Details

analyze126.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

sample30.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
0.0ms	1×	body	80	nan

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4947	28
1	4947	28

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.3b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(* PI t)
0.3b	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
0.4b	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`flip3--` `sqrt-div` `associate-r` `associate-/r/` `flip--`
7×	`associate-l` `pow-prod-down`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
4.0ms	(* PI t)
18.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
11.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 5.0 (* v v))
2.0ms	(* PI t)
41.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
26.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify79.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4965	1908
1	4965	1908

prune255.0ms

Filtered

76 candidates to 106 candidates (-39.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Merged error: 0.1b

Counts

108 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.3b	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI (* t (sqrt 2.0))) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
0.3b	(* PI (* t (sqrt 2.0)))
0.4b	(* t (sqrt 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log` `add-cbrt-cube`
17×	`prod-exp` `cbrt-unprod`
16×	`pow1` `add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`associate-r/` `associate-r*` `associate-/r/`
7×	`flip3--` `pow-prod-down` `flip--`
6×	`sqrt-div`
5×	`cbrt-undiv` `div-exp`
4×	`frac-times` `sqrt-prod` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 97

Calls

4 calls:

5.0ms	(* 5.0 (* v v))
20.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI (* t (sqrt 2.0))) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
6.0ms	(* PI (* t (sqrt 2.0)))
6.0ms	(* t (sqrt 2.0))

series54.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 5.0 (* v v))
41.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI (* t (sqrt 2.0))) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
5.0ms	(* PI (* t (sqrt 2.0)))
4.0ms	(* t (sqrt 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4997	1818
1	4997	1818

prune238.0ms

Filtered

70 candidates to 109 candidates (-55.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Merged error: 0.1b

Counts

116 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* t (* PI (* (sqrt 2.0) (sqrt 1.0)))) (- 1.0 (* v v)))
0.2b	(* 5.0 (* v v))
0.3b	(/ (- 1.0 (* 5.0 (* v v))) (* (* t (* PI (* (sqrt 2.0) (sqrt 1.0)))) (- 1.0 (* v v))))
0.3b	(* t (* PI (* (sqrt 2.0) (sqrt 1.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
32×	`pow1`
29×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`associate-r`
5×	`cbrt-undiv` `div-exp`
4×	`associate-*r/` `add-log-exp`
3×	`flip3--` `times-frac` `-commutative` `flip--` `associate-/l`
2×	`sub-neg` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-sub` `clear-num` `associate-/r*` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

13.0ms	(* (* t (* PI (* (sqrt 2.0) (sqrt 1.0)))) (- 1.0 (* v v)))
5.0ms	(* 5.0 (* v v))
18.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* t (* PI (* (sqrt 2.0) (sqrt 1.0)))) (- 1.0 (* v v))))
9.0ms	(* t (* PI (* (sqrt 2.0) (sqrt 1.0))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* t (* PI (* (sqrt 2.0) (sqrt 1.0)))) (- 1.0 (* v v)))
3.0ms	(* 5.0 (* v v))
31.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* t (* PI (* (sqrt 2.0) (sqrt 1.0)))) (- 1.0 (* v v))))
11.0ms	(* t (* PI (* (sqrt 2.0) (sqrt 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5525	1808

prune190.0ms

Filtered

63 candidates to 113 candidates (-79.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	112	9	121

Merged error: 0.1b

Counts

121 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
0.5b	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
0.5b	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
0.6b	(* (cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))))) (cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

169×	`associate-*r/`
109×	`cbrt-prod`
56×	`associate-/r/`
42×	`flip3--` `sqrt-div` `flip--`
30×	`add-sqr-sqrt`
29×	`frac-times`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
18×	`swap-sqr` `associate-r` `associate-l`
15×	`associate-*l/`
11×	`pow1`
9×	`pow1/3`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 151

Calls

4 calls:

15.0ms	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
15.0ms	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
18.0ms	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
25.0ms	(* (cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))))) (cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
69.0ms	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
69.0ms	(cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))))))
97.0ms	(* (cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))))) (cbrt (/ (- 1.0 (* v (* v 5.0))) (* PI (* t (* (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4963	8241
1	4963	8241

prune1.5s

Filtered

150 candidates to 163 candidates (-8.7%)

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	156	16	172

Merged error: 0.0b

Counts

172 → 16

regimes690.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	140	28
1	140	28

end0.0ms

sample738.0ms

Algorithm

intervals

Results

570.0ms	8000×	body	80	valid
0.0ms	7×	body	80	nan
0.0ms	1×	body	80	invalid

Details

analyze126.0ms

sample30.0ms

simplify38.0ms

prune15.0ms

localize17.0ms

rewrite43.0ms

series73.0ms

simplify79.0ms

prune255.0ms

localize18.0ms

rewrite41.0ms

series54.0ms

simplify70.0ms

prune238.0ms

localize13.0ms

rewrite49.0ms

series72.0ms

simplify47.0ms

prune190.0ms

localize27.0ms

rewrite85.0ms

series305.0ms

simplify105.0ms

prune1.5s

regimes690.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample738.0ms

Profiling