Details

sample77.0ms

Algorithm

intervals

Results

26.0ms	83×	body	1280	valid
15.0ms	70×	body	640	valid
12.0ms	245×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	19×	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))

rewrite17.0ms

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)))
10.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series374.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma a1 a1 (* a2 a2))
111.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
222.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

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

prune181.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.3b	(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
0.4b	(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
93×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
25×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`associate-/r/` `fma-udef`

Counts

3 → 159

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
9.0ms	(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
4.0ms	(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

series342.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma a1 a1 (* a2 a2))
219.0ms	(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
83.0ms	(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	480	1844
1	2233	1642
2	5001	1633

prune430.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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-r`
10×	`associate-l` `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:

7.0ms	(/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
4.0ms	(* (cos th) (hypot a1 a2))
6.0ms	(/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0)))
16.0ms	(* (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

384.0ms	(/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
113.0ms	(* (cos th) (hypot a1 a2))
445.0ms	(/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0)))
212.0ms	(* (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (cos th) (hypot a1 a2)) (cbrt (sqrt 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	522	1672
1	2617	1363
2	5001	1268

prune414.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
44×	`add-cbrt-cube`
24×	`prod-exp` `cbrt-unprod`
18×	`add-sqr-sqrt`
17×	`cbrt-undiv` `div-exp`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`cbrt-prod`
11×	`pow1`
10×	`associate-l` `associate-/r*`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`associate-/l/` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

7.0ms	(/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
4.0ms	(* (cos th) (hypot a1 a2))
12.0ms	(* (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cos th) (hypot a1 a2)))
14.0ms	(/ (* (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cos th) (hypot a1 a2))) (cbrt (sqrt 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

583.0ms	(/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
107.0ms	(* (cos th) (hypot a1 a2))
605.0ms	(* (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cos th) (hypot a1 a2)))
215.0ms	(/ (* (/ (hypot a1 a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cos th) (hypot a1 a2))) (cbrt (sqrt 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	487	1735
1	2350	1349
2	5002	1197

prune348.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes170.0ms

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	15	14
1	15	14

end0.0ms

sample2.2s

Algorithm

intervals

Results

812.0ms	2508×	body	1280	valid
436.0ms	2039×	body	640	valid
403.0ms	8067×	body	80	valid
172.0ms	1110×	body	320	valid
61.0ms	547×	body	160	valid