Details

analyze638.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

sample25.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
2.0ms	66×	body	80	invalid

simplify264.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (263.0ms)

Iter	Nodes	Cost
0	1852	11
1	1852	11

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.4b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ t (- 1.0 z))
0.0b	(- (/ y z) (/ t (- 1.0 z)))
3.3b	(* x (- (/ y z) (/ t (- 1.0 z))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
31×	`times-frac`
15×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-r`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*` `add-log-exp`
3×	`sub-neg` `flip3--` `associate-r/` `associate-l` `flip--` `associate-/l`
2×	`associate-/r/` `frac-sub`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 86

Calls

3 calls:

5.0ms	(/ t (- 1.0 z))
18.0ms	(- (/ y z) (/ t (- 1.0 z)))
26.0ms	(* x (- (/ y z) (/ t (- 1.0 z))))

series29.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ t (- 1.0 z))
9.0ms	(- (/ y z) (/ t (- 1.0 z)))
15.0ms	(* x (- (/ y z) (/ t (- 1.0 z))))

simplify59.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5463	1120

prune187.0ms

Filtered

71 candidates to 95 candidates (-33.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.5b

Counts

96 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (neg t) (- 1.0 z))
0.0b	(+ (* x (/ y z)) (* x (/ (neg t) (- 1.0 z))))
2.9b	(* x (/ (neg t) (- 1.0 z)))
4.6b	(* x (/ y z))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
111×	`times-frac`
110×	`*-un-lft-identity`
69×	`associate-r`
68×	`add-cube-cbrt`
33×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
21×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log` `add-cbrt-cube`
11×	`neg-mul-1`
10×	`associate-/l*`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`associate-/r*`
4×	`associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
3×	`cbrt-undiv` `distribute-frac-neg` `div-exp` `div-inv`
2×	`flip3--` `pow-prod-down` `*-commutative` `distribute-rgt-neg-out` `flip--`
1×	`+-commutative` `neg-sub0` `frac-2neg` `flip3-+` `div-sub` `unsub-neg` `frac-add` `clear-num` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 203

Calls

4 calls:

7.0ms	(/ (neg t) (- 1.0 z))
5.0ms	(+ (* x (/ y z)) (* x (/ (neg t) (- 1.0 z))))
17.0ms	(* x (/ (neg t) (- 1.0 z)))
7.0ms	(* x (/ y z))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (neg t) (- 1.0 z))
16.0ms	(+ (* x (/ y z)) (* x (/ (neg t) (- 1.0 z))))
11.0ms	(* x (/ (neg t) (- 1.0 z)))
5.0ms	(* x (/ y z))

simplify76.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4967	2225
1	4967	2225

prune300.0ms

Filtered

148 candidates to 215 candidates (-45.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	208	7	215
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	214	12	226

Merged error: 0.1b

Counts

226 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
2.9b	(* x (/ (neg t) (- 1.0 z)))
4.8b	(* (* x (* (cbrt y) (cbrt y))) (/ (cbrt y) z))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

78×	`associate-r`
71×	`add-sqr-sqrt`
69×	`times-frac`
66×	`*-un-lft-identity`
46×	`add-cube-cbrt`
30×	`add-exp-log`
23×	`add-cbrt-cube`
15×	`pow1` `cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
14×	`prod-exp` `cbrt-unprod`
10×	`distribute-lft-out--` `difference-of-squares`
7×	`pow-prod-down`
5×	`neg-mul-1`
4×	`cbrt-undiv` `div-exp` `associate-l` `add-log-exp`
2×	`pow1/3` `associate-r/` `associate-/r/` `-commutative` `div-inv` `unswap-sqr`
1×	`flip3--` `distribute-frac-neg` `distribute-rgt-neg-out` `flip--`

Counts

4 → 145

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
18.0ms	(* x (/ (neg t) (- 1.0 z)))
12.0ms	(* (* x (* (cbrt y) (cbrt y))) (/ (cbrt y) z))

series60.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt y)
21.0ms	(cbrt y)
10.0ms	(* x (/ (neg t) (- 1.0 z)))
8.0ms	(* (* x (* (cbrt y) (cbrt y))) (/ (cbrt y) z))

simplify77.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4944	1285
1	4944	1285

prune321.0ms

Filtered

100 candidates to 157 candidates (-57.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	156	13	169

Merged error: 0.0b

Counts

169 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.8b	(* (* x (* (pow (cbrt y) 2) (/ (cbrt (pow (cbrt y) 2)) (* (cbrt z) (cbrt z))))) (/ (cbrt (cbrt y)) (cbrt z)))
2.0b	(* x (* (pow (cbrt y) 2) (/ (cbrt (pow (cbrt y) 2)) (* (cbrt z) (cbrt z)))))
2.9b	(* x (/ (neg t) (- 1.0 z)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-exp-log`
115×	`associate-r`
105×	`times-frac`
95×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `prod-exp`
84×	`cbrt-prod`
70×	`add-cube-cbrt`
46×	`add-cbrt-cube`
36×	`cbrt-unprod`
30×	`div-exp`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`pow1`
12×	`cbrt-undiv`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow-to-exp` `pow-exp`
8×	`associate-*r/`
7×	`associate-l`
5×	`neg-mul-1` `pow-prod-down`
4×	`add-log-exp`
3×	`*-commutative`
2×	`associate-/r/` `div-inv` `unswap-sqr`
1×	`frac-times` `flip3--` `pow1/3` `distribute-frac-neg` `associate-*l/` `distribute-rgt-neg-out` `flip--`

Counts

4 → 219

Calls

4 calls:

1.0ms	(cbrt z)
26.0ms	(* (* x (* (pow (cbrt y) 2) (/ (cbrt (pow (cbrt y) 2)) (* (cbrt z) (cbrt z))))) (/ (cbrt (cbrt y)) (cbrt z)))
13.0ms	(* x (* (pow (cbrt y) 2) (/ (cbrt (pow (cbrt y) 2)) (* (cbrt z) (cbrt z)))))
16.0ms	(* x (/ (neg t) (- 1.0 z)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt z)
6.0ms	(* (* x (* (pow (cbrt y) 2) (/ (cbrt (pow (cbrt y) 2)) (* (cbrt z) (cbrt z))))) (/ (cbrt (cbrt y)) (cbrt z)))
48.0ms	(* x (* (pow (cbrt y) 2) (/ (cbrt (pow (cbrt y) 2)) (* (cbrt z) (cbrt z)))))
11.0ms	(* x (/ (neg t) (- 1.0 z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4993	4209
1	4993	4209

prune438.0ms

Filtered

164 candidates to 231 candidates (-40.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	232	12	244

Merged error: 0.0b

Counts

244 → 12

regimes526.0ms

Accuracy

52.2% (1.5b remaining)

Error of 1.6b against oracle of 0.1b and baseline of 3.2b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	143	53
1	143	53

end0.0ms

sample662.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
74.0ms	1937×	body	80	invalid

Details

analyze638.0ms

sample25.0ms

simplify264.0ms

prune8.0ms

localize8.0ms

rewrite52.0ms

series29.0ms

simplify59.0ms

prune187.0ms

localize10.0ms

rewrite47.0ms

series39.0ms

simplify76.0ms

prune300.0ms

localize13.0ms

rewrite39.0ms

series60.0ms

simplify77.0ms

prune321.0ms

localize23.0ms

rewrite68.0ms

series85.0ms

simplify56.0ms

prune438.0ms

regimes526.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample662.0ms

Profiling