Details

sample49.0ms

Algorithm

intervals

Results

9.0ms	235×	body	80	valid
3.0ms	22×	body	640	valid
3.0ms	14×	body	1280	valid
2.0ms	17×	body	320	valid
1.0ms	9×	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

prune4.0ms

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: 24.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.5b	(+ x (/ (* (- y z) (- t x)) (- a z)))
15.9b	(/ (* (- y z) (- t x)) (- a z))

rewrite34.0ms

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:

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

series98.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
53.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
36.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune143.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

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: 5.2b

Counts

91 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
11.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite50.0ms

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))
35.0ms	(* (/ (- 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)))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
57.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
54.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (68.0ms)

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

prune199.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	141	16	157

Merged error: 5.1b

Counts

157 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.9b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
5.4b	(+ 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))))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- y z))
28.0ms	(cbrt (- y z))
56.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
53.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	660	2069
1	2521	1616
2	5001	1458

prune163.0ms

Filtered

68 candidates to 115 candidates (-69.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	116	15	131

Merged error: 5.1b

Counts

131 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (* (cbrt (- y z)) (cbrt (- y z))))
0.9b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
8.1b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

3.0ms	(cbrt (- y z))
8.0ms	(cbrt (* (cbrt (- y z)) (cbrt (- y z))))
37.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- y z))
32.0ms	(cbrt (* (cbrt (- y z)) (cbrt (- y z))))
58.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
56.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	879	3522
1	3418	2705
2	5002	2612

prune103.0ms

Filtered

69 candidates to 129 candidates (-87.0%)

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: 5.1b

Counts

144 → 16

regimes671.0ms

Accuracy

-5.7% (9.1b remaining)

Error of 13.2b against oracle of 4.0b and baseline of 12.7b

bsearch53.0ms

Steps

Iters	Range		Point
9	1.0705433353774265e+137	5.105980547430544e+144	5.560344573476349e+142
8	-3.984610823833534e+123	-2.1419311801132968e+120	-3.704489745769741e+123

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	34
1	42	34

end0.0ms

sample917.0ms

Algorithm

intervals

Results

298.0ms	7782×	body	80	valid
66.0ms	459×	body	640	valid
55.0ms	305×	body	1280	valid
48.0ms	419×	body	320	valid
19.0ms	267×	body	160	valid
4.0ms	17×	body	2560	valid

Details

sample49.0ms

simplify67.0ms

prune4.0ms

localize10.0ms

rewrite34.0ms

series98.0ms

simplify52.0ms

prune143.0ms

localize15.0ms

rewrite50.0ms

series163.0ms

simplify86.0ms

prune199.0ms

localize17.0ms

rewrite49.0ms

series164.0ms

simplify70.0ms

prune163.0ms

localize24.0ms

rewrite58.0ms

series174.0ms

simplify95.0ms

prune103.0ms

regimes671.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample917.0ms

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