Details

analyze1.0s

Algorithm: search

sample30.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
2.0ms	21×	body	320	valid
2.0ms	15×	body	640	valid
2.0ms	48×	body	80	invalid
1.0ms	17×	body	160	valid
1.0ms	6×	body	1280	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune4.0ms

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: 27.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.9b	(+ x (/ (* (- y x) (- z t)) (- a t)))
19.3b	(/ (* (- y x) (- z t)) (- a t))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

12.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
11.0ms	(/ (* (- y x) (- z t)) (- a t))

series92.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
51.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
31.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify55.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune153.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 5.7b

Counts

91 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.6b	(/ (- y x) (/ (- a t) (- z t)))
3.9b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

7.0ms	(/ (- a t) (- z t))
17.0ms	(/ (- y x) (/ (- a t) (- z t)))
37.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series103.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- a t) (- z t))
41.0ms	(/ (- y x) (/ (- a t) (- z t)))
53.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify107.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5001	2984

prune254.0ms

Filtered

172 candidates to 283 candidates (-64.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	274	9	283
Fresh	7	4	11
Picked	0	1	1
Done	0	0	0
Total	281	14	295

Merged error: 5.4b

Counts

295 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y x))
0.6b	(cbrt (- y x))
1.0b	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
11.0b	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

728×	`times-frac`
603×	`add-sqr-sqrt` `*-un-lft-identity`
470×	`cbrt-prod`
271×	`add-cube-cbrt`
166×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/r*`
19×	`associate-/r/`
12×	`flip3--` `flip--`
10×	`div-inv`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/3` `associate-/l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`

Counts

4 → 480

Calls

4 calls:

3.0ms	(cbrt (- y x))
3.0ms	(cbrt (- y x))
22.0ms	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
3.0ms	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- y x))
26.0ms	(cbrt (- y x))
64.0ms	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
49.0ms	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

492 → 492

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1438	8170
1	5001	8005

prune442.0ms

Filtered

327 candidates to 492 candidates (-50.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	491	1	492
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	491	15	506

Merged error: 5.4b

Counts

506 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

3.4b	(cbrt (/ (- y x) (/ (- a t) (- z t))))
3.4b	(cbrt (/ (- y x) (/ (- a t) (- z t))))
3.4b	(cbrt (/ (- y x) (/ (- a t) (- z t))))
10.3b	(+ x (* (* (cbrt (/ (- y x) (/ (- a t) (- z t)))) (cbrt (/ (- y x) (/ (- a t) (- z t))))) (cbrt (/ (- y x) (/ (- a t) (- z t))))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

840×	`times-frac`
751×	`add-sqr-sqrt` `*-un-lft-identity`
480×	`cbrt-prod`
265×	`add-cube-cbrt`
243×	`distribute-lft-out--` `difference-of-squares`
33×	`associate-/r/`
18×	`div-inv`
15×	`flip3--` `flip--`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 518

Calls

4 calls:

17.0ms	(cbrt (/ (- y x) (/ (- a t) (- z t))))
20.0ms	(cbrt (/ (- y x) (/ (- a t) (- z t))))
18.0ms	(cbrt (/ (- y x) (/ (- a t) (- z t))))
3.0ms	(+ x (* (* (cbrt (/ (- y x) (/ (- a t) (- z t)))) (cbrt (/ (- y x) (/ (- a t) (- z t))))) (cbrt (/ (- y x) (/ (- a t) (- z t))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

514.0ms	(cbrt (/ (- y x) (/ (- a t) (- z t))))
512.0ms	(cbrt (/ (- y x) (/ (- a t) (- z t))))
518.0ms	(cbrt (/ (- y x) (/ (- a t) (- z t))))
49.0ms	(+ x (* (* (cbrt (/ (- y x) (/ (- a t) (- z t)))) (cbrt (/ (- y x) (/ (- a t) (- z t))))) (cbrt (/ (- y x) (/ (- a t) (- z t))))))

simplify148.0ms

Algorithm

egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	1029	8659
1	3335	8537
2	5001	8498

prune411.0ms

Filtered

305 candidates to 530 candidates (-73.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	529	1	530
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	530	15	545

Merged error: 5.4b

Counts

545 → 15

regimes752.0ms

Accuracy

43.1% (4.8b remaining)

Error of 8.9b against oracle of 4.1b and baseline of 12.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	44
1	43	44

end0.0ms

analyze1.2s

Algorithm: search

sample829.0ms

Algorithm

intervals

Results

279.0ms	6513×	body	80	valid
81.0ms	496×	body	640	valid
55.0ms	276×	body	1280	valid
50.0ms	440×	body	320	valid
48.0ms	1214×	body	80	invalid
20.0ms	260×	body	160	valid
4.0ms	15×	body	2560	valid

Details

analyze1.0s

sample30.0ms

simplify60.0ms

prune4.0ms

localize9.0ms

rewrite33.0ms

series92.0ms

simplify55.0ms

prune153.0ms

localize9.0ms

rewrite79.0ms

series103.0ms

simplify107.0ms

prune254.0ms

localize21.0ms

rewrite74.0ms

series168.0ms

simplify101.0ms

prune442.0ms

localize14.0ms

rewrite110.0ms

series1.6s

simplify148.0ms

prune411.0ms

regimes752.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze1.2s

sample829.0ms

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