Details

sample245.0ms

Algorithm

intervals

Results

85.0ms	78×	body	640	valid
59.0ms	80×	body	1280	valid
31.0ms	260×	body	80	valid
17.0ms	46×	body	320	valid
4.0ms	15×	body	160	valid

simplify305.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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))

rewrite41.0ms

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))
16.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
22.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series701.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma a1 a1 (* a2 a2))
222.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
406.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: done (1.8s)

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

prune597.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

234×	`sqrt-prod`
216×	`times-frac`
96×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`associate-/l*`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 225

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
18.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
54.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
30.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma a1 a1 (* a2 a2))
225.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
435.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
595.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify2.6s

Counts

237 → 237

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	269	5586
1	640	4970
2	3360	4599
done	5000	4496

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
0.1b	(* (cos th) (pow a2 2))
0.3b	(/ (pow a1 2) (sqrt 2.0))
0.3b	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
49×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`unpow-prod-down`
24×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`associate-/r*`
9×	`associate-/l*` `unpow2` `sqr-pow`
8×	`associate-r`
7×	`div-exp`
6×	`prod-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `pow-to-exp` `associate-l` `pow-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod` `div-inv`
1×	`*-commutative` `fma-udef`

Counts

4 → 148

Calls

4 calls:

1.0ms	(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
32.0ms	(* (cos th) (pow a2 2))
17.0ms	(/ (pow a1 2) (sqrt 2.0))
26.0ms	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series865.0ms

Counts

4 → 12

Calls

4 calls:

468.0ms	(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
84.0ms	(* (cos th) (pow a2 2))
118.0ms	(/ (pow a1 2) (sqrt 2.0))
196.0ms	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify2.7s

Counts

160 → 160

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	229	2047
1	433	1858
2	2422	1631
done	5000	1630

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

2118×	`times-frac`
1737×	`sqrt-prod`
865×	`add-sqr-sqrt`
863×	`add-cube-cbrt` `*-un-lft-identity`
468×	`cbrt-prod`
146×	`div-inv`
96×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
16×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num`
2×	`fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 1077

Calls

4 calls:

18.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
119.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (fabs (cbrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
25.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (fabs (cbrt (sqrt 2.0))))
41.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (fabs (cbrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

series4.0s

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
1.8s	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (fabs (cbrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
572.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (fabs (cbrt (sqrt 2.0))))
1.4s	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (fabs (cbrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

simplify2.8s

Counts

1089 → 1089

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	1103	44698
1	2684	41151
done	5000	40636

prune7.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes517.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	23
1	17	23
done	17	23

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.1s	2571×	body	1280	valid
1.9s	2103×	body	640	valid
1.4s	8065×	body	80	valid
1.1s	1055×	body	320	valid
177.0ms	496×	body	160	valid