Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	250×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	9×	body	160	valid

simplify70.0ms

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: 26.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.3b	(+ x (/ (* (- y z) (- t x)) (- a z)))
18.8b	(/ (* (- 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))
8.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms	(/ (* (- y z) (- t x)) (- a z))

series302.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* (- y z) (- t x))
144.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
125.0ms	(/ (* (- 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

prune218.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	13	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	13	91

Merged error: 5.0b

Counts

91 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite53.0ms

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))
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)))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- a z))
163.0ms	(cbrt (- a z))
311.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
147.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (72.0ms)

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

prune406.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	145	14	159

Merged error: 5.0b

Counts

159 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt (- a z)))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
2.5b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
8.4b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
164×	`add-sqr-sqrt`
119×	`cbrt-prod`
101×	`*-un-lft-identity`
96×	`cbrt-div`
80×	`associate-l`
61×	`associate-r`
59×	`add-cube-cbrt`
42×	`associate-/r/`
38×	`flip3--` `flip--`
36×	`add-exp-log`
25×	`frac-times`
22×	`add-cbrt-cube`
21×	`distribute-lft-out--` `difference-of-squares`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv` `add-log-exp`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 235

Calls

4 calls:

4.0ms	(cbrt (cbrt (- a z)))
9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
101.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
4.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (cbrt (- a z)))
125.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
288.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
156.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1420	5129
1	5001	4883

prune1.1s

Filtered

247 candidates to 204 candidates (82.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	245	2	247
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	249	12	261

Merged error: 5.0b

Counts

261 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
7.2b	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-div`
13×	`flip3--` `flip--`
8×	`frac-times`
7×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `associate-r/` `associate-l/` `add-cbrt-cube`
3×	`pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (- y z))
9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- y z))
117.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
119.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
153.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	386	1216
1	1115	1110
2	5001	1102

prune332.0ms

Filtered

72 candidates to 59 candidates (81.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	70	14	84

Merged error: 5.0b

Counts

84 → 14

regimes340.0ms

Accuracy

19.7% (6.2b remaining)

Error of 10.3b against oracle of 4.1b and baseline of 11.8b

bsearch88.0ms

Steps

Iters	Range		Point
8	1.3340097847044237e-166	4.777774611339487e-163	2.153009758024033e-165
5	-7.282177669803191e-141	-1.958862663897064e-141	-4.167821473234132e-141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	43
1	44	43

end0.0ms

sample764.0ms

Algorithm

intervals

Results

299.0ms	7808×	body	80	valid
69.0ms	466×	body	640	valid
53.0ms	281×	body	1280	valid
43.0ms	381×	body	320	valid
22.0ms	265×	body	160	valid
4.0ms	19×	body	2560	valid

Details

sample28.0ms

simplify70.0ms

prune2.0ms

localize12.0ms

rewrite33.0ms

series302.0ms

simplify57.0ms

prune218.0ms

localize16.0ms

rewrite53.0ms

series766.0ms

simplify88.0ms

prune406.0ms

localize17.0ms

rewrite134.0ms

series708.0ms

simplify71.0ms

prune1.1s

localize30.0ms

rewrite28.0ms

series532.0ms

simplify42.0ms

prune332.0ms

regimes340.0ms

bsearch88.0ms

simplify2.0ms

end0.0ms

sample764.0ms

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