Details

analyze106.0ms

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

sample27.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5222	28

prune10.0ms

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: 0.2b

Counts

2 → 2

localize15.0ms

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

rewrite40.0ms

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:

5.0ms	(* 5.0 (* v v))
16.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
3.0ms	(* PI t)
10.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series67.0ms

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 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
2.0ms	(* PI t)
21.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4981	1908
1	4981	1908

prune221.0ms

Filtered

76 candidates to 106 candidates (-39.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 0.0b

Counts

108 → 8

localize15.0ms

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 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
0.4b	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
9×	`flip3--` `associate-l` `flip--`
8×	`associate-/r/`
7×	`pow-prod-down`
6×	`associate-r`
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 → 96

Calls

4 calls:

5.0ms	(* 5.0 (* v v))
15.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
10.0ms	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
8.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 5.0 (* v v))
40.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
23.0ms	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
19.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5016	2144

prune224.0ms

Filtered

82 candidates to 108 candidates (-31.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	109	7	116

Merged error: 0.0b

Counts

116 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (* v v))
0.3b	(/ (cbrt (- 1.0 (* v (* v 5.0)))) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
0.4b	(* (/ (cbrt (- 1.0 (* v (* v 5.0)))) PI) (/ (cbrt (- 1.0 (* v (* v 5.0)))) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`add-exp-log`
32×	`times-frac`
28×	`associate-l` `add-cbrt-cube`
27×	`add-cube-cbrt` `*-un-lft-identity`
19×	`cbrt-prod`
17×	`associate-r`
13×	`pow1` `associate-*r/` `prod-exp` `cbrt-unprod`
9×	`cbrt-undiv` `div-exp`
6×	`sqrt-div` `associate-/l*`
5×	`pow-prod-down` `unswap-sqr`
4×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`cbrt-div` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `sqrt-prod`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* 3.0 (* v v))
11.0ms	(/ (cbrt (- 1.0 (* v (* v 5.0)))) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
7.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
20.0ms	(* (/ (cbrt (- 1.0 (* v (* v 5.0)))) PI) (/ (cbrt (- 1.0 (* v (* v 5.0)))) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* v v))
69.0ms	(/ (cbrt (- 1.0 (* v (* v 5.0)))) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
18.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
79.0ms	(* (/ (cbrt (- 1.0 (* v (* v 5.0)))) PI) (/ (cbrt (- 1.0 (* v (* v 5.0)))) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4989	3735
1	4989	3735

prune589.0ms

Filtered

119 candidates to 144 candidates (-21.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	3	4
Picked	0	1	1
Done	2	0	2
Total	145	6	151

Merged error: 0b

Counts

151 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* v (* v 5.0))
0.4b	(* (/ (cbrt (- 1.0 (* v (* v 5.0)))) PI) (* (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) t) (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0))))))))
0.5b	(* (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) t) (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0)))))))
1.0b	(/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0))))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
140×	`add-sqr-sqrt`
97×	`cbrt-prod`
84×	`add-cube-cbrt` `*-un-lft-identity`
64×	`add-exp-log`
63×	`sqrt-prod`
56×	`associate-l`
46×	`add-cbrt-cube`
44×	`associate-r`
25×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
16×	`pow1` `unswap-sqr`
10×	`associate-*r/`
9×	`associate-/l*`
7×	`pow-prod-down`
6×	`frac-times` `sqrt-div`
4×	`associate-l/` `associate-/r` `associate-/r/` `div-inv` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`cbrt-div` `associate-/l/`
1×	`frac-2neg` `clear-num`

Counts

4 → 252

Calls

4 calls:

5.0ms	(* v (* v 5.0))
27.0ms	(* (/ (cbrt (- 1.0 (* v (* v 5.0)))) PI) (* (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) t) (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0))))))))
34.0ms	(* (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) t) (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0)))))))
11.0ms	(/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0))))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* v (* v 5.0))
76.0ms	(* (/ (cbrt (- 1.0 (* v (* v 5.0)))) PI) (* (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) t) (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0))))))))
73.0ms	(* (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) t) (/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0)))))))
34.0ms	(/ (cbrt (sqrt (- 1.0 (* v (* v 5.0))))) (sqrt (* 2.0 (- 1.0 (* v (* v 3.0))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5111	9866

prune2.0s

Filtered

202 candidates to 264 candidates (-30.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	264	6	270

Merged error: 0b

Counts

270 → 6

regimes219.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	47
1	94	47

end0.0ms

sample631.0ms

Algorithm

intervals

Results

502.0ms	8000×	body	80	valid
1.0ms	12×	body	80	nan

Details

analyze106.0ms

sample27.0ms

simplify32.0ms

prune10.0ms

localize15.0ms

rewrite40.0ms

series67.0ms

simplify71.0ms

prune221.0ms

localize15.0ms

rewrite41.0ms

series85.0ms

simplify54.0ms

prune224.0ms

localize24.0ms

rewrite49.0ms

series169.0ms

simplify74.0ms

prune589.0ms

localize29.0ms

rewrite89.0ms

series187.0ms

simplify72.0ms

prune2.0s

regimes219.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample631.0ms

Profiling