Details

sample184.0ms

Algorithm

intervals

Results

72.0ms	157×	body	160	valid
42.0ms	95×	body	320	valid
30.0ms	230×	body	80	nan
1.0ms	4×	body	80	valid

simplify7.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
8	2118
7	1307
6	1071
5	849
4	542
3	270
2	121
1	43
0	19

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize82.0ms

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)))

rewrite179.0ms

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` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `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 → 60

Calls

4 calls:

57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series1.4s

Counts

4 → 12

Calls

4 calls:

574.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
609.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
80.0ms	(sqrt (- (* g g) (* h h)))
91.0ms	(sqrt (- (* g g) (* h h)))

simplify5.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5006
3	4543
2	1258
1	386
0	166

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.1b

localize122.0ms

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)))

rewrite136.0ms

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` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

21.0ms	(- (* g g) (* h h))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series877.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* g g) (* h h))
615.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
109.0ms	(sqrt (- (* g g) (* h h)))
94.0ms	(sqrt (- (* g g) (* h h)))

simplify5.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	3860
2	990
1	304
0	135

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize110.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`sqrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-log-exp`
5×	`cbrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `cbrt-div` `times-frac` `pow1/3` `diff-log` `div-inv`

Counts

4 → 59

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
88.0ms	(cbrt (/ (* 1.0 (- (+ (sqrt (- (* g g) (* h h))) g))) (* 2.0 a)))
18.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* g g) (* h h))
482.0ms	(cbrt (/ (* 1.0 (- (+ (sqrt (- (* g g) (* h h))) g))) (* 2.0 a)))
101.0ms	(sqrt (- (* g g) (* h h)))
92.0ms	(sqrt (- (* g g) (* h h)))

simplify3.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	2650
2	758
1	301
0	142

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.3b

localize126.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod` `*-un-lft-identity`
36×	`times-frac`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`sqrt-prod`
6×	`pow1` `distribute-lft-out` `add-log-exp`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`neg-mul-1` `flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `cbrt-div` `pow1/3` `diff-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

20.0ms	(- (* g g) (* h h))
79.0ms	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) a))
24.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* g g) (* h h))
475.0ms	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) a))
93.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify4.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5011
3	3464
2	974
1	442
0	237

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.3b

regimes2.6s

Accuracy

0% (1.7b remaining)

Error of 32.6b against oracle of 30.9b and baseline of 32.6b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.5s	4154×	body	160	valid
2.5s	8039×	body	80	nan
2.3s	3697×	body	320	valid
23.0ms	149×	body	80	valid