Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	269×	body	80	valid
2.0ms	9×	body	1280	valid
2.0ms	15×	body	320	valid
2.0ms	10×	body	640	valid
1.0ms	8×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune3.0ms

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: 14.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.8b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.9b	(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
18.0ms	(* (- y z) (/ (- t x) (- a z)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
144.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
127.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5002	820

prune299.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	13	129

Merged error: 4.4b

Counts

129 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.0b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.7b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
24.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- t x))
139.0ms	(cbrt (- t x))
267.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
147.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	680	1363
1	2654	1151
2	5001	1129

prune336.0ms

Filtered

97 candidates to 74 candidates (76.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	95	15	110

Merged error: 4.4b

Counts

110 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.9b	(* (/ (- 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)))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
292.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
151.0ms	(+ 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 (70.0ms)

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

prune392.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	11	12
Picked	1	0	1
Done	0	2	2
Total	146	15	161

Merged error: 4.4b

Counts

161 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
1.4b	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
1.4b	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.2b	(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod` `cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
12×	`frac-times`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`times-frac` `pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

17.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
21.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
17.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
195.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
186.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
152.0ms	(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	372	2240
1	1002	2012
2	5001	1948

prune393.0ms

Filtered

89 candidates to 75 candidates (84.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	12	12
Picked	0	1	1
Done	1	1	2
Total	87	17	104

Merged error: 3.4b

Counts

104 → 17

regimes375.0ms

Accuracy

19.4% (6.9b remaining)

Error of 10.3b against oracle of 3.4b and baseline of 12.0b

bsearch108.0ms

Steps

Iters	Range		Point
10	5.2794340318752433e-135	9.639441827347957e-121	2.7380745442269558e-123
5	-1.8911439556125175e-78	-7.606123504077671e-79	-8.172311130711965e-79

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	25
1	36	25

end0.0ms

sample794.0ms

Algorithm

intervals

Results

328.0ms	7865×	body	80	valid
75.0ms	447×	body	640	valid
52.0ms	271×	body	1280	valid
49.0ms	426×	body	320	valid
20.0ms	255×	body	160	valid
2.0ms	10×	body	2560	valid

Details

sample33.0ms

simplify75.0ms

prune3.0ms

localize10.0ms

rewrite34.0ms

series320.0ms

simplify54.0ms

prune299.0ms

localize22.0ms

rewrite37.0ms

series696.0ms

simplify73.0ms

prune336.0ms

localize14.0ms

rewrite53.0ms

series741.0ms

simplify86.0ms

prune392.0ms

localize24.0ms

rewrite61.0ms

series724.0ms

simplify48.0ms

prune393.0ms

regimes375.0ms

bsearch108.0ms

simplify1.0ms

end0.0ms

sample794.0ms

Profiling