Details

sample74.0ms

Algorithm

intervals

Results

22.0ms	74×	body	1280	valid
13.0ms	278×	body	80	valid
13.0ms	62×	body	640	valid
4.0ms	28×	body	320	valid
2.0ms	16×	body	160	valid

simplify19.0ms

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

localize15.0ms

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))

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))

series348.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma a1 a1 (* a2 a2))
103.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
206.0ms	(/ (* (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

prune190.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))) (* (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)))

rewrite60.0ms

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))
9.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
20.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
26.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series986.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma a1 a1 (* a2 a2))
103.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
639.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
206.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	491	2250
1	2535	1935
2	5001	1905

prune446.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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 (cbrt (sqrt 2.0))))
0.2b	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
180×	`cbrt-prod`
171×	`times-frac`
117×	`add-sqr-sqrt`
100×	`div-exp`
97×	`prod-exp`
83×	`*-un-lft-identity`
78×	`add-cube-cbrt`
77×	`add-cbrt-cube`
67×	`associate-r`
52×	`cbrt-undiv`
45×	`cbrt-unprod`
36×	`sqrt-prod`
29×	`div-inv`
16×	`unswap-sqr`
13×	`associate-/r*`
12×	`rec-exp` `1-exp`
10×	`associate-l`
8×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-r/` `associate-l/` `associate-/l/`

Counts

4 → 305

Calls

4 calls:

11.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
27.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
129.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
21.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series2.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
994.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
217.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
640.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1331	7346
1	5001	6415

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize23.0ms

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

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

265×	`add-exp-log`
143×	`prod-exp`
89×	`add-cbrt-cube`
76×	`div-exp`
65×	`cbrt-unprod`
38×	`cbrt-undiv`
16×	`add-sqr-sqrt`
14×	`rec-exp` `1-exp`
10×	`-un-lft-identity` `associate-l*`
9×	`add-cube-cbrt`
8×	`pow1` `associate-r`
7×	`times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef` `div-inv`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `frac-2neg` `distribute-lft-in` `associate-r/` `associate-l/` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 158

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
9.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
152.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))))
34.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma a1 a1 (* a2 a2))
100.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
215.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))))
810.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	768	3735
1	4299	2672
2	5002	2311

prune331.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes224.0ms

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	23	23
1	23	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

812.0ms	2632×	body	1280	valid
421.0ms	2029×	body	640	valid
386.0ms	8090×	body	80	valid
155.0ms	1086×	body	320	valid
56.0ms	545×	body	160	valid