Details

sample35.0ms

Algorithm

intervals

Results

16.0ms	73×	body	1280	valid
6.0ms	145×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune7.0ms

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: 16.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
3.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

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:

1.0ms	(hypot 1.0 x)
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1986	411
3	5001	411

prune130.0ms

Filtered

73 candidates to 52 candidates (28.8%)

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: 15.6b

Counts

74 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

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

series28.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify140.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4837	560
3	5001	560

prune213.0ms

Filtered

96 candidates to 69 candidates (28.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Merged error: 15.6b

Counts

99 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.6b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 81

Calls

4 calls:

4.0ms	(/ 0.5 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.5 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	280	524
1	902	488
2	2752	487
3	5001	487

prune191.0ms

Filtered

93 candidates to 67 candidates (28.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	94	2	96

Merged error: 15.3b

Counts

96 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 0.5 (hypot 1.0 x)))
0.1b	(sqrt (/ 0.5 (hypot 1.0 x)))
0.5b	(* (+ (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x)))) (- (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x)))))
2.6b	(- (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
46×	`sqrt-prod`
32×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`associate-r`
8×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-l`
4×	`frac-times` `rem-sqrt-square` `flip3--` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sqrt-div` `associate-r/` `associate-l/` `div-inv` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

3.0ms	(sqrt (/ 0.5 (hypot 1.0 x)))
3.0ms	(sqrt (/ 0.5 (hypot 1.0 x)))
20.0ms	(* (+ (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x)))) (- (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x)))))
9.0ms	(- (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (/ 0.5 (hypot 1.0 x)))
9.0ms	(sqrt (/ 0.5 (hypot 1.0 x)))
29.0ms	(* (+ (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x)))) (- (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x)))))
12.0ms	(- (sqrt 0.5) (sqrt (/ 0.5 (hypot 1.0 x))))

simplify44.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	283	1172
1	1258	1064
2	5002	1037

prune384.0ms

Filtered

122 candidates to 86 candidates (29.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	2	124

Merged error: 15.3b

Counts

124 → 2

regimes70.0ms

Accuracy

0% (0.7b remaining)

Error of 15.4b against oracle of 14.7b and baseline of 15.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	45
1	25	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

628.0ms	2859×	body	1280	valid
159.0ms	4068×	body	80	valid
111.0ms	622×	body	640	valid
34.0ms	278×	body	320	valid
14.0ms	173×	body	160	valid

Details

sample35.0ms

simplify12.0ms

prune7.0ms

localize9.0ms

rewrite15.0ms

series32.0ms

simplify60.0ms

prune130.0ms

localize13.0ms

rewrite17.0ms

series28.0ms

simplify140.0ms

prune213.0ms

localize11.0ms

rewrite18.0ms

series29.0ms

simplify75.0ms

prune191.0ms

localize18.0ms

rewrite39.0ms

series59.0ms

simplify44.0ms

prune384.0ms

regimes70.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

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