Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	16×	body	160	valid
1.0ms	9×	body	320	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 24.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
3.9b	(+ x (/ (* (- y z) (- t x)) (- a z)))
15.7b	(/ (* (- y z) (- t x)) (- a z))

rewrite30.0ms

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:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series292.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* (- y z) (- t x))
140.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
120.0ms	(/ (* (- 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

prune215.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 3.5b

Counts

91 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`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 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
38.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- a z))
144.0ms	(cbrt (- a z))
277.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
138.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune448.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	143	11	154

Merged error: 3.5b

Counts

154 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b	(cbrt (/ (- t x) (cbrt (- a z))))
1.6b	(cbrt (/ (- t x) (cbrt (- a z))))
1.6b	(cbrt (/ (- t x) (cbrt (- a z))))
10.7b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod`
139×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`times-frac`
61×	`add-cube-cbrt`
39×	`distribute-lft-out--` `difference-of-squares`
9×	`cbrt-div`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 176

Calls

4 calls:

11.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
8.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
8.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
229.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
263.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
143.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	474	2666
1	1142	2535
2	5001	2502

prune760.0ms

Filtered

188 candidates to 144 candidates (76.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	187	12	199

Merged error: 3.3b

Counts

199 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(cbrt (/ (- t x) (cbrt (- a z))))
1.6b	(cbrt (/ (- t x) (cbrt (- a z))))
1.6b	(cbrt (/ (- t x) (cbrt (- a z))))
10.9b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (* (cbrt (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (cbrt (/ (- t x) (cbrt (- a z))))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod`
139×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`times-frac`
61×	`add-cube-cbrt`
39×	`distribute-lft-out--` `difference-of-squares`
9×	`cbrt-div`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 176

Calls

4 calls:

8.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
12.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (* (cbrt (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (cbrt (/ (- t x) (cbrt (- a z))))))))

series887.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
244.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
241.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
154.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (* (cbrt (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (cbrt (/ (- t x) (cbrt (- a z))))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	480	2904
1	1240	2787
2	5001	2775

prune846.0ms

Filtered

188 candidates to 143 candidates (76.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	188	12	200

Merged error: 3.3b

Counts

200 → 12

regimes353.0ms

Accuracy

28.2% (6.8b remaining)

Error of 10.3b against oracle of 3.5b and baseline of 13.0b

bsearch90.0ms

Steps

Iters	Range		Point
7	2.3171177227223138e+151	7.1007851833342075e+152	2.5419455029683397e+152
7	-5.5353460225548844e+147	-2.2422785610801346e+146	-5.247565116560335e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	32
1	40	32

end0.0ms

sample706.0ms

Algorithm

intervals

Results

257.0ms	7702×	body	80	valid
61.0ms	512×	body	640	valid
49.0ms	269×	body	1280	valid
38.0ms	395×	body	320	valid
17.0ms	284×	body	160	valid
3.0ms	15×	body	2560	valid