Details

sample166.0ms

Algorithm

intervals

Results

74.0ms	77×	body	1280	valid
27.0ms	65×	body	640	valid
26.0ms	252×	body	80	valid
7.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid

simplify233.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	57	12
3	87	12
4	114	12
5	132	12
6	151	12
7	173	12
8	175	12
done	175	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
11.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
19.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series488.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma a1 a1 (* a2 a2))
173.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
274.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	103	947
1	216	911
2	1322	777
done	5000	775

prune294.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
36×	`add-exp-log` `cbrt-prod` `add-sqr-sqrt`
34×	`add-cube-cbrt` `*-un-lft-identity`
23×	`add-cbrt-cube`
18×	`sqrt-prod`
13×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `fma-udef`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 137

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
10.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
26.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
53.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma a1 a1 (* a2 a2))
150.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
884.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
335.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify1.8s

Counts

149 → 149

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	215	3852
1	502	3510
2	2743	3078
done	5000	3031

prune739.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
0.1b	(* (hypot a1 a2) (cos th))
0.4b	(/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
5.3b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `sqrt-prod`
9×	`associate-r`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `fma-udef` `hypot-def` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

37.0ms	(* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
20.0ms	(* (hypot a1 a2) (cos th))
55.0ms	(/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
3.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series938.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
150.0ms	(* (hypot a1 a2) (cos th))
395.0ms	(/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
80.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	137	1582
1	315	1450
2	1977	1021
done	5001	965

prune427.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot a1 a2) (cos th))
0.2b	(/ (* (hypot a1 a2) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
0.3b	(* (/ (* (hypot a1 a2) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-sqr-sqrt`
59×	`times-frac`
48×	`add-cube-cbrt` `*-un-lft-identity`
44×	`cbrt-prod`
43×	`add-cbrt-cube`
34×	`associate-r`
23×	`prod-exp` `cbrt-unprod`
22×	`sqrt-prod`
18×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`pow1` `associate-l`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 170

Calls

4 calls:

24.0ms	(* (hypot a1 a2) (cos th))
38.0ms	(/ (* (hypot a1 a2) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
10.0ms	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
98.0ms	(* (/ (* (hypot a1 a2) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (hypot a1 a2) (cos th))
668.0ms	(/ (* (hypot a1 a2) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
399.0ms	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
289.0ms	(* (/ (* (hypot a1 a2) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

simplify565.0ms

Counts

182 → 182

Iterations

Useful iterations: done (557.0ms)

Iter	Nodes	Cost
0	240	3751
1	668	3557
done	5000	2925

prune791.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes288.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	14	21
done	14	21

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.5s	2519×	body	1280	valid
1.1s	7835×	body	80	valid
992.0ms	2110×	body	640	valid
455.0ms	1010×	body	320	valid
104.0ms	527×	body	160	valid