Details

sample184.0ms

Algorithm

intervals

Results

60.0ms	66×	body	640	valid
53.0ms	85×	body	1280	valid
25.0ms	259×	body	80	valid
12.0ms	39×	body	320	valid
3.0ms	13×	body	160	valid

simplify282.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.5b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite44.0ms

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))
14.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
28.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series562.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma a1 a1 (* a2 a2))
172.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
348.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.2s

Counts

70 → 70

Iterations

Useful iterations: done (3.2s)

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

prune357.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (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)))

rewrite101.0ms

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)))
28.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
57.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma a1 a1 (* a2 a2))
153.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
988.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
327.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify1.1s

Counts

149 → 149

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	215	3852
1	473	3510
2	1760	3026
done	5001	3009

prune596.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

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)))

rewrite103.0ms

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))
13.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
50.0ms	(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
36.0ms	(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

series1.2s

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma a1 a1 (* a2 a2))
149.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
727.0ms	(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
203.0ms	(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: 2 (286.0ms)

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

prune579.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (cbrt (cbrt (sqrt 2.0))))
0.2b	(* (/ (cbrt (/ 1 2.0)) (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (cbrt (cbrt (sqrt 2.0)))))
1.0b	(cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
1.0b	(/ (cbrt (/ 1 2.0)) (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

245×	`times-frac`
206×	`cbrt-prod`
147×	`add-sqr-sqrt`
125×	`*-un-lft-identity`
123×	`add-cube-cbrt`
68×	`associate-l`
32×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`associate-/l*`
16×	`associate-r` `associate-/r*`
13×	`div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `cbrt-div` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 270

Calls

4 calls:

20.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (cbrt (cbrt (sqrt 2.0))))
119.0ms	(* (/ (cbrt (/ 1 2.0)) (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (cbrt (cbrt (sqrt 2.0)))))
8.0ms	(cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
17.0ms	(/ (cbrt (/ 1 2.0)) (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

series1.3s

Counts

4 → 8

Calls

4 calls:

595.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (cbrt (cbrt (sqrt 2.0))))
719.0ms	(* (/ (cbrt (/ 1 2.0)) (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (cbrt (cbrt (sqrt 2.0)))))
0.0ms	(cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.0ms	(/ (cbrt (/ 1 2.0)) (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

simplify1.7s

Counts

278 → 278

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	399	7377
1	925	7082
2	2568	6665
done	5000	6651

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes292.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	35
1	26	35
done	26	35

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.0s	2128×	body	640	valid
2.0s	2529×	body	1280	valid
1.0s	8050×	body	80	valid
386.0ms	1047×	body	320	valid
101.0ms	487×	body	160	valid