Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	308×	body	80	nan
7.0ms	279×	body	80	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	5
1	51	4
2	86	4
3	126	4
4	151	4
5	169	4
6	185	4
7	187	4
8	187	4

prune7.0ms

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

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sqrt z) y x)
0.2b	(/ (* (fma (sqrt z) y x) 1.0) 2.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

1.0ms	(fma (sqrt z) y x)
4.0ms	(/ (* (fma (sqrt z) y x) 1.0) 2.0)

series137.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(fma (sqrt z) y x)
74.0ms	(/ (* (fma (sqrt z) y x) 1.0) 2.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	191	219
1	691	184
2	3882	184
3	5001	176

prune93.0ms

Filtered

39 candidates to 32 candidates (82.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	32	7	39
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Merged error: 0.3b

Counts

41 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sqrt z) y x)
0.5b	(/ (fma (sqrt z) y x) (sqrt 2.0))
0.7b	(* (/ (fma (sqrt z) y x) (sqrt 2.0)) (/ 1.0 (sqrt 2.0)))
1.0b	(/ 1.0 (sqrt 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
84×	`times-frac`
60×	`add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`unswap-sqr`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 167

Calls

4 calls:

1.0ms	(fma (sqrt z) y x)
4.0ms	(/ (fma (sqrt z) y x) (sqrt 2.0))
20.0ms	(* (/ (fma (sqrt z) y x) (sqrt 2.0)) (/ 1.0 (sqrt 2.0)))
4.0ms	(/ 1.0 (sqrt 2.0))

series525.0ms

Counts

4 → 10

Calls

4 calls:

62.0ms	(fma (sqrt z) y x)
165.0ms	(/ (fma (sqrt z) y x) (sqrt 2.0))
298.0ms	(* (/ (fma (sqrt z) y x) (sqrt 2.0)) (/ 1.0 (sqrt 2.0)))
0.0ms	(/ 1.0 (sqrt 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	599	1486
1	2513	1360
2	5002	1309

prune399.0ms

Filtered

177 candidates to 121 candidates (68.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	178	7	185

Merged error: 0.3b

Counts

185 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (fma (sqrt z) y x) (sqrt 2.0))
0.7b	(* (/ (fma (sqrt z) y x) (sqrt 2.0)) (/ (/ 1.0 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
1.0b	(/ 1.0 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1.0 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

1223×	`times-frac`
1213×	`sqrt-prod`
772×	`add-sqr-sqrt`
605×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-r`
39×	`unswap-sqr`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*` `div-inv`
22×	`associate-l`
14×	`cbrt-undiv` `div-exp`
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 → 800

Calls

4 calls:

4.0ms	(/ (fma (sqrt z) y x) (sqrt 2.0))
120.0ms	(* (/ (fma (sqrt z) y x) (sqrt 2.0)) (/ (/ 1.0 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
5.0ms	(/ 1.0 (sqrt (sqrt 2.0)))
19.0ms	(/ (/ 1.0 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series483.0ms

Counts

4 → 8

Calls

4 calls:

169.0ms	(/ (fma (sqrt z) y x) (sqrt 2.0))
313.0ms	(* (/ (fma (sqrt z) y x) (sqrt 2.0)) (/ (/ 1.0 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.0ms	(/ 1.0 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1.0 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify138.0ms

Algorithm

egg-herbie

Counts

808 → 808

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2130	11467
1	5001	9999

prune1.2s

Filtered

808 candidates to 323 candidates (40.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	807	1	808
Fresh	3	1	4
Picked	0	1	1
Done	0	2	2
Total	810	5	815

Merged error: 0.3b

Counts

815 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sqrt z) y x)
0.3b	(* (fma (sqrt z) y x) (/ 1.0 (sqrt (sqrt 2.0))))
0.5b	(/ (* (fma (sqrt z) y x) (/ 1.0 (sqrt (sqrt 2.0)))) (pow (sqrt (sqrt 2.0)) 3))
1.0b	(/ 1.0 (sqrt (sqrt 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
81×	`times-frac`
71×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
35×	`add-exp-log`
33×	`associate-/r*`
31×	`associate-r`
20×	`add-cbrt-cube`
18×	`unpow-prod-down` `cube-prod`
14×	`div-exp`
8×	`prod-exp`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `associate-l` `pow-exp` `div-inv`
2×	`cube-mult` `frac-2neg` `unpow3` `associate-*r/` `clear-num` `sqr-pow`
1×	`pow-prod-down` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 191

Calls

4 calls:

1.0ms	(fma (sqrt z) y x)
14.0ms	(* (fma (sqrt z) y x) (/ 1.0 (sqrt (sqrt 2.0))))
12.0ms	(/ (* (fma (sqrt z) y x) (/ 1.0 (sqrt (sqrt 2.0)))) (pow (sqrt (sqrt 2.0)) 3))
5.0ms	(/ 1.0 (sqrt (sqrt 2.0)))

series758.0ms

Counts

4 → 10

Calls

4 calls:

64.0ms	(fma (sqrt z) y x)
398.0ms	(* (fma (sqrt z) y x) (/ 1.0 (sqrt (sqrt 2.0))))
296.0ms	(/ (* (fma (sqrt z) y x) (/ 1.0 (sqrt (sqrt 2.0)))) (pow (sqrt (sqrt 2.0)) 3))
0.0ms	(/ 1.0 (sqrt (sqrt 2.0)))

simplify107.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	693	1897
1	3622	1596
2	5002	1517

prune382.0ms

Filtered

201 candidates to 110 candidates (54.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	201	5	206

Merged error: 0.3b

Counts

206 → 5

regimes102.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	4
1	10	4

end0.0ms

sample767.0ms

Algorithm

intervals

Results

227.0ms	8498×	body	80	valid
205.0ms	8505×	body	80	nan