Details

sample18.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.196289%

Guaranteed chance to sample good point: 35.739437%

Results

8.0ms	210×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	39×	body	80	invalid
1.0ms	11×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	10×	body	160	valid

simplify67.0ms

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

prune7.0ms

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: 24.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.2b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.1b	(/ (* (- y z) (- t x)) (- a z))

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:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms	(/ (* (- y z) (- t x)) (- a z))

series95.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
51.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
35.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune152.0ms

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: 4.8b

Counts

91 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite55.0ms

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))
39.0ms	(* (/ (- 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)))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
28.0ms	(cbrt (- a z))
56.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
49.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune200.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	143	15	158

Merged error: 4.8b

Counts

158 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (cbrt (- a z)))
1.5b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
8.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
38×	`cbrt-div`
27×	`add-sqr-sqrt`
22×	`add-cbrt-cube`
21×	`cbrt-prod`
17×	`-un-lft-identity` `associate-l*`
16×	`times-frac` `associate-r` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
14×	`flip3--` `flip--`
12×	`cbrt-undiv` `div-exp`
11×	`add-cube-cbrt`
9×	`frac-times`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 113

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (cbrt (- a z)))
31.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
28.0ms	(cbrt (cbrt (- a z)))
119.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
54.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	962	2579
1	3549	2212
2	5001	2170

prune210.0ms

Filtered

94 candidates to 125 candidates (-33.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	124	16	140

Merged error: 4.8b

Counts

140 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (cbrt (- a z)))
1.1b	(* (/ 1 (cbrt (- a z))) (* (/ (- y z) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))))
9.3b	(+ x (* (* (/ 1 (cbrt (- a z))) (* (/ (- y z) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-exp-log`
60×	`prod-exp`
42×	`div-exp`
40×	`add-cbrt-cube`
33×	`cbrt-prod`
32×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`associate-l` `cbrt-unprod`
24×	`times-frac`
22×	`add-cube-cbrt`
21×	`cbrt-undiv`
9×	`pow1`
8×	`cbrt-div`
7×	`rec-exp` `1-exp`
6×	`add-log-exp`
5×	`frac-times` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `pow-prod-down` `associate-*l/` `flip--`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
5.0ms	(cbrt (cbrt (- a z)))
33.0ms	(* (/ 1 (cbrt (- a z))) (* (/ (- y z) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))))
4.0ms	(+ x (* (* (/ 1 (cbrt (- a z))) (* (/ (- y z) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
29.0ms	(cbrt (cbrt (- a z)))
91.0ms	(* (/ 1 (cbrt (- a z))) (* (/ (- y z) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))))
50.0ms	(+ x (* (* (/ 1 (cbrt (- a z))) (* (/ (- y z) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify129.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	1034	3227
1	4631	2745
2	5001	2713

prune178.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	146	16	162

Merged error: 4.8b

Counts

162 → 16

regimes681.0ms

Accuracy

13.7% (7.0b remaining)

Error of 11.4b against oracle of 4.4b and baseline of 12.5b

bsearch113.0ms

Steps

Iters	Range		Point
7	6.92877084624537e-178	1.5395400747017067e-176	4.564934225143487e-177
8	-6.488142245615214e-119	-4.795068439356804e-123	-5.0383582052941544e-123

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	34
1	41	34

end0.0ms

sample20.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.196289%

Guaranteed chance to sample good point: 35.739437%

Results

300.0ms	250×	body	160	valid
267.0ms	6520×	body	80	valid
78.0ms	509×	body	640	valid
53.0ms	431×	body	320	valid
52.0ms	278×	body	1280	valid
44.0ms	1107×	body	80	invalid
3.0ms	12×	body	2560	valid

Details

sample18.6s

simplify67.0ms

prune7.0ms

localize9.0ms

rewrite33.0ms

series95.0ms

simplify57.0ms

prune152.0ms

localize13.0ms

rewrite55.0ms

series158.0ms

simplify92.0ms

prune200.0ms

localize26.0ms

rewrite47.0ms

series227.0ms

simplify97.0ms

prune210.0ms

localize25.0ms

rewrite52.0ms

series195.0ms

simplify129.0ms

prune178.0ms

regimes681.0ms

bsearch113.0ms

simplify2.0ms

end0.0ms

sample20.6s

Profiling