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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

sample29.0ms

Algorithm

intervals

Results

8.0ms	209×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	14×	body	320	valid
2.0ms	9×	body	1280	valid
1.0ms	34×	body	80	invalid
0.0ms	5×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune12.0ms

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: 11.3b

Counts

2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.1b	(+ x (* (- y x) (/ (- z t) (- a t))))
1.7b	(* (- y x) (/ (- z t) (- a t)))

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

series93.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
49.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
34.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify43.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5068	1606

prune167.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Merged error: 2.6b

Counts

130 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
1.7b	(* (- y x) (* (- z t) (/ 1 (- a t))))
2.8b	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

5.0ms	(/ 1 (- a t))
13.0ms	(* (- z t) (/ 1 (- a t)))
15.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
4.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (- a t))
9.0ms	(* (- z t) (/ 1 (- a t)))
31.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
50.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5748	1773

prune161.0ms

Filtered

97 candidates to 158 candidates (-62.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	158	10	168

Merged error: 2.6b

Counts

168 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.2b	(/ 1 (/ (- a t) (- z t)))
1.1b	(+ x (* (- y x) (/ 1 (/ (- a t) (- z t)))))
1.7b	(* (- y x) (/ 1 (/ (- a t) (- z t))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 344

Calls

4 calls:

8.0ms	(/ (- a t) (- z t))
12.0ms	(/ 1 (/ (- a t) (- z t)))
4.0ms	(+ x (* (- y x) (/ 1 (/ (- a t) (- z t)))))
33.0ms	(* (- y x) (/ 1 (/ (- a t) (- z t))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (- a t) (- z t))
16.0ms	(/ 1 (/ (- a t) (- z t)))
51.0ms	(+ x (* (- y x) (/ 1 (/ (- a t) (- z t)))))
41.0ms	(* (- y x) (/ 1 (/ (- a t) (- z t))))

simplify92.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5059	4991

prune293.0ms

Filtered

208 candidates to 356 candidates (-71.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	354	2	356
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	357	9	366

Merged error: 2.6b

Counts

366 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
1.7b	(* (- y x) (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))))
7.2b	(+ x (* (- y x) (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

133×	`frac-times`
110×	`cbrt-div`
65×	`associate-*l/`
62×	`associate-*r/`
50×	`flip3--` `flip--`
42×	`cbrt-prod`
37×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
23×	`add-cube-cbrt`
18×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-log-exp`
5×	`associate-l`
4×	`associate-/r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 168

Calls

4 calls:

5.0ms	(cbrt (/ 1 (- a t)))
5.0ms	(cbrt (/ 1 (- a t)))
35.0ms	(* (- y x) (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))))
4.0ms	(+ x (* (- y x) (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t))))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (/ 1 (- a t)))
26.0ms	(cbrt (/ 1 (- a t)))
33.0ms	(* (- y x) (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))))
53.0ms	(+ x (* (- y x) (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5039	3737

prune180.0ms

Filtered

97 candidates to 180 candidates (-85.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	180	9	189

Merged error: 2.6b

Counts

189 → 9

regimes481.0ms

Accuracy

22% (6.3b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 11.9b

bsearch52.0ms

Steps

Iters	Range		Point
11	1.3560247159165915e-82	5.746271030105305e-62	1.3780460953492288e-82
7	-2.087995206668015e-138	-6.317424258844764e-140	-8.279965384186068e-139

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	51
1	88	51

end0.0ms

sample845.0ms

Algorithm

intervals

Results

278.0ms	6541×	body	80	valid
81.0ms	492×	body	640	valid
63.0ms	278×	body	1280	valid
51.0ms	445×	body	320	valid
50.0ms	1218×	body	80	invalid
18.0ms	231×	body	160	valid
3.0ms	13×	body	2560	valid

Details

analyze1.0s

sample29.0ms

simplify57.0ms

prune12.0ms

localize9.0ms

rewrite34.0ms

series93.0ms

simplify43.0ms

prune167.0ms

localize10.0ms

rewrite42.0ms

series95.0ms

simplify44.0ms

prune161.0ms

localize10.0ms

rewrite78.0ms

series118.0ms

simplify92.0ms

prune293.0ms

localize14.0ms

rewrite59.0ms

series140.0ms

simplify73.0ms

prune180.0ms

regimes481.0ms

bsearch52.0ms

simplify2.0ms

end0.0ms

sample845.0ms

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