Details

sample52.0ms

Algorithm

intervals

Results

29.0ms	88×	body	1280	valid
7.0ms	133×	body	80	valid
5.0ms	20×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune3.0ms

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: 13.6b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(hypot 1.0 x)
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms	(hypot 1.0 x)
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms	(hypot 1.0 x)
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1984	411
3	5001	411

prune127.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 13.1b

Counts

74 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp`
6×	`*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `associate-*r/` `associate--l+` `add-cbrt-cube`
3×	`sub-neg`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `frac-sub` `flip--`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 44

Calls

4 calls:

1.0ms	(hypot 1.0 x)
1.0ms	(hypot 1.0 x)
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
1.0ms	(hypot 1.0 x)
13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify104.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	244	384
1	738	348
2	4039	341
3	5001	341

prune121.0ms

Filtered

39 candidates to 56 candidates (-43.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	56	3	59

Merged error: 13.1b

Counts

59 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (hypot 1.0 x) 3)
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (cbrt (pow (hypot 1.0 x) 3)))))
21.3b	(cbrt (pow (hypot 1.0 x) 3))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`add-log-exp`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`associate-*r/` `associate--l+`
3×	`sub-neg` `pow-unpow`
2×	`distribute-rgt-in` `cube-mult` `flip3--` `distribute-lft-in` `unpow3` `frac-sub` `flip--` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `diff-log` `pow-exp` `sum-log` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 74

Calls

4 calls:

2.0ms	(pow (hypot 1.0 x) 3)
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (cbrt (pow (hypot 1.0 x) 3)))))
2.0ms	(cbrt (pow (hypot 1.0 x) 3))

series26.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (hypot 1.0 x) 3)
13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (cbrt (pow (hypot 1.0 x) 3)))))
1.0ms	(cbrt (pow (hypot 1.0 x) 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	321	538
1	1294	479
2	5001	467

prune158.0ms

Filtered

48 candidates to 86 candidates (-79.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 13.1b

Counts

89 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
1.5b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-*r/`
10×	`associate-*l/`
8×	`frac-sub` `add-log-exp`
6×	`flip3--` `*-un-lft-identity` `flip3-+` `flip--` `flip-+` `associate-/l/`
4×	`pow1` `cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `div-exp` `prod-exp` `cbrt-unprod`
2×	`associate-/r/` `associate--r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `times-frac` `diff-log` `clear-num` `associate-/r` `sum-log` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 66

Calls

4 calls:

1.0ms	(hypot 1.0 x)
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
13.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
6.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
10.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
3.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	565	1049
1	2865	874
2	5002	874

prune239.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 13.0b

Counts

81 → 4

regimes306.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.8b and baseline of 14.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	36
1	43	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

674.0ms	2969×	body	1280	valid
161.0ms	3980×	body	80	valid
108.0ms	602×	body	640	valid
38.0ms	303×	body	320	valid
12.0ms	146×	body	160	valid

Details

sample52.0ms

simplify8.0ms

prune3.0ms

localize7.0ms

rewrite14.0ms

series31.0ms

simplify56.0ms

prune127.0ms

localize13.0ms

rewrite11.0ms

series21.0ms

simplify104.0ms

prune121.0ms

localize18.0ms

rewrite16.0ms

series26.0ms

simplify47.0ms

prune158.0ms

localize22.0ms

rewrite25.0ms

series27.0ms

simplify74.0ms

prune239.0ms

regimes306.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

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