Details

sample84.0ms

Algorithm

intervals

Results

29.0ms	82×	body	1280	valid
14.0ms	68×	body	640	valid
13.0ms	272×	body	80	valid
6.0ms	37×	body	320	valid
1.0ms	13×	body	160	valid

simplify170.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	57	12
3	87	12
4	114	12
5	132	12
6	150	12
7	170	12
8	172	12
done	172	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite24.0ms

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))
9.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series519.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a1 a1 (* a2 a2))
261.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
224.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	103	947
1	201	911
2	750	777
3	3465	759
done	5000	758

prune188.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
0.1b	(* (hypot a2 a1) (cos th))
0.4b	(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
6.7b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite65.0ms

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:

26.0ms	(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
9.0ms	(* (hypot a2 a1) (cos th))
26.0ms	(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
104.0ms	(* (hypot a2 a1) (cos th))
258.0ms	(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
45.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	137	1582
1	301	1450
2	1081	967
done	5000	965

prune290.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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`
2×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `*-commutative` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
9.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
18.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
30.0ms	(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma a1 a1 (* a2 a2))
100.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
545.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
186.0ms	(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify727.0ms

Counts

147 → 147

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	212	3820
1	463	3478
2	1689	2994
done	5000	2977

prune393.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (fma a1 a1 (* a2 a2)) (cos th))
0.3b	(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
0.4b	(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
9.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
32.0ms	(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
30.0ms	(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

series752.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma a1 a1 (* a2 a2))
99.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
473.0ms	(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
146.0ms	(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

simplify970.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (175.0ms)

Iter	Nodes	Cost
0	177	1965
1	372	1866
2	1328	1608
done	5000	1608

prune350.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes255.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	19	18
done	19	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

802.0ms	2546×	body	1280	valid
448.0ms	2117×	body	640	valid
391.0ms	8036×	body	80	valid
164.0ms	1047×	body	320	valid
60.0ms	561×	body	160	valid