Details

analyze1.0s

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
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

sample240.0ms

Algorithm

intervals

Results

8.0ms	217×	body	80	valid
2.0ms	12×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	28×	body	80	invalid
0.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4893	13
1	4893	13

prune14.0ms

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: 7.2b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ y (* y (/ (- z t) (- t a)))))
0.0b	(/ (- z t) (- t a))
2.9b	(* y (/ (- z t) (- t a)))
3.8b	(+ y (* y (/ (- z t) (- t a))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

5.0ms	(+ x (+ y (* y (/ (- z t) (- t a)))))
8.0ms	(/ (- z t) (- t a))
13.0ms	(* y (/ (- z t) (- t a)))
3.0ms	(+ y (* y (/ (- z t) (- t a))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ x (+ y (* y (/ (- z t) (- t a)))))
9.0ms	(/ (- z t) (- t a))
16.0ms	(* y (/ (- z t) (- t a)))
23.0ms	(+ y (* y (/ (- z t) (- t a))))

simplify49.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5072	1615

prune171.0ms

Filtered

96 candidates to 139 candidates (-44.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	9	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Merged error: 2.6b

Counts

141 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- t a))
0.2b	(* (- z t) (/ 1 (- t a)))
2.9b	(* y (* (- z t) (/ 1 (- t a))))
5.4b	(+ y (* y (* (- z t) (/ 1 (- t a)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`frac-times` `pow-prod-down` `associate-*l/` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ 1 (- t a))
14.0ms	(* (- z t) (/ 1 (- t a)))
12.0ms	(* y (* (- z t) (/ 1 (- t a))))
4.0ms	(+ y (* y (* (- z t) (/ 1 (- t a)))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (- t a))
9.0ms	(* (- z t) (/ 1 (- t a)))
16.0ms	(* y (* (- z t) (/ 1 (- t a))))
22.0ms	(+ y (* y (* (- z t) (/ 1 (- t a)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5105	1273

prune182.0ms

Filtered

86 candidates to 142 candidates (-65.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	141	10	151

Merged error: 2.6b

Counts

151 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t a))
0.6b	(cbrt (- t a))
6.3b	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a))))
12.5b	(+ y (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
50×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
15×	`associate-l` `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 → 132

Calls

4 calls:

3.0ms	(cbrt (- t a))
3.0ms	(cbrt (- t a))
35.0ms	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a))))
4.0ms	(+ y (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a)))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- t a))
30.0ms	(cbrt (- t a))
22.0ms	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a))))
30.0ms	(+ y (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4976	2254
1	4976	2254

prune173.0ms

Filtered

106 candidates to 144 candidates (-35.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	143	11	154

Merged error: 2.6b

Counts

154 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t a))
1.1b	(* (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))
4.9b	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a))))))
14.6b	(+ y (* (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

261×	`add-exp-log`
164×	`cbrt-prod`
128×	`prod-exp` `cbrt-unprod`
127×	`add-cbrt-cube`
96×	`add-sqr-sqrt`
95×	`associate-r`
94×	`*-un-lft-identity`
92×	`times-frac`
82×	`cbrt-undiv` `div-exp`
54×	`add-cube-cbrt`
26×	`frac-times`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`pow1` `cbrt-div` `associate-r/` `associate-l/`
16×	`associate-l`
10×	`associate-/r/`
9×	`pow-prod-down`
8×	`flip3--` `flip--`
6×	`add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+`

Counts

4 → 276

Calls

4 calls:

3.0ms	(cbrt (- t a))
64.0ms	(* (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))
40.0ms	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a))))))
6.0ms	(+ y (* (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a))))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- t a))
23.0ms	(* (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))
75.0ms	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a))))))
36.0ms	(+ y (* (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (* (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- t a))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4982	9882
1	4982	9882

prune256.0ms

Filtered

170 candidates to 288 candidates (-69.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	285	3	288
Fresh	0	8	8
Picked	1	0	1
Done	1	1	2
Total	287	12	299

Merged error: 2.6b

Counts

299 → 12

regimes563.0ms

Accuracy

20.5% (3.9b remaining)

Error of 7.0b against oracle of 3.1b and baseline of 8.0b

bsearch42.0ms

Steps

Iters	Range		Point
9	6.255110256284255e-24	4.875963617856801e-18	7.60177063837458e-20
8	-1.7925175874756535e-115	-1.0961357629564754e-119	-9.459372584668667e-116

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	37
1	51	37

end0.0ms

sample754.0ms

Algorithm

intervals

Results

269.0ms	6683×	body	80	valid
63.0ms	455×	body	640	valid
44.0ms	237×	body	1280	valid
39.0ms	374×	body	320	valid
30.0ms	733×	body	80	invalid
17.0ms	237×	body	160	valid
3.0ms	14×	body	2560	valid

Details

analyze1.0s

sample240.0ms

simplify100.0ms

prune14.0ms

localize9.0ms

rewrite38.0ms

series85.0ms

simplify49.0ms

prune171.0ms

localize11.0ms

rewrite42.0ms

series52.0ms

simplify42.0ms

prune182.0ms

localize14.0ms

rewrite51.0ms

series107.0ms

simplify56.0ms

prune173.0ms

localize24.0ms

rewrite131.0ms

series159.0ms

simplify86.0ms

prune256.0ms

regimes563.0ms

bsearch42.0ms

simplify1.0ms

end0.0ms

sample754.0ms

Profiling