Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	245×	body	80	valid
2.0ms	12×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify63.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 22.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite29.0ms

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:

8.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
11.0ms	(/ (* (- y z) (- t x)) (- a z))

series93.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (- y z) (- t x))
47.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
35.0ms	(/ (* (- 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

prune128.0ms

Filtered

90 candidates to 67 candidates (25.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 4.7b

Counts

91 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.0b	(* (/ (- 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)))))

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)))))

series153.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
52.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
50.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (69.0ms)

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

prune191.0ms

Filtered

146 candidates to 104 candidates (28.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	140	14	154

Merged error: 4.7b

Counts

154 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
2.0b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
2.0b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
9.1b	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
16×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`frac-times`
10×	`add-cube-cbrt`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 89

Calls

4 calls:

12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
4.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
91.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
91.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
53.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

simplify125.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	424	1880
1	1055	1713
2	4157	1665
3	5001	1632

prune172.0ms

Filtered

101 candidates to 81 candidates (19.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	102	13	115

Merged error: 3.8b

Counts

115 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
2.0b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
2.0b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
8.9b	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (* (* (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (- t x) (cbrt (- a z))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
16×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`frac-times`
10×	`add-cube-cbrt`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 89

Calls

4 calls:

12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (* (* (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (- t x) (cbrt (- a z))))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
89.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
89.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
52.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (* (* (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (- t x) (cbrt (- a z))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	429	2237
1	1113	2042
2	5001	2000

prune144.0ms

Filtered

101 candidates to 83 candidates (17.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	101	13	114

Merged error: 3.8b

Counts

114 → 13

regimes576.0ms

Accuracy

23.6% (7.3b remaining)

Error of 10.4b against oracle of 3.1b and baseline of 12.6b

bsearch57.0ms

Steps

Iters	Range		Point
10	3.418100554883497e-133	4.795669382585278e-114	3.7364955924764993e-121
7	-3.6993112117761513e-152	-1.1151613236099998e-153	-4.176368533382217e-153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample917.0ms

Algorithm

intervals

Results

275.0ms	7759×	body	80	valid
66.0ms	492×	body	640	valid
45.0ms	437×	body	320	valid
42.0ms	243×	body	1280	valid
17.0ms	253×	body	160	valid
4.0ms	18×	body	2560	valid

Details

sample36.0ms

simplify63.0ms

prune4.0ms

localize9.0ms

rewrite29.0ms

series93.0ms

simplify52.0ms

prune128.0ms

localize12.0ms

rewrite50.0ms

series153.0ms

simplify84.0ms

prune191.0ms

localize22.0ms

rewrite43.0ms

series324.0ms

simplify125.0ms

prune172.0ms

localize26.0ms

rewrite42.0ms

series321.0ms

simplify50.0ms

prune144.0ms

regimes576.0ms

bsearch57.0ms

simplify1.0ms

end0.0ms

sample917.0ms

Profiling