Details

analyze895.0ms

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

sample21.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	18×	body	80	invalid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4786	11
1	4786	11

prune16.0ms

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: 0.1b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (- y z) (/ t (- a z))))
0.0b	(/ t (- a z))
10.8b	(* (- y z) (/ t (- a z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

3.0ms	(+ x (* (- y z) (/ t (- a z))))
5.0ms	(/ t (- a z))
12.0ms	(* (- y z) (/ t (- a z)))

series49.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ x (* (- y z) (/ t (- a z))))
7.0ms	(/ t (- a z))
15.0ms	(* (- y z) (/ t (- a z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4978	1059
1	4978	1059

prune119.0ms

Filtered

75 candidates to 103 candidates (-37.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
4.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ t (cbrt (- a z))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`cbrt-prod`
38×	`associate-r`
36×	`times-frac`
31×	`add-cube-cbrt`
30×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
12×	`distribute-lft-out--`
10×	`swap-sqr` `associate-/r/` `difference-of-squares` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
8×	`pow1/3`
7×	`cbrt-undiv` `div-exp`
5×	`associate-r/` `associate-l/`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `pow-plus`

Counts

4 → 163

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
10.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
31.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ t (cbrt (- a z))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
28.0ms	(cbrt (- a z))
28.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
22.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ t (cbrt (- a z))))

simplify64.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4946	2242
1	4946	2242

prune181.0ms

Filtered

120 candidates to 175 candidates (-45.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	174	9	183

Merged error: 0b

Counts

183 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (- y z) (* (cbrt (/ t (- a z))) (cbrt (/ t (- a z)))))
14.3b	(cbrt (/ t (- a z)))
14.3b	(cbrt (/ t (- a z)))
14.3b	(cbrt (/ t (- a z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
45×	`times-frac`
32×	`add-cube-cbrt`
15×	`cbrt-div`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1` `add-exp-log` `frac-times`
7×	`flip3--` `add-cbrt-cube` `flip--`
6×	`associate-*r/` `associate-/r/`
5×	`associate-l` `associate-*l/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

18.0ms	(* (- y z) (* (cbrt (/ t (- a z))) (cbrt (/ t (- a z)))))
5.0ms	(cbrt (/ t (- a z)))
5.0ms	(cbrt (/ t (- a z)))
5.0ms	(cbrt (/ t (- a z)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (- y z) (* (cbrt (/ t (- a z))) (cbrt (/ t (- a z)))))
36.0ms	(cbrt (/ t (- a z)))
37.0ms	(cbrt (/ t (- a z)))
39.0ms	(cbrt (/ t (- a z)))

simplify69.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5159	1803

prune157.0ms

Filtered

107 candidates to 134 candidates (-25.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	134	9	143

Merged error: 0b

Counts

143 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
3.6b	(* (- y z) (/ t (cbrt (- a z))))
5.6b	(/ (* (- y z) (/ t (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
49×	`cbrt-prod`
38×	`associate-r`
32×	`add-exp-log`
29×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`times-frac`
21×	`add-cbrt-cube`
18×	`flip3--` `flip--`
13×	`pow1` `associate-l`
12×	`frac-times`
11×	`distribute-lft-out--`
10×	`swap-sqr` `prod-exp` `associate-/r/` `cbrt-unprod`
9×	`cbrt-undiv` `div-exp` `difference-of-squares`
8×	`associate-*l/`
7×	`pow1/3` `unswap-sqr`
6×	`associate-*r/`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 165

Calls

4 calls:

3.0ms	(cbrt (- a z))
10.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
16.0ms	(* (- y z) (/ t (cbrt (- a z))))
22.0ms	(/ (* (- y z) (/ t (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
29.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
39.0ms	(* (- y z) (/ t (cbrt (- a z))))
15.0ms	(/ (* (- y z) (/ t (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))

simplify66.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5025	2026

prune151.0ms

Filtered

117 candidates to 177 candidates (-51.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	4	5
Picked	0	1	1
Done	2	1	3
Total	179	7	186

Merged error: 0b

Counts

186 → 7

regimes743.0ms

Accuracy

78.6% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 3.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	47
1	37	47

end0.0ms

sample567.0ms

Algorithm

intervals

Results

289.0ms	7995×	body	80	valid
25.0ms	725×	body	80	invalid
0.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

Details

analyze895.0ms

sample21.0ms

simplify117.0ms

prune16.0ms

localize8.0ms

rewrite24.0ms

series49.0ms

simplify58.0ms

prune119.0ms

localize12.0ms

rewrite54.0ms

series103.0ms

simplify64.0ms

prune181.0ms

localize12.0ms

rewrite37.0ms

series192.0ms

simplify69.0ms

prune157.0ms

localize12.0ms

rewrite58.0ms

series108.0ms

simplify66.0ms

prune151.0ms

regimes743.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample567.0ms

Profiling