Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	254×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	8×	body	160	valid

simplify65.0ms

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	1498	6
6	3410	6
7	5001	6

prune2.0ms

Filtered

1 candidates to 0 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: 24.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.9b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.0b	(/ (* (- y z) (- t x)) (- a z))

rewrite35.0ms

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

series299.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* (- y z) (- t x))
144.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
122.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune234.0ms

Filtered

90 candidates to 67 candidates (74.4%)

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: 3.8b

Counts

91 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
1.5b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

3.0ms	(cbrt (- a z))
11.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
43.0ms	(* (/ (- 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)))))

series888.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt (- a z))
122.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
289.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
155.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify116.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	844	2163
1	4193	1974
2	5003	1855

prune462.0ms

Filtered

187 candidates to 124 candidates (66.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	184	15	199

Merged error: 3.8b

Counts

199 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

3.2b	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.2b	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.2b	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
6.5b	(+ x (* (* (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-div`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 47

Calls

4 calls:

26.0ms	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
23.0ms	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
22.0ms	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(+ x (* (* (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))))

series15.1s

Counts

4 → 12

Calls

4 calls:

5.0s	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
5.1s	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
4.9s	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
156.0ms	(+ x (* (* (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	217	1405
1	602	1146
2	2574	957
3	5003	921

prune257.0ms

Filtered

59 candidates to 56 candidates (94.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	60	14	74

Merged error: 3.5b

Counts

74 → 14

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.6b	(+ x (/ (- y z) (/ (- a z) (- t x))))
5.4b	(/ (- y z) (/ (- a z) (- t x)))

rewrite89.0ms

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:

8.0ms	(/ (- a z) (- t x))
47.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
16.0ms	(/ (- y z) (/ (- a z) (- t x)))

series518.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- a z) (- t x))
159.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
311.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify117.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1021	3042
1	4255	2973
2	5001	2973

prune553.0ms

Filtered

283 candidates to 169 candidates (59.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	279	4	283
Fresh	4	8	12
Picked	0	1	1
Done	1	0	1
Total	284	13	297

Merged error: 3.5b

Counts

297 → 13

regimes336.0ms

Accuracy

29.4% (8.1b remaining)

Error of 11.7b against oracle of 3.5b and baseline of 15.0b

bsearch131.0ms

Steps

Iters	Range	Point
8	8.334010653731551e+229	3.6163186216674506e+234	8.772350252936933e+229
7	6.799537187716957e-224	6.219332546703312e-222	6.3038971632522705e-223
7	-2.759058300683335e+143	-7.886542253082436e+141	-2.095604812439643e+143

Iters

Range

Point

8.334010653731551e+229

3.6163186216674506e+234

8.772350252936933e+229

6.799537187716957e-224

6.219332546703312e-222

6.3038971632522705e-223

-2.759058300683335e+143

-7.886542253082436e+141

-2.095604812439643e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	30
1	41	30

end0.0ms

sample837.0ms

Algorithm

intervals

Results

325.0ms	7716×	body	80	valid
84.0ms	499×	body	640	valid
58.0ms	437×	body	320	valid
53.0ms	265×	body	1280	valid
28.0ms	283×	body	160	valid
3.0ms	13×	body	2560	valid

Details

sample28.0ms

simplify65.0ms

prune2.0ms

localize10.0ms

rewrite35.0ms

series299.0ms

simplify54.0ms

prune234.0ms

localize14.0ms

rewrite71.0ms

series888.0ms

simplify116.0ms

prune462.0ms

localize23.0ms

rewrite74.0ms

series15.1s

simplify80.0ms

prune257.0ms

localize10.0ms

rewrite89.0ms

series518.0ms

simplify117.0ms

prune553.0ms

regimes336.0ms

bsearch131.0ms

simplify2.0ms

end0.0ms

sample837.0ms

Profiling