Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	242×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	8×	body	1280	valid
0.0ms	6×	body	160	valid

simplify68.0ms

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

prune9.0ms

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: 26.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
18.7b	(/ (* (- y z) (- t x)) (- a z))

rewrite32.0ms

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))

series307.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y z) (- t x))
146.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
124.0ms	(/ (* (- 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

prune422.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 4.6b

Counts

91 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
1.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.4b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite66.0ms

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)))
37.0ms	(* (/ (- 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)))))

series693.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- a z))
117.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
289.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
144.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify120.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (100.0ms)

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

prune837.0ms

Filtered

187 candidates to 124 candidates (66.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	184	13	197

Merged error: 4.6b

Counts

197 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
0.6b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.5b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
3×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

3.0ms	(cbrt (- y z))
3.0ms	(cbrt (- y z))
37.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
4.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- y z))
145.0ms	(cbrt (- y z))
301.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
154.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	652	2061
1	2489	1608
2	5003	1462

prune515.0ms

Filtered

115 candidates to 69 candidates (60.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	116	12	128

Merged error: 4.6b

Counts

128 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (cbrt (- a z)))
1.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
8.9b	(+ 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))))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms	(cbrt (cbrt (- a z)))
36.0ms	(* (/ (- 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))))))

series712.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
144.0ms	(cbrt (cbrt (- a z)))
286.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
153.0ms	(+ 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

127 → 127

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	885	2637
1	3509	2287
2	5001	2247

prune915.0ms

Filtered

127 candidates to 93 candidates (73.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	127	12	139

Merged error: 4.6b

Counts

139 → 12

regimes606.0ms

Accuracy

13% (7.0b remaining)

Error of 11.3b against oracle of 4.3b and baseline of 12.4b

bsearch81.0ms

Steps

Iters	Range		Point
5	9.038463714766809e-110	1.8421315701184744e-109	9.81114801824371e-110
6	-1.714805652636918e-277	-1.5793440548946624e-278	-5.0582359873143543e-278

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	54
1	49	54

end0.0ms

sample934.0ms

Algorithm

intervals

Results

274.0ms	7748×	body	80	valid
65.0ms	491×	body	640	valid
45.0ms	267×	body	1280	valid
43.0ms	435×	body	320	valid
16.0ms	245×	body	160	valid
3.0ms	16×	body	2560	valid

Details

sample36.0ms

simplify68.0ms

prune9.0ms

localize10.0ms

rewrite32.0ms

series307.0ms

simplify54.0ms

prune422.0ms

localize14.0ms

rewrite66.0ms

series693.0ms

simplify120.0ms

prune837.0ms

localize21.0ms

rewrite51.0ms

series749.0ms

simplify76.0ms

prune515.0ms

localize23.0ms

rewrite57.0ms

series712.0ms

simplify97.0ms

prune915.0ms

regimes606.0ms

bsearch81.0ms

simplify2.0ms

end0.0ms

sample934.0ms

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