Details

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.196289%

Guaranteed chance to sample good point: 35.82592%

Results

12.0ms	212×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	37×	body	80	invalid
1.0ms	13×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify68.0ms

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

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: 15.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.6b	(* (- y z) (/ (- t x) (- a z)))

rewrite32.0ms

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))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- t x) (- a z))
49.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
38.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify78.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (16.0ms)

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

prune193.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	113	15	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	15	129

Merged error: 5.8b

Counts

129 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- a z))
0.0b	(- (/ t (- a z)) (/ x (- a z)))
3.7b	(+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))
6.6b	(* (- y z) (- (/ t (- a z)) (/ x (- a z))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
51×	`times-frac`
29×	`distribute-lft-out--`
20×	`add-cube-cbrt`
18×	`associate-r`
17×	`difference-of-squares`
14×	`flip3--` `flip--`
10×	`associate-/r/`
8×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `distribute-rgt-out--`
5×	`sub-neg` `associate-l` `associate-/r*` `div-inv`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*r/` `frac-sub` `sub-div`
3×	`associate-/l*`
2×	`associate-*l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

5.0ms	(/ t (- a z))
27.0ms	(- (/ t (- a z)) (/ x (- a z)))
7.0ms	(+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))
37.0ms	(* (- y z) (- (/ t (- a z)) (/ x (- a z))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ t (- a z))
22.0ms	(- (/ t (- a z)) (/ x (- a z)))
49.0ms	(+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))
42.0ms	(* (- y z) (- (/ t (- a z)) (/ x (- a z))))

simplify61.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	544	1113
1	2354	1059
2	5001	1059

prune178.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	145	16	161

Merged error: 5.8b

Counts

161 → 16

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.2b	(+ x (* (/ (- y z) (- a z)) (- t x)))
2.6b	(* (/ (- y z) (- a z)) (- t x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

8.0ms	(/ (- y z) (- a z))
5.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))
16.0ms	(* (/ (- y z) (- a z)) (- t x))

series115.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- y z) (- a z))
51.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))
54.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify51.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	522	929
1	1920	879
2	5002	879

prune155.0ms

Filtered

90 candidates to 136 candidates (-51.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	4	10	14
Picked	0	1	1
Done	0	1	1
Total	138	14	152

Merged error: 5.8b

Counts

152 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

2.7b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.7b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.7b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
8.6b	(+ x (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (cbrt (* (/ (- y z) (- a z)) (- t x)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

11.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
13.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
11.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
3.0ms	(+ x (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (cbrt (* (/ (- y z) (- a z)) (- t x)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.0s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.1s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
50.0ms	(+ x (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (cbrt (* (/ (- y z) (- a z)) (- t x)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	262	874
1	774	752
2	3220	727
3	5002	691

prune84.0ms

Filtered

60 candidates to 65 candidates (-8.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	9	11
Picked	0	1	1
Done	1	1	2
Total	66	13	79

Merged error: 4.0b

Counts

79 → 13

regimes600.0ms

Accuracy

26.8% (6.7b remaining)

Error of 10.2b against oracle of 3.6b and baseline of 12.7b

bsearch99.0ms

Steps

Iters	Range		Point
8	1.0390187617887603e+133	9.049621483497026e+135	8.497305396520181e+135
9	-1.8172396859609918e+166	-2.2828490547989735e+159	-7.377669269718365e+165

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	33	26

end0.0ms

sample3.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.196289%

Guaranteed chance to sample good point: 35.82592%

Results

290.0ms	6501×	body	80	valid
69.0ms	491×	body	640	valid
55.0ms	309×	body	1280	valid
46.0ms	1181×	body	80	invalid
45.0ms	420×	body	320	valid
20.0ms	266×	body	160	valid
3.0ms	13×	body	2560	valid

Details

sample2.6s

simplify68.0ms

prune4.0ms

localize9.0ms

rewrite32.0ms

series100.0ms

simplify78.0ms

prune193.0ms

localize10.0ms

rewrite81.0ms

series120.0ms

simplify61.0ms

prune178.0ms

localize9.0ms

rewrite35.0ms

series115.0ms

simplify51.0ms

prune155.0ms

localize13.0ms

rewrite39.0ms

series6.1s

simplify78.0ms

prune84.0ms

regimes600.0ms

bsearch99.0ms

simplify1.0ms

end0.0ms

sample3.7s

Profiling