Details

sample198.0ms

Algorithm

intervals

Results

78.0ms	95×	body	320	valid
45.0ms	157×	body	160	valid
29.0ms	230×	body	80	nan
1.0ms	4×	body	80	valid

simplify13.6s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize103.0ms

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)))

rewrite182.0ms

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:

57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(sqrt (- (* g g) (* h h)))
25.0ms	(sqrt (- (* g g) (* h h)))

series1.4s

Counts

4 → 12

Calls

4 calls:

592.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
636.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
81.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify6.1s

Counts

80 → 80

Iterations

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

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.1b

localize120.0ms

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)))

rewrite143.0ms

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:

18.0ms	(- (* g g) (* h h))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* g g) (* h h))
594.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(sqrt (- (* g g) (* h h)))
100.0ms	(sqrt (- (* g g) (* h h)))

simplify5.2s

Counts

81 → 81

Iterations

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

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize106.0ms

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)))

rewrite159.0ms

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))
83.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* g g) (* h h))
653.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
88.0ms	(sqrt (- (* g g) (* h h)))
94.0ms	(sqrt (- (* g g) (* h h)))

simplify5.3s

Counts

81 → 81

Iterations

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

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize77.0ms

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)))

rewrite142.0ms

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))
77.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
21.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* g g) (* h h))
580.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
86.0ms	(sqrt (- (* g g) (* h h)))
101.0ms	(sqrt (- (* g g) (* h h)))

simplify5.3s

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

bsearch413.0ms

Steps

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

simplify23.0ms

Iterations

Iter	Nodes
done	48
1	48
0	37

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.6s	3697×	body	320	valid
2.3s	4154×	body	160	valid
1.6s	8039×	body	80	nan
21.0ms	149×	body	80	valid