Details

sample212.0ms

Algorithm

intervals

Results

87.0ms	95×	body	320	valid
46.0ms	157×	body	160	valid
31.0ms	230×	body	80	nan
1.0ms	4×	body	80	valid

simplify13.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	2543
7	1640
6	1310
5	984
4	595
3	287
2	124
1	44
0	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize94.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite190.0ms

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:

67.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
74.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
23.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series1.4s

Counts

4 → 12

Calls

4 calls:

610.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
611.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
101.0ms	(sqrt (- (* g g) (* h h)))
84.0ms	(sqrt (- (* g g) (* h h)))

simplify5.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	4954
2	1300
1	406
0	172

prune1.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.1b

localize109.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
5.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite138.0ms

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:

17.0ms	(- (* g g) (* h h))
75.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
23.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series851.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* g g) (* h h))
598.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
91.0ms	(sqrt (- (* g g) (* h h)))
91.0ms	(sqrt (- (* g g) (* h h)))

simplify4.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4084
2	1018
1	320
0	144

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize94.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
5.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite127.0ms

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:

16.0ms	(- (* g g) (* h h))
66.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
21.0ms	(sqrt (- (* g g) (* h h)))
22.0ms	(sqrt (- (* g g) (* h h)))

series892.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* g g) (* h h))
668.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
83.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify5.5s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4084
2	1018
1	320
0	144

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize113.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite191.0ms

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:

19.0ms	(- (* g g) (* h h))
119.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
25.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))

series849.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* g g) (* h h))
603.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
93.0ms	(sqrt (- (* g g) (* h h)))
98.0ms	(sqrt (- (* g g) (* h h)))

simplify5.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4483
2	1079
1	342
0	146

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.3b

regimes2.1s

Accuracy

63.8% (1.2b remaining)

Error of 32.2b against oracle of 31.0b and baseline of 34.2b

bsearch394.0ms

Steps

Iters	Range		Point
9	1.4626542713387867e-203	9.105897558526997e-196	8.889202414083867e-196

simplify24.0ms

Iterations

Iter	Nodes
done	48
1	48
0	37

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.2s	4154×	body	160	valid
2.1s	3697×	body	320	valid
1.9s	8039×	body	80	nan
20.0ms	149×	body	80	valid