Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	247×	body	80	valid
4.0ms	10×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	5×	body	1280	valid
1.0ms	9×	body	160	valid

simplify68.0ms

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: 22.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.3b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.3b	(/ (* (- 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))

series312.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* (- y z) (- t x))
146.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
127.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (14.0ms)

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

prune237.0ms

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: 3.2b

Counts

91 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
2.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.7b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

3.0ms	(cbrt (- a z))
11.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
38.0ms	(* (/ (- 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)))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
126.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
288.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
150.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	844	2163
1	4193	1974
2	5003	1855

prune488.0ms

Filtered

187 candidates to 124 candidates (66.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	179	8	187
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	183	17	200

Merged error: 3.1b

Counts

200 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
1.0b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite73.0ms

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:

6.0ms	(cbrt (- y z))
6.0ms	(cbrt (- y z))
50.0ms	(* (/ (* (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))))))

series750.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- y z))
147.0ms	(cbrt (- y z))
300.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
152.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (64.0ms)

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

prune319.0ms

Filtered

115 candidates to 70 candidates (60.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	114	18	132

Merged error: 3.1b

Counts

132 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
7.4b	(+ 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))))))

rewrite53.0ms

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 (- t x))
3.0ms	(cbrt (- t x))
37.0ms	(* (/ (- 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))))))

series750.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- t x))
152.0ms	(cbrt (- t x))
296.0ms	(* (/ (- 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))))))

simplify120.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	920	2830
1	4106	2189
2	5001	2089

prune410.0ms

Filtered

129 candidates to 85 candidates (65.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	129	18	147

Merged error: 3.1b

Counts

147 → 18

regimes414.0ms

Accuracy

16.6% (6.6b remaining)

Error of 10.8b against oracle of 4.1b and baseline of 12.1b

bsearch69.0ms

Steps

Iters	Range		Point
7	3.4762917274977053e-161	1.7117167047813395e-159	5.984808289790356e-160
3	-1.1765508514238616e-115	-9.497613603758391e-116	-9.954183706255959e-116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	99
1	49	99

end0.0ms

sample778.0ms

Algorithm

intervals

Results

305.0ms	7832×	body	80	valid
67.0ms	450×	body	640	valid
58.0ms	294×	body	1280	valid
43.0ms	402×	body	320	valid
22.0ms	262×	body	160	valid
4.0ms	17×	body	2560	valid

Details

sample28.0ms

simplify68.0ms

prune2.0ms

localize9.0ms

rewrite30.0ms

series312.0ms

simplify61.0ms

prune237.0ms

localize13.0ms

rewrite63.0ms

series713.0ms

simplify124.0ms

prune488.0ms

localize17.0ms

rewrite73.0ms

series750.0ms

simplify80.0ms

prune319.0ms

localize24.0ms

rewrite53.0ms

series750.0ms

simplify120.0ms

prune410.0ms

regimes414.0ms

bsearch69.0ms

simplify2.0ms

end0.0ms

sample778.0ms

Profiling