Details

sample134.0ms

Algorithm

intervals

Results

51.0ms	96×	body	1280	valid
28.0ms	268×	body	80	valid
24.0ms	66×	body	640	valid
7.0ms	28×	body	320	valid
4.0ms	20×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	7
1	57	6
2	87	6
3	114	6
4	132	6
5	151	6
6	171	6
7	173	6
8	173	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

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))

rewrite10.0ms

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))
3.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series354.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma a1 a1 (* a2 a2))
110.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
211.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	205	467
1	1002	399
2	5001	393

prune183.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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

rewrite36.0ms

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:

0.0ms	(fma a1 a1 (* a2 a2))
3.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
15.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma a1 a1 (* a2 a2))
107.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
218.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
299.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	626	3262
1	2999	2821
2	5001	2819

prune476.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
72×	`sqrt-prod`
45×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
15×	`div-inv`
13×	`cbrt-undiv` `div-exp` `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 → 155

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
3.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
12.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

series1.8s

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma a1 a1 (* a2 a2))
302.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
560.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
906.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

simplify95.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	618	3150
1	3360	2859
2	5003	2841

prune554.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))))
1.0b	(cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

1301×	`times-frac`
944×	`sqrt-prod`
687×	`cbrt-prod`
512×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
139×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
45×	`associate-/l*`
28×	`cbrt-undiv` `div-exp`
23×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`pow1/3`

Counts

4 → 768

Calls

4 calls:

7.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
37.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
11.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))))
4.0ms	(cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series2.6s

Counts

4 → 10

Calls

4 calls:

562.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
903.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
1.1s	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))))
0.0ms	(cbrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify245.0ms

Algorithm

egg-herbie

Counts

778 → 778

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2135	31537
1	5001	30728

prune3.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes184.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	24
1	23	24

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	2538×	body	1280	valid
840.0ms	7998×	body	80	valid
773.0ms	2117×	body	640	valid
293.0ms	1056×	body	320	valid
96.0ms	485×	body	160	valid