Details

sample90.0ms

Algorithm

intervals

Results

31.0ms	76×	body	1280	valid
18.0ms	71×	body	640	valid
16.0ms	264×	body	80	valid
5.0ms	30×	body	320	valid
3.0ms	21×	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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (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))

series371.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma a1 a1 (* a2 a2))
116.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
219.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

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

prune188.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 0.0b

Counts

72 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b	(/ (/ (* (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)))

rewrite41.0ms

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))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
7.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma a1 a1 (* a2 a2))
115.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
223.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
317.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (57.0ms)

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

prune422.0ms

Filtered

237 candidates to 111 candidates (46.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	235	2	237
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	240	6	246

Merged error: 0b

Counts

246 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt` `times-frac`
110×	`sqrt-prod`
79×	`add-cube-cbrt` `*-un-lft-identity`
46×	`cbrt-prod`
40×	`associate-r`
38×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
15×	`cbrt-undiv` `div-exp`
13×	`associate-l`
10×	`unswap-sqr`
8×	`prod-exp` `cbrt-unprod`
7×	`associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`frac-times` `associate-r/` `associate-l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 223

Calls

4 calls:

4.0ms	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
14.0ms	(/ (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (fma a1 a1 (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))) (sqrt (sqrt 2.0)))
21.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (fma a1 a1 (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))))
6.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))

series2.1s

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
937.0ms	(/ (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (fma a1 a1 (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))) (sqrt (sqrt 2.0)))
784.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (fma a1 a1 (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))))
305.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))

simplify119.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	847	3500
1	4291	3066
2	5002	3014

prune954.0ms

Filtered

235 candidates to 156 candidates (66.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	235	6	241

Merged error: 0b

Counts

241 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

1537×	`times-frac`
1523×	`sqrt-prod`
910×	`add-sqr-sqrt`
769×	`add-cube-cbrt` `*-un-lft-identity`
394×	`cbrt-prod`
376×	`associate-r`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
30×	`div-inv`
24×	`associate-/r*`
14×	`cbrt-undiv` `div-exp`
13×	`associate-l`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 963

Calls

4 calls:

4.0ms	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
5.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
132.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
20.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

series1.6s

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
167.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
914.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
388.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

simplify209.0ms

Algorithm

egg-herbie

Counts

975 → 975

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2735	18824
1	5001	17960

prune2.2s

Filtered

975 candidates to 429 candidates (44.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	975	0	975
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	975	6	981

Merged error: 0b

Counts

981 → 6

regimes154.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	15
1	17	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

921.0ms	2516×	body	1280	valid
526.0ms	2098×	body	640	valid
482.0ms	7930×	body	80	valid
198.0ms	1057×	body	320	valid
70.0ms	546×	body	160	valid