Details

sample82.0ms

Algorithm

intervals

Results

30.0ms	94×	body	1280	valid
16.0ms	259×	body	80	valid
15.0ms	68×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	14×	body	160	valid

simplify21.0ms

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: 0.6b

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)))
0.6b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite12.0ms

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:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series389.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(fma a1 a1 (* a2 a2))
114.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
238.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (28.0ms)

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

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

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

rewrite33.0ms

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:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
10.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

242.0ms	(fma a1 a1 (* a2 a2))
112.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
228.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
696.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	491	2250
1	2535	1935
2	5002	1898

prune435.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.2b	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.4b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
7.0b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
56×	`times-frac`
40×	`add-cbrt-cube`
36×	`cbrt-prod` `add-sqr-sqrt`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`pow1` `associate-/r*`
6×	`associate-r` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `fma-udef` `hypot-def` `associate-/l/`

Counts

4 → 152

Calls

4 calls:

6.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
15.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
12.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
322.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
769.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
50.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify88.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	568	2920
1	3220	2380
2	5002	2274

prune498.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
36×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod` `prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp` `associate-l`
10×	`associate-r` `associate-/r*`
9×	`sqrt-prod`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 132

Calls

4 calls:

4.0ms	(* (cos th) (hypot a1 a2))
7.0ms	(/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
9.0ms	(/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0)))
15.0ms	(* (/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0))) (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (cos th) (hypot a1 a2))
423.0ms	(/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
466.0ms	(/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0)))
258.0ms	(* (/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0))) (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	502	1638
1	2450	1312
2	5002	1192

prune410.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	18	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

807.0ms	2514×	body	1280	valid
479.0ms	2107×	body	640	valid
422.0ms	8090×	body	80	valid
163.0ms	1057×	body	320	valid
62.0ms	549×	body	160	valid