Details

sample175.0ms

Algorithm

intervals

Results

51.0ms	113×	body	320	valid
41.0ms	137×	body	160	valid
38.0ms	268×	body	80	nan
1.0ms	6×	body	80	valid

simplify13.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	314	36
4	633	36
5	1023	36
6	1325	36
7	1628	36
8	2988	36
done	5001	36

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize24.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite162.0ms

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:

69.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
64.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series985.0ms

Counts

4 → 12

Calls

4 calls:

451.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
417.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
55.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	172	1528
1	402	1345
2	1359	1225
done	5000	1180

prune768.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 29.8b

localize39.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite110.0ms

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))
64.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
479.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
86.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify3.0s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune803.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.2b

localize42.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite96.0ms

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:

11.0ms	(- (* g g) (* h h))
59.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
499.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify3.4s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune745.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize33.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

15.0ms	(- (* g g) (* h h))
9.0ms	(- (* g g) (* h h))
23.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* g g) (* h h))
56.0ms	(- (* g g) (* h h))
69.0ms	(sqrt (- (* g g) (* h h)))
87.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

82 → 82

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	62	912
1	132	824
2	347	722
3	1112	722
done	5001	712

prune568.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.2b

Details

sample175.0ms

simplify13.9s

prune14.0ms

localize24.0ms

rewrite162.0ms

series985.0ms

simplify1.3s

prune768.0ms

localize39.0ms

rewrite110.0ms

series678.0ms

simplify3.0s

prune803.0ms

localize42.0ms

rewrite96.0ms

series676.0ms

simplify3.4s

prune745.0ms

localize33.0ms

rewrite68.0ms

series276.0ms

simplify1.5s

prune568.0ms

regimes34.0ms