
10.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite85.0ms

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:

14.0ms	(- (* g g) (* h h))
33.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* g g) (* h h))
418.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
73.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify892.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2002
2	1042
1	322
0	145

prune743.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.3b

localize64.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
8.3b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite83.0ms

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))
52.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
383.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
59.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify845.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2006
2	1111
1	342
0	146

prune525.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.3b

regimes1.2s

Accuracy

63.3% (1.3b remaining)

Error of 30.5b against oracle of 29.2b and baseline of 32.8b

bsearch324.0ms

Steps

Iters	Range		Point
10	-1.0781370330403964e-148	-1.0357331721752398e-162	-1.2129274808481617e-158

simplify15.0ms

Iterations

Iter	Nodes
done	48
1	48
0	36

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.9s	3756×	body	320	valid
1.9s	8161×	body	80	nan
1.7s	4087×	body	160	valid
25.0ms	157×	body	80	valid