Details

analyze1.3s

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample74.0ms

Algorithm

intervals

Results

7.0ms	206×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	2560	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

prune6.0ms

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: 16.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
6.2b	(* (- y z) (/ (- t x) (- a z)))
11.8b	(+ x (* (- y z) (/ (- t x) (- a z))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
17.0ms	(* (- y z) (/ (- t x) (- a z)))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))

series103.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- t x) (- a z))
36.0ms	(* (- y z) (/ (- t x) (- a z)))
53.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))

simplify44.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5183	1602

prune189.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 4.2b

Counts

129 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
11.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
39.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- a z))
28.0ms	(cbrt (- a z))
56.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
54.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5314	2524

prune197.0ms

Filtered

108 candidates to 146 candidates (-35.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	144	14	158

Merged error: 4.2b

Counts

158 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
11.8b	(+ x (* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

296×	`cbrt-div`
137×	`frac-times`
111×	`flip3--` `flip--`
89×	`associate-l`
84×	`add-sqr-sqrt`
82×	`associate-/r/`
78×	`cbrt-prod`
73×	`*-un-lft-identity`
63×	`times-frac`
61×	`associate-r`
45×	`associate-r/` `associate-l/`
36×	`add-exp-log`
35×	`add-cube-cbrt`
24×	`add-cbrt-cube`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
4×	`unswap-sqr`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 223

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
106.0ms	(* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
6.0ms	(+ x (* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- a z))
27.0ms	(cbrt (- a z))
58.0ms	(* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
51.0ms	(+ x (* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5174	7022

prune406.0ms

Filtered

195 candidates to 235 candidates (-20.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	233	16	249

Merged error: 4.2b

Counts

249 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (/ (- t x) (cbrt (- a z))))
1.8b	(cbrt (/ (- t x) (cbrt (- a z))))
1.8b	(cbrt (/ (- t x) (cbrt (- a z))))
11.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod`
139×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`times-frac`
61×	`add-cube-cbrt`
39×	`distribute-lft-out--` `difference-of-squares`
9×	`cbrt-div`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 176

Calls

4 calls:

9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
62.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
63.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
51.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5369	3729

prune185.0ms

Filtered

140 candidates to 188 candidates (-34.3%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	12	13
Picked	0	1	1
Done	0	2	2
Total	187	17	204

Merged error: 4.2b

Counts

204 → 17

regimes910.0ms

Accuracy

61% (3.5b remaining)

Error of 7.0b against oracle of 3.5b and baseline of 12.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	80
1	76	80

end0.0ms

sample1.6s

Algorithm

intervals

Results

215.0ms	6551×	body	80	valid
64.0ms	497×	body	640	valid
45.0ms	275×	body	1280	valid
38.0ms	391×	body	320	valid
17.0ms	264×	body	160	valid
4.0ms	22×	body	2560	valid

Details

analyze1.3s

sample74.0ms

simplify66.0ms

prune6.0ms

localize10.0ms

rewrite34.0ms

series103.0ms

simplify44.0ms

prune189.0ms

localize15.0ms

rewrite56.0ms

series165.0ms

simplify39.0ms

prune197.0ms

localize21.0ms

rewrite142.0ms

series164.0ms

simplify67.0ms

prune406.0ms

localize21.0ms

rewrite43.0ms

series238.0ms

simplify59.0ms

prune185.0ms

regimes910.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling