Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	244×	body	80	valid
2.0ms	15×	body	640	valid
2.0ms	18×	body	320	valid
2.0ms	10×	body	1280	valid
0.0ms	5×	body	160	valid

simplify72.0ms

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: 27.7b

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)))
19.1b	(/ (* (- 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))

series356.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y z) (- t x))
194.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify55.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune223.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 4.7b

Counts

91 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.4b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.6b	(+ 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)))))

series740.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
294.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
152.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (75.0ms)

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

prune432.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	142	15	157

Merged error: 4.7b

Counts

157 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.7b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.2b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite49.0ms

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))
35.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- y z))
143.0ms	(cbrt (- y z))
307.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
160.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify83.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (67.0ms)

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

prune328.0ms

Filtered

115 candidates to 70 candidates (60.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	115	15	130

Merged error: 4.7b

Counts

130 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
10.2b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
36.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
4.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
294.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
156.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify128.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	892	2830
1	4041	2189
2	5002	2089

prune441.0ms

Filtered

129 candidates to 85 candidates (65.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	128	16	144

Merged error: 4.7b

Counts

144 → 16

regimes405.0ms

Accuracy

12.6% (7.3b remaining)

Error of 11.4b against oracle of 4.1b and baseline of 12.4b

bsearch112.0ms

Steps

Iters	Range		Point
8	1.1993518949321924e-151	4.5142189629891866e-148	2.1165353499057916e-148
9	-1.985268489771751e-154	-1.8766265918936216e-161	-6.5727836634690075e-155

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	32
1	39	32

end0.0ms

sample804.0ms

Algorithm

intervals

Results

311.0ms	7731×	body	80	valid
70.0ms	464×	body	640	valid
49.0ms	274×	body	1280	valid
49.0ms	431×	body	320	valid
26.0ms	279×	body	160	valid
4.0ms	17×	body	2560	valid

Details

sample29.0ms

simplify72.0ms

prune2.0ms

localize9.0ms

rewrite30.0ms

series356.0ms

simplify55.0ms

prune223.0ms

localize12.0ms

rewrite53.0ms

series740.0ms

simplify97.0ms

prune432.0ms

localize17.0ms

rewrite49.0ms

series762.0ms

simplify83.0ms

prune328.0ms

localize25.0ms

rewrite52.0ms

series759.0ms

simplify128.0ms

prune441.0ms

regimes405.0ms

bsearch112.0ms

simplify2.0ms

end0.0ms

sample804.0ms

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